TSTP Solution File: SET813+4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:05:12 EDT 2022
% Result : Theorem 0.43s 0.67s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 55
% Syntax : Number of formulae : 700 ( 317 unt; 35 typ; 0 def)
% Number of atoms : 5137 (1348 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 12741 (2340 ~;1832 |; 120 &;8391 @)
% ( 34 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 6 con; 0-3 aty)
% Number of variables : 2061 ( 0 ^2055 !; 6 ?;2061 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i > $o ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_set,type,
equal_set: $i > $i > $o ).
thf(tp_initial_segment,type,
initial_segment: $i > $i > $i > $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_least,type,
least: $i > $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_member_predicate,type,
member_predicate: $i ).
thf(tp_on,type,
on: $i ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_sK10_SY61,type,
sK10_SY61: $i > $i > $i ).
thf(tp_sK11_X,type,
sK11_X: $i > $i ).
thf(tp_sK12_Y,type,
sK12_Y: $i > $i > $i ).
thf(tp_sK13_Y,type,
sK13_Y: $i > $i > $i ).
thf(tp_sK14_X,type,
sK14_X: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_X,type,
sK2_X: $i > $i > $i ).
thf(tp_sK3_SY57,type,
sK3_SY57: $i > $i > $i ).
thf(tp_sK4_SY59,type,
sK4_SY59: $i > $i > $i ).
thf(tp_sK5_X,type,
sK5_X: $i > $i > $i ).
thf(tp_sK6_SY60,type,
sK6_SY60: $i > $i > $i ).
thf(tp_sK7_X,type,
sK7_X: $i > $i > $i > $i ).
thf(tp_sK8_Y,type,
sK8_Y: $i > $i > $i > $i ).
thf(tp_sK9_A,type,
sK9_A: $i > $i > $i ).
thf(tp_set,type,
set: $i > $o ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_strict_order,type,
strict_order: $i > $i > $o ).
thf(tp_strict_well_order,type,
strict_well_order: $i > $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_suc,type,
suc: $i > $i ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,X: $i] :
( ( member @ X @ ( suc @ A ) )
<=> ( member @ X @ ( union @ A @ ( singleton @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(2,axiom,
! [X: $i,R: $i,A: $i,Y: $i] :
( ( member @ Y @ ( initial_segment @ X @ R @ A ) )
<=> ( ( member @ Y @ A )
& ( apply @ R @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_segment) ).
thf(3,axiom,
! [X: $i] :
( ( set @ X )
=> ! [Y: $i] :
( ( member @ Y @ X )
=> ( set @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_member) ).
thf(4,axiom,
! [R: $i,E: $i] :
( ( strict_order @ R @ E )
<=> ( ! [X: $i,Y: $i] :
( ( ( member @ X @ E )
& ( member @ Y @ E ) )
=> ~ ( ( apply @ R @ X @ Y )
& ( apply @ R @ Y @ X ) ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( member @ X @ E )
& ( member @ Y @ E )
& ( member @ Z @ E ) )
=> ( ( ( apply @ R @ X @ Y )
& ( apply @ R @ Y @ Z ) )
=> ( apply @ R @ X @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_order) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( apply @ member_predicate @ X @ Y )
<=> ( member @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rel_member) ).
thf(6,axiom,
! [R: $i,E: $i,M: $i] :
( ( least @ M @ R @ E )
<=> ( ( member @ M @ E )
& ! [X: $i] :
( ( member @ X @ E )
=> ( ( M = X )
| ( apply @ R @ M @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
thf(7,axiom,
! [R: $i,E: $i] :
( ( strict_well_order @ R @ E )
<=> ( ( strict_order @ R @ E )
& ! [A: $i] :
( ( ( subset @ A @ E )
& ? [X: $i] : ( member @ X @ A ) )
=> ? [Y: $i] : ( least @ Y @ R @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strict_well_order) ).
thf(8,axiom,
! [A: $i] :
( ( member @ A @ on )
<=> ( ( set @ A )
& ( strict_well_order @ member_predicate @ A )
& ! [X: $i] :
( ( member @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal_number) ).
thf(9,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
thf(10,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
thf(11,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(12,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(13,axiom,
! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
thf(14,axiom,
! [X: $i] :
~ ( member @ X @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(15,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(16,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(17,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(20,conjecture,
! [A: $i] :
( ( member @ A @ on )
=> ( member @ A @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV12) ).
thf(21,negated_conjecture,
( ( ! [A: $i] :
( ( member @ A @ on )
=> ( member @ A @ ( suc @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( member @ A @ on )
=> ( member @ A @ ( suc @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [A: $i,X: $i] :
( ( member @ X @ ( suc @ A ) )
<=> ( member @ X @ ( union @ A @ ( singleton @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [X: $i,R: $i,A: $i,Y: $i] :
( ( member @ Y @ ( initial_segment @ X @ R @ A ) )
<=> ( ( member @ Y @ A )
& ( apply @ R @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( set @ X )
=> ! [Y: $i] :
( ( member @ Y @ X )
=> ( set @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [R: $i,E: $i] :
( ( strict_order @ R @ E )
<=> ( ! [X: $i,Y: $i] :
( ( ( member @ X @ E )
& ( member @ Y @ E ) )
=> ~ ( ( apply @ R @ X @ Y )
& ( apply @ R @ Y @ X ) ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( member @ X @ E )
& ( member @ Y @ E )
& ( member @ Z @ E ) )
=> ( ( ( apply @ R @ X @ Y )
& ( apply @ R @ Y @ Z ) )
=> ( apply @ R @ X @ Z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ member_predicate @ X @ Y )
<=> ( member @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(28,plain,
( ( ! [R: $i,E: $i,M: $i] :
( ( least @ M @ R @ E )
<=> ( ( member @ M @ E )
& ! [X: $i] :
( ( member @ X @ E )
=> ( ( M = X )
| ( apply @ R @ M @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [R: $i,E: $i] :
( ( strict_well_order @ R @ E )
<=> ( ( strict_order @ R @ E )
& ! [A: $i] :
( ( ( subset @ A @ E )
& ? [X: $i] : ( member @ X @ A ) )
=> ? [Y: $i] : ( least @ Y @ R @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( member @ A @ on )
<=> ( ( set @ A )
& ( strict_well_order @ member_predicate @ A )
& ! [X: $i] :
( ( member @ X @ A )
=> ( subset @ X @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(39,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(42,plain,
( ( ( member @ sK1_A @ on )
=> ( member @ sK1_A @ ( suc @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(43,plain,
( ( member @ sK1_A @ on )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(44,plain,
( ( member @ sK1_A @ ( suc @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ( member @ sK1_A @ ( suc @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [A: $i,X: $i] :
( ~ ( member @ X @ ( suc @ A ) )
| ( member @ X @ ( union @ A @ ( singleton @ A ) ) ) )
& ! [A: $i,X: $i] :
( ~ ( member @ X @ ( union @ A @ ( singleton @ A ) ) )
| ( member @ X @ ( suc @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(47,plain,
( ( ! [X: $i,R: $i] :
( ! [A: $i,Y: $i] :
( ~ ( apply @ R @ Y @ X )
| ~ ( member @ Y @ A )
| ( member @ Y @ ( initial_segment @ X @ R @ A ) ) )
& ! [A: $i,Y: $i] :
( ~ ( member @ Y @ ( initial_segment @ X @ R @ A ) )
| ( apply @ R @ Y @ X ) )
& ! [A: $i,Y: $i] :
( ~ ( member @ Y @ ( initial_segment @ X @ R @ A ) )
| ( member @ Y @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(48,plain,
( ( ! [X: $i] :
( ~ ( set @ X )
| ! [Y: $i] :
( ~ ( member @ Y @ X )
| ( set @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(49,plain,
( ( ! [R: $i,E: $i] :
( ( ( member @ ( sK5_X @ E @ R ) @ E )
& ( member @ ( sK6_SY60 @ E @ R ) @ E )
& ( apply @ R @ ( sK5_X @ E @ R ) @ ( sK6_SY60 @ E @ R ) )
& ( apply @ R @ ( sK6_SY60 @ E @ R ) @ ( sK5_X @ E @ R ) ) )
| ( ( member @ ( sK2_X @ E @ R ) @ E )
& ( member @ ( sK3_SY57 @ E @ R ) @ E )
& ( member @ ( sK4_SY59 @ E @ R ) @ E )
& ( apply @ R @ ( sK2_X @ E @ R ) @ ( sK3_SY57 @ E @ R ) )
& ( apply @ R @ ( sK3_SY57 @ E @ R ) @ ( sK4_SY59 @ E @ R ) )
& ~ ( apply @ R @ ( sK2_X @ E @ R ) @ ( sK4_SY59 @ E @ R ) ) )
| ( strict_order @ R @ E ) )
& ! [R: $i,E: $i] :
( ~ ( strict_order @ R @ E )
| ! [X: $i,Y: $i] :
( ~ ( member @ X @ E )
| ~ ( member @ Y @ E )
| ~ ( apply @ R @ X @ Y )
| ~ ( apply @ R @ Y @ X ) ) )
& ! [R: $i,E: $i] :
( ~ ( strict_order @ R @ E )
| ! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ X @ E )
| ~ ( member @ Y @ E )
| ~ ( member @ Z @ E )
| ~ ( apply @ R @ X @ Y )
| ~ ( apply @ R @ Y @ Z )
| ( apply @ R @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apply @ member_predicate @ X @ Y )
| ( member @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( apply @ member_predicate @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(51,plain,
( ( ! [R: $i] :
( ! [E: $i,M: $i] :
( ( ( member @ ( sK7_X @ M @ E @ R ) @ E )
& ( M
!= ( sK7_X @ M @ E @ R ) )
& ~ ( apply @ R @ M @ ( sK7_X @ M @ E @ R ) ) )
| ~ ( member @ M @ E )
| ( least @ M @ R @ E ) )
& ! [E: $i,M: $i] :
( ~ ( least @ M @ R @ E )
| ! [X: $i] :
( ~ ( member @ X @ E )
| ( M = X )
| ( apply @ R @ M @ X ) ) )
& ! [E: $i,M: $i] :
( ~ ( least @ M @ R @ E )
| ( member @ M @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(52,plain,
( ( ! [R: $i,E: $i] :
( ( ( member @ ( sK10_SY61 @ E @ R ) @ ( sK9_A @ E @ R ) )
& ( subset @ ( sK9_A @ E @ R ) @ E )
& ! [SY62: $i] :
~ ( least @ SY62 @ R @ ( sK9_A @ E @ R ) ) )
| ~ ( strict_order @ R @ E )
| ( strict_well_order @ R @ E ) )
& ! [R: $i,E: $i] :
( ~ ( strict_well_order @ R @ E )
| ! [A: $i] :
( ! [X: $i] :
~ ( member @ X @ A )
| ~ ( subset @ A @ E )
| ( least @ ( sK8_Y @ A @ E @ R ) @ R @ A ) ) )
& ! [R: $i,E: $i] :
( ~ ( strict_well_order @ R @ E )
| ( strict_order @ R @ E ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( ( member @ ( sK11_X @ A ) @ A )
& ~ ( subset @ ( sK11_X @ A ) @ A ) )
| ~ ( set @ A )
| ~ ( strict_well_order @ member_predicate @ A )
| ( member @ A @ on ) )
& ! [A: $i] :
( ~ ( member @ A @ on )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( subset @ X @ A ) ) )
& ! [A: $i] :
( ~ ( member @ A @ on )
| ( set @ A ) )
& ! [A: $i] :
( ~ ( member @ A @ on )
| ( strict_well_order @ member_predicate @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(54,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK12_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK12_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(55,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK13_Y @ A @ X ) @ A )
& ( member @ X @ ( sK13_Y @ A @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(56,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(57,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(58,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(59,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(60,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(61,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK14_X @ B @ A ) @ A )
& ~ ( member @ ( sK14_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK14_X @ B @ A ) @ A )
& ~ ( member @ ( sK14_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(66,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(67,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(68,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(69,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(70,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(71,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(72,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(73,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK13_Y @ A @ X ) @ A )
& ( member @ X @ ( sK13_Y @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(74,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK12_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK12_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( ( member @ ( sK11_X @ A ) @ A )
& ~ ( subset @ ( sK11_X @ A ) @ A ) )
| ~ ( set @ A )
| ~ ( strict_well_order @ member_predicate @ A )
| ( member @ A @ on ) )
& ! [A: $i] :
( ~ ( member @ A @ on )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( subset @ X @ A ) ) )
& ! [A: $i] :
( ~ ( member @ A @ on )
| ( set @ A ) )
& ! [A: $i] :
( ~ ( member @ A @ on )
| ( strict_well_order @ member_predicate @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(76,plain,
( ( ! [R: $i,E: $i] :
( ( ( member @ ( sK10_SY61 @ E @ R ) @ ( sK9_A @ E @ R ) )
& ( subset @ ( sK9_A @ E @ R ) @ E )
& ! [SY62: $i] :
~ ( least @ SY62 @ R @ ( sK9_A @ E @ R ) ) )
| ~ ( strict_order @ R @ E )
| ( strict_well_order @ R @ E ) )
& ! [R: $i,E: $i] :
( ~ ( strict_well_order @ R @ E )
| ! [A: $i] :
( ! [X: $i] :
~ ( member @ X @ A )
| ~ ( subset @ A @ E )
| ( least @ ( sK8_Y @ A @ E @ R ) @ R @ A ) ) )
& ! [R: $i,E: $i] :
( ~ ( strict_well_order @ R @ E )
| ( strict_order @ R @ E ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(77,plain,
( ( ! [R: $i] :
( ! [E: $i,M: $i] :
( ( ( member @ ( sK7_X @ M @ E @ R ) @ E )
& ( M
!= ( sK7_X @ M @ E @ R ) )
& ~ ( apply @ R @ M @ ( sK7_X @ M @ E @ R ) ) )
| ~ ( member @ M @ E )
| ( least @ M @ R @ E ) )
& ! [E: $i,M: $i] :
( ~ ( least @ M @ R @ E )
| ! [X: $i] :
( ~ ( member @ X @ E )
| ( M = X )
| ( apply @ R @ M @ X ) ) )
& ! [E: $i,M: $i] :
( ~ ( least @ M @ R @ E )
| ( member @ M @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( apply @ member_predicate @ X @ Y )
| ( member @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( apply @ member_predicate @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(79,plain,
( ( ! [R: $i,E: $i] :
( ( ( member @ ( sK5_X @ E @ R ) @ E )
& ( member @ ( sK6_SY60 @ E @ R ) @ E )
& ( apply @ R @ ( sK5_X @ E @ R ) @ ( sK6_SY60 @ E @ R ) )
& ( apply @ R @ ( sK6_SY60 @ E @ R ) @ ( sK5_X @ E @ R ) ) )
| ( ( member @ ( sK2_X @ E @ R ) @ E )
& ( member @ ( sK3_SY57 @ E @ R ) @ E )
& ( member @ ( sK4_SY59 @ E @ R ) @ E )
& ( apply @ R @ ( sK2_X @ E @ R ) @ ( sK3_SY57 @ E @ R ) )
& ( apply @ R @ ( sK3_SY57 @ E @ R ) @ ( sK4_SY59 @ E @ R ) )
& ~ ( apply @ R @ ( sK2_X @ E @ R ) @ ( sK4_SY59 @ E @ R ) ) )
| ( strict_order @ R @ E ) )
& ! [R: $i,E: $i] :
( ~ ( strict_order @ R @ E )
| ! [X: $i,Y: $i] :
( ~ ( member @ X @ E )
| ~ ( member @ Y @ E )
| ~ ( apply @ R @ X @ Y )
| ~ ( apply @ R @ Y @ X ) ) )
& ! [R: $i,E: $i] :
( ~ ( strict_order @ R @ E )
| ! [X: $i,Y: $i,Z: $i] :
( ~ ( member @ X @ E )
| ~ ( member @ Y @ E )
| ~ ( member @ Z @ E )
| ~ ( apply @ R @ X @ Y )
| ~ ( apply @ R @ Y @ Z )
| ( apply @ R @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(80,plain,
( ( ! [X: $i] :
( ~ ( set @ X )
| ! [Y: $i] :
( ~ ( member @ Y @ X )
| ( set @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(81,plain,
( ( ! [X: $i,R: $i] :
( ! [A: $i,Y: $i] :
( ~ ( apply @ R @ Y @ X )
| ~ ( member @ Y @ A )
| ( member @ Y @ ( initial_segment @ X @ R @ A ) ) )
& ! [A: $i,Y: $i] :
( ~ ( member @ Y @ ( initial_segment @ X @ R @ A ) )
| ( apply @ R @ Y @ X ) )
& ! [A: $i,Y: $i] :
( ~ ( member @ Y @ ( initial_segment @ X @ R @ A ) )
| ( member @ Y @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(82,plain,
( ( ! [A: $i,X: $i] :
( ~ ( member @ X @ ( suc @ A ) )
| ( member @ X @ ( union @ A @ ( singleton @ A ) ) ) )
& ! [A: $i,X: $i] :
( ~ ( member @ X @ ( union @ A @ ( singleton @ A ) ) )
| ( member @ X @ ( suc @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(83,plain,
( ( member @ sK1_A @ on )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(84,plain,
( ( ~ ( member @ sK1_A @ ( suc @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(85,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(86,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(87,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(88,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK13_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK13_Y @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(89,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(90,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(91,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( member @ ( sK11_X @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK11_X @ SX0 ) @ SX0 ) )
| ~ ( set @ SX0 )
| ~ ( strict_well_order @ member_predicate @ SX0 )
| ( member @ SX0 @ on ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(92,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK12_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK12_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(93,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(94,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(95,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SX1 @ SX0 ) @ ( sK9_A @ SX1 @ SX0 ) )
| ~ ( subset @ ( sK9_A @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
~ ( least @ SX2 @ SX0 @ ( sK9_A @ SX1 @ SX0 ) ) )
| ~ ( strict_order @ SX0 @ SX1 )
| ( strict_well_order @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SX2 )
| ~ ( subset @ SX2 @ SX1 )
| ( least @ ( sK8_Y @ SX2 @ SX1 @ SX0 ) @ SX0 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ( strict_order @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(96,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(97,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( member @ ( sK7_X @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( ( SX2
!= ( sK7_X @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( apply @ SX0 @ SX2 @ ( sK7_X @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( member @ SX2 @ SX1 )
| ( least @ SX2 @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( least @ SX2 @ SX0 @ SX1 )
| ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ( SX2 = SX3 )
| ( apply @ SX0 @ SX2 @ SX3 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( least @ SX2 @ SX0 @ SX1 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( apply @ SX1 @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX2 )
| ( member @ SX3 @ ( initial_segment @ SX0 @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX3 @ ( initial_segment @ SX0 @ SX1 @ SX2 ) )
| ( apply @ SX1 @ SX3 @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX3 @ ( initial_segment @ SX0 @ SX1 @ SX2 ) )
| ( member @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(99,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apply @ member_predicate @ SX0 @ SX1 )
| ( member @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ( apply @ member_predicate @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(100,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK6_SY60 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ( apply @ SX0 @ ( sK5_X @ SX1 @ SX0 ) @ ( sK6_SY60 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK6_SY60 @ SX1 @ SX0 ) @ ( sK5_X @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK3_SY57 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK4_SY59 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK3_SY57 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK3_SY57 @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) )
| ~ ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) ) )
| ( strict_order @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ SX0 @ SX2 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(101,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( suc @ SX0 ) )
| ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) )
| ( member @ SX1 @ ( suc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(102,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(103,plain,
! [SV2: $i] :
( ( ~ ( set @ SV2 )
| ! [SY63: $i] :
( ~ ( member @ SY63 @ SV2 )
| ( set @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(104,plain,
( ( member @ sK1_A @ ( suc @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(105,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(106,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(107,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY64: $i,SY65: $i] :
( ~ ( member @ SV3 @ ( unordered_pair @ SY64 @ SY65 ) )
| ( SV3 = SY64 )
| ( SV3 = SY65 ) )
| ~ ~ ( ~ ! [SY66: $i] :
( ( SV3 != SY66 )
| ! [SY67: $i] : ( member @ SV3 @ ( unordered_pair @ SY66 @ SY67 ) ) )
| ~ ! [SY68: $i,SY69: $i] :
( ( SV3 != SY69 )
| ( member @ SV3 @ ( unordered_pair @ SY68 @ SY69 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(108,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK13_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK13_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(110,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(111,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( member @ ( sK11_X @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK11_X @ SX0 ) @ SX0 ) )
| ~ ( set @ SX0 )
| ~ ( strict_well_order @ member_predicate @ SX0 )
| ( member @ SX0 @ on ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(112,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK12_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK12_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY70: $i,SY71: $i] :
( ~ ( member @ SV4 @ SY70 )
| ~ ( member @ SV4 @ SY71 )
| ( member @ SV4 @ ( intersection @ SY70 @ SY71 ) ) )
| ~ ~ ( ~ ! [SY72: $i] :
( ! [SY73: $i] :
~ ( member @ SV4 @ ( intersection @ SY72 @ SY73 ) )
| ( member @ SV4 @ SY72 ) )
| ~ ! [SY74: $i,SY75: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY74 @ SY75 ) )
| ( member @ SV4 @ SY75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY76: $i,SY77: $i] :
( ~ ( member @ SV5 @ ( union @ SY76 @ SY77 ) )
| ( member @ SV5 @ SY76 )
| ( member @ SV5 @ SY77 ) )
| ~ ~ ( ~ ! [SY78: $i] :
( ~ ( member @ SV5 @ SY78 )
| ! [SY79: $i] : ( member @ SV5 @ ( union @ SY78 @ SY79 ) ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV5 @ SY81 )
| ( member @ SV5 @ ( union @ SY80 @ SY81 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(115,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SX1 @ SX0 ) @ ( sK9_A @ SX1 @ SX0 ) )
| ~ ( subset @ ( sK9_A @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
~ ( least @ SX2 @ SX0 @ ( sK9_A @ SX1 @ SX0 ) ) )
| ~ ( strict_order @ SX0 @ SX1 )
| ( strict_well_order @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SX2 )
| ~ ( subset @ SX2 @ SX1 )
| ( least @ ( sK8_Y @ SX2 @ SX1 @ SX0 ) @ SX0 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ( strict_order @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(116,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY82: $i,SY83: $i] :
( ~ ( member @ SV6 @ SY83 )
| ( member @ SV6 @ SY82 )
| ( member @ SV6 @ ( difference @ SY83 @ SY82 ) ) )
| ~ ~ ( ~ ! [SY84: $i,SY85: $i] :
( ~ ( member @ SV6 @ ( difference @ SY85 @ SY84 ) )
| ( member @ SV6 @ SY85 ) )
| ~ ! [SY86: $i] :
( ! [SY87: $i] :
~ ( member @ SV6 @ ( difference @ SY87 @ SY86 ) )
| ~ ( member @ SV6 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(117,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY88: $i,SY89: $i] :
( ~ ( ~ ( member @ ( sK7_X @ SY89 @ SY88 @ SV7 ) @ SY88 )
| ~ ~ ( ~ ( ( SY89
!= ( sK7_X @ SY89 @ SY88 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SY89 @ ( sK7_X @ SY89 @ SY88 @ SV7 ) ) ) )
| ~ ( member @ SY89 @ SY88 )
| ( least @ SY89 @ SV7 @ SY88 ) )
| ~ ~ ( ~ ! [SY90: $i,SY91: $i] :
( ~ ( least @ SY91 @ SV7 @ SY90 )
| ! [SY92: $i] :
( ~ ( member @ SY92 @ SY90 )
| ( SY91 = SY92 )
| ( apply @ SV7 @ SY91 @ SY92 ) ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( least @ SY94 @ SV7 @ SY93 )
| ( member @ SY94 @ SY93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(118,plain,
! [SV8: $i] :
( ( ! [SY95: $i] :
~ ( ~ ! [SY96: $i,SY97: $i] :
( ~ ( apply @ SY95 @ SY97 @ SV8 )
| ~ ( member @ SY97 @ SY96 )
| ( member @ SY97 @ ( initial_segment @ SV8 @ SY95 @ SY96 ) ) )
| ~ ~ ( ~ ! [SY98: $i,SY99: $i] :
( ~ ( member @ SY99 @ ( initial_segment @ SV8 @ SY95 @ SY98 ) )
| ( apply @ SY95 @ SY99 @ SV8 ) )
| ~ ! [SY100: $i,SY101: $i] :
( ~ ( member @ SY101 @ ( initial_segment @ SV8 @ SY95 @ SY100 ) )
| ( member @ SY101 @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(119,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apply @ member_predicate @ SX0 @ SX1 )
| ( member @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ( apply @ member_predicate @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(120,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK6_SY60 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ( apply @ SX0 @ ( sK5_X @ SX1 @ SX0 ) @ ( sK6_SY60 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK6_SY60 @ SX1 @ SX0 ) @ ( sK5_X @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK3_SY57 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK4_SY59 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK3_SY57 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK3_SY57 @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) )
| ~ ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) ) )
| ( strict_order @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( suc @ SX0 ) )
| ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) )
| ( member @ SX1 @ ( suc @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(122,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(123,plain,
! [SV2: $i] :
( ( ( ~ ( set @ SV2 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( member @ SY63 @ SV2 )
| ( set @ SY63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(124,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(125,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(126,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(127,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(128,plain,
! [SV3: $i] :
( ( ~ ! [SY64: $i,SY65: $i] :
( ~ ( member @ SV3 @ ( unordered_pair @ SY64 @ SY65 ) )
| ( SV3 = SY64 )
| ( SV3 = SY65 ) )
| ~ ~ ( ~ ! [SY66: $i] :
( ( SV3 != SY66 )
| ! [SY67: $i] : ( member @ SV3 @ ( unordered_pair @ SY66 @ SY67 ) ) )
| ~ ! [SY68: $i,SY69: $i] :
( ( SV3 != SY69 )
| ( member @ SV3 @ ( unordered_pair @ SY68 @ SY69 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(129,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(130,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK13_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK13_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(131,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(132,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(133,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(134,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(135,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( member @ ( sK11_X @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK11_X @ SX0 ) @ SX0 ) )
| ~ ( set @ SX0 )
| ~ ( strict_well_order @ member_predicate @ SX0 )
| ( member @ SX0 @ on ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(136,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(137,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK12_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK12_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(138,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(139,plain,
! [SV4: $i] :
( ( ~ ! [SY70: $i,SY71: $i] :
( ~ ( member @ SV4 @ SY70 )
| ~ ( member @ SV4 @ SY71 )
| ( member @ SV4 @ ( intersection @ SY70 @ SY71 ) ) )
| ~ ~ ( ~ ! [SY72: $i] :
( ! [SY73: $i] :
~ ( member @ SV4 @ ( intersection @ SY72 @ SY73 ) )
| ( member @ SV4 @ SY72 ) )
| ~ ! [SY74: $i,SY75: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY74 @ SY75 ) )
| ( member @ SV4 @ SY75 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(140,plain,
! [SV5: $i] :
( ( ~ ! [SY76: $i,SY77: $i] :
( ~ ( member @ SV5 @ ( union @ SY76 @ SY77 ) )
| ( member @ SV5 @ SY76 )
| ( member @ SV5 @ SY77 ) )
| ~ ~ ( ~ ! [SY78: $i] :
( ~ ( member @ SV5 @ SY78 )
| ! [SY79: $i] : ( member @ SV5 @ ( union @ SY78 @ SY79 ) ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV5 @ SY81 )
| ( member @ SV5 @ ( union @ SY80 @ SY81 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(141,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SX1 @ SX0 ) @ ( sK9_A @ SX1 @ SX0 ) )
| ~ ( subset @ ( sK9_A @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
~ ( least @ SX2 @ SX0 @ ( sK9_A @ SX1 @ SX0 ) ) )
| ~ ( strict_order @ SX0 @ SX1 )
| ( strict_well_order @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(142,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SX2 )
| ~ ( subset @ SX2 @ SX1 )
| ( least @ ( sK8_Y @ SX2 @ SX1 @ SX0 ) @ SX0 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ( strict_order @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(143,plain,
! [SV6: $i] :
( ( ~ ! [SY82: $i,SY83: $i] :
( ~ ( member @ SV6 @ SY83 )
| ( member @ SV6 @ SY82 )
| ( member @ SV6 @ ( difference @ SY83 @ SY82 ) ) )
| ~ ~ ( ~ ! [SY84: $i,SY85: $i] :
( ~ ( member @ SV6 @ ( difference @ SY85 @ SY84 ) )
| ( member @ SV6 @ SY85 ) )
| ~ ! [SY86: $i] :
( ! [SY87: $i] :
~ ( member @ SV6 @ ( difference @ SY87 @ SY86 ) )
| ~ ( member @ SV6 @ SY86 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(144,plain,
! [SV7: $i] :
( ( ~ ! [SY88: $i,SY89: $i] :
( ~ ( ~ ( member @ ( sK7_X @ SY89 @ SY88 @ SV7 ) @ SY88 )
| ~ ~ ( ~ ( ( SY89
!= ( sK7_X @ SY89 @ SY88 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SY89 @ ( sK7_X @ SY89 @ SY88 @ SV7 ) ) ) )
| ~ ( member @ SY89 @ SY88 )
| ( least @ SY89 @ SV7 @ SY88 ) )
| ~ ~ ( ~ ! [SY90: $i,SY91: $i] :
( ~ ( least @ SY91 @ SV7 @ SY90 )
| ! [SY92: $i] :
( ~ ( member @ SY92 @ SY90 )
| ( SY91 = SY92 )
| ( apply @ SV7 @ SY91 @ SY92 ) ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( least @ SY94 @ SV7 @ SY93 )
| ( member @ SY94 @ SY93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(145,plain,
! [SV8: $i,SV9: $i] :
( ( ~ ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( apply @ SV9 @ SY103 @ SV8 )
| ~ ( member @ SY103 @ SY102 )
| ( member @ SY103 @ ( initial_segment @ SV8 @ SV9 @ SY102 ) ) )
| ~ ~ ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( initial_segment @ SV8 @ SV9 @ SY104 ) )
| ( apply @ SV9 @ SY105 @ SV8 ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ ( initial_segment @ SV8 @ SV9 @ SY106 ) )
| ( member @ SY107 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(146,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( apply @ member_predicate @ SX0 @ SX1 )
| ( member @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(147,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ( apply @ member_predicate @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(148,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK6_SY60 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ( apply @ SX0 @ ( sK5_X @ SX1 @ SX0 ) @ ( sK6_SY60 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK6_SY60 @ SX1 @ SX0 ) @ ( sK5_X @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK3_SY57 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK4_SY59 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK3_SY57 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK3_SY57 @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) )
| ~ ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) ) )
| ( strict_order @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(149,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(150,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( suc @ SX0 ) )
| ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(151,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) )
| ( member @ SX1 @ ( suc @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(152,plain,
! [SV2: $i] :
( ( ( set @ SV2 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( member @ SY63 @ SV2 )
| ( set @ SY63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK14_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(157,plain,
! [SV3: $i] :
( ( ~ ! [SY64: $i,SY65: $i] :
( ~ ( member @ SV3 @ ( unordered_pair @ SY64 @ SY65 ) )
| ( SV3 = SY64 )
| ( SV3 = SY65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(158,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ! [SY66: $i] :
( ( SV3 != SY66 )
| ! [SY67: $i] : ( member @ SV3 @ ( unordered_pair @ SY66 @ SY67 ) ) )
| ~ ! [SY68: $i,SY69: $i] :
( ( SV3 != SY69 )
| ( member @ SV3 @ ( unordered_pair @ SY68 @ SY69 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK13_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK13_Y @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(162,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(165,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( member @ ( sK11_X @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK11_X @ SX0 ) @ SX0 ) )
| ~ ( set @ SX0 )
| ~ ( strict_well_order @ member_predicate @ SX0 )
| ( member @ SX0 @ on ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(166,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK12_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK12_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(168,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(169,plain,
! [SV4: $i] :
( ( ~ ! [SY70: $i,SY71: $i] :
( ~ ( member @ SV4 @ SY70 )
| ~ ( member @ SV4 @ SY71 )
| ( member @ SV4 @ ( intersection @ SY70 @ SY71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(170,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ! [SY72: $i] :
( ! [SY73: $i] :
~ ( member @ SV4 @ ( intersection @ SY72 @ SY73 ) )
| ( member @ SV4 @ SY72 ) )
| ~ ! [SY74: $i,SY75: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY74 @ SY75 ) )
| ( member @ SV4 @ SY75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(171,plain,
! [SV5: $i] :
( ( ~ ! [SY76: $i,SY77: $i] :
( ~ ( member @ SV5 @ ( union @ SY76 @ SY77 ) )
| ( member @ SV5 @ SY76 )
| ( member @ SV5 @ SY77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(172,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ! [SY78: $i] :
( ~ ( member @ SV5 @ SY78 )
| ! [SY79: $i] : ( member @ SV5 @ ( union @ SY78 @ SY79 ) ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV5 @ SY81 )
| ( member @ SV5 @ ( union @ SY80 @ SY81 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SX1 @ SX0 ) @ ( sK9_A @ SX1 @ SX0 ) )
| ~ ( subset @ ( sK9_A @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
~ ( least @ SX2 @ SX0 @ ( sK9_A @ SX1 @ SX0 ) ) )
| ~ ( strict_order @ SX0 @ SX1 )
| ( strict_well_order @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(174,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SX2 )
| ~ ( subset @ SX2 @ SX1 )
| ( least @ ( sK8_Y @ SX2 @ SX1 @ SX0 ) @ SX0 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ( strict_order @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(175,plain,
! [SV6: $i] :
( ( ~ ! [SY82: $i,SY83: $i] :
( ~ ( member @ SV6 @ SY83 )
| ( member @ SV6 @ SY82 )
| ( member @ SV6 @ ( difference @ SY83 @ SY82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(176,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ! [SY84: $i,SY85: $i] :
( ~ ( member @ SV6 @ ( difference @ SY85 @ SY84 ) )
| ( member @ SV6 @ SY85 ) )
| ~ ! [SY86: $i] :
( ! [SY87: $i] :
~ ( member @ SV6 @ ( difference @ SY87 @ SY86 ) )
| ~ ( member @ SV6 @ SY86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(177,plain,
! [SV7: $i] :
( ( ~ ! [SY88: $i,SY89: $i] :
( ~ ( ~ ( member @ ( sK7_X @ SY89 @ SY88 @ SV7 ) @ SY88 )
| ~ ~ ( ~ ( ( SY89
!= ( sK7_X @ SY89 @ SY88 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SY89 @ ( sK7_X @ SY89 @ SY88 @ SV7 ) ) ) )
| ~ ( member @ SY89 @ SY88 )
| ( least @ SY89 @ SV7 @ SY88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(178,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ! [SY90: $i,SY91: $i] :
( ~ ( least @ SY91 @ SV7 @ SY90 )
| ! [SY92: $i] :
( ~ ( member @ SY92 @ SY90 )
| ( SY91 = SY92 )
| ( apply @ SV7 @ SY91 @ SY92 ) ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( least @ SY94 @ SV7 @ SY93 )
| ( member @ SY94 @ SY93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(179,plain,
! [SV8: $i,SV9: $i] :
( ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( apply @ SV9 @ SY103 @ SV8 )
| ~ ( member @ SY103 @ SY102 )
| ( member @ SY103 @ ( initial_segment @ SV8 @ SV9 @ SY102 ) ) )
| ~ ~ ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( initial_segment @ SV8 @ SV9 @ SY104 ) )
| ( apply @ SV9 @ SY105 @ SV8 ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ ( initial_segment @ SV8 @ SV9 @ SY106 ) )
| ( member @ SY107 @ SY106 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(180,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( apply @ member_predicate @ SX0 @ SX1 )
| ( member @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ( apply @ member_predicate @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(182,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK6_SY60 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ( apply @ SX0 @ ( sK5_X @ SX1 @ SX0 ) @ ( sK6_SY60 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK6_SY60 @ SX1 @ SX0 ) @ ( sK5_X @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ ( sK3_SY57 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( member @ ( sK4_SY59 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK3_SY57 @ SX1 @ SX0 ) )
| ~ ( apply @ SX0 @ ( sK3_SY57 @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) )
| ~ ~ ( apply @ SX0 @ ( sK2_X @ SX1 @ SX0 ) @ ( sK4_SY59 @ SX1 @ SX0 ) ) ) )
| ( strict_order @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(183,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(184,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( suc @ SX0 ) )
| ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(185,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) )
| ( member @ SX1 @ ( suc @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(186,plain,
! [SV2: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV2 )
| ( set @ SV10 ) )
= $true )
| ( ( set @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(187,plain,
! [SV11: $i] :
( ( ! [SY108: $i] :
( ~ ( member @ SV11 @ ( power_set @ SY108 ) )
| ( subset @ SV11 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(188,plain,
! [SV12: $i] :
( ( ! [SY109: $i] :
( ~ ( subset @ SV12 @ SY109 )
| ( member @ SV12 @ ( power_set @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(189,plain,
! [SV13: $i] :
( ( ! [SY110: $i] :
( ~ ( ~ ( member @ ( sK14_X @ SY110 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK14_X @ SY110 @ SV13 ) @ SY110 ) )
| ( subset @ SV13 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(190,plain,
! [SV14: $i] :
( ( ! [SY111: $i] :
( ~ ( subset @ SV14 @ SY111 )
| ! [SY112: $i] :
( ~ ( member @ SY112 @ SV14 )
| ( member @ SY112 @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(191,plain,
! [SV3: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ( member @ SV3 @ ( unordered_pair @ SY64 @ SY65 ) )
| ( SV3 = SY64 )
| ( SV3 = SY65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(192,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY66: $i] :
( ( SV3 != SY66 )
| ! [SY67: $i] : ( member @ SV3 @ ( unordered_pair @ SY66 @ SY67 ) ) )
| ~ ! [SY68: $i,SY69: $i] :
( ( SV3 != SY69 )
| ( member @ SV3 @ ( unordered_pair @ SY68 @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(193,plain,
! [SV15: $i] :
( ( ! [SY113: $i] :
( ! [SY114: $i] :
( ~ ( member @ SY114 @ SY113 )
| ~ ( member @ SV15 @ SY114 ) )
| ( member @ SV15 @ ( sum @ SY113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(194,plain,
! [SV16: $i] :
( ( ! [SY115: $i] :
( ~ ( member @ SV16 @ ( sum @ SY115 ) )
| ~ ( ~ ( member @ ( sK13_Y @ SY115 @ SV16 ) @ SY115 )
| ~ ( member @ SV16 @ ( sK13_Y @ SY115 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(195,plain,
! [SV17: $i] :
( ( ! [SY116: $i] :
( ~ ( subset @ SV17 @ SY116 )
| ~ ( subset @ SY116 @ SV17 )
| ( equal_set @ SV17 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(196,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(197,plain,
! [SV18: $i] :
( ( ! [SY117: $i] :
( ( SV18 != SY117 )
| ( member @ SV18 @ ( singleton @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(198,plain,
! [SV19: $i] :
( ( ! [SY118: $i] :
( ~ ( member @ SV19 @ ( singleton @ SY118 ) )
| ( SV19 = SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(199,plain,
! [SV20: $i] :
( ( ~ ( ~ ( member @ ( sK11_X @ SV20 ) @ SV20 )
| ~ ~ ( subset @ ( sK11_X @ SV20 ) @ SV20 ) )
| ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 )
| ( member @ SV20 @ on ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(200,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(201,plain,
! [SV21: $i] :
( ( ! [SY119: $i] :
( ~ ( ~ ( member @ ( sK12_Y @ SY119 @ SV21 ) @ SY119 )
| ~ ~ ( member @ SV21 @ ( sK12_Y @ SY119 @ SV21 ) ) )
| ( member @ SV21 @ ( product @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(202,plain,
! [SV22: $i] :
( ( ! [SY120: $i] :
( ~ ( member @ SV22 @ ( product @ SY120 ) )
| ! [SY121: $i] :
( ~ ( member @ SY121 @ SY120 )
| ( member @ SV22 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(203,plain,
! [SV4: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ( member @ SV4 @ SY70 )
| ~ ( member @ SV4 @ SY71 )
| ( member @ SV4 @ ( intersection @ SY70 @ SY71 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(204,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY72: $i] :
( ! [SY73: $i] :
~ ( member @ SV4 @ ( intersection @ SY72 @ SY73 ) )
| ( member @ SV4 @ SY72 ) )
| ~ ! [SY74: $i,SY75: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY74 @ SY75 ) )
| ( member @ SV4 @ SY75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(205,plain,
! [SV5: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( member @ SV5 @ ( union @ SY76 @ SY77 ) )
| ( member @ SV5 @ SY76 )
| ( member @ SV5 @ SY77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(206,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY78: $i] :
( ~ ( member @ SV5 @ SY78 )
| ! [SY79: $i] : ( member @ SV5 @ ( union @ SY78 @ SY79 ) ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV5 @ SY81 )
| ( member @ SV5 @ ( union @ SY80 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(207,plain,
! [SV23: $i] :
( ( ! [SY122: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SY122 @ SV23 ) @ ( sK9_A @ SY122 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SY122 @ SV23 ) @ SY122 ) )
| ~ ! [SY123: $i] :
~ ( least @ SY123 @ SV23 @ ( sK9_A @ SY122 @ SV23 ) ) )
| ~ ( strict_order @ SV23 @ SY122 )
| ( strict_well_order @ SV23 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(208,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SX2 )
| ~ ( subset @ SX2 @ SX1 )
| ( least @ ( sK8_Y @ SX2 @ SX1 @ SX0 ) @ SX0 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ( strict_order @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(209,plain,
! [SV6: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ( member @ SV6 @ SY83 )
| ( member @ SV6 @ SY82 )
| ( member @ SV6 @ ( difference @ SY83 @ SY82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(210,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY84: $i,SY85: $i] :
( ~ ( member @ SV6 @ ( difference @ SY85 @ SY84 ) )
| ( member @ SV6 @ SY85 ) )
| ~ ! [SY86: $i] :
( ! [SY87: $i] :
~ ( member @ SV6 @ ( difference @ SY87 @ SY86 ) )
| ~ ( member @ SV6 @ SY86 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(211,plain,
! [SV7: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( ~ ( member @ ( sK7_X @ SY89 @ SY88 @ SV7 ) @ SY88 )
| ~ ~ ( ~ ( ( SY89
!= ( sK7_X @ SY89 @ SY88 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SY89 @ ( sK7_X @ SY89 @ SY88 @ SV7 ) ) ) )
| ~ ( member @ SY89 @ SY88 )
| ( least @ SY89 @ SV7 @ SY88 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(212,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY90: $i,SY91: $i] :
( ~ ( least @ SY91 @ SV7 @ SY90 )
| ! [SY92: $i] :
( ~ ( member @ SY92 @ SY90 )
| ( SY91 = SY92 )
| ( apply @ SV7 @ SY91 @ SY92 ) ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( least @ SY94 @ SV7 @ SY93 )
| ( member @ SY94 @ SY93 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(213,plain,
! [SV8: $i,SV9: $i] :
( ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( apply @ SV9 @ SY103 @ SV8 )
| ~ ( member @ SY103 @ SY102 )
| ( member @ SY103 @ ( initial_segment @ SV8 @ SV9 @ SY102 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(214,plain,
! [SV9: $i,SV8: $i] :
( ( ~ ~ ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( initial_segment @ SV8 @ SV9 @ SY104 ) )
| ( apply @ SV9 @ SY105 @ SV8 ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ ( initial_segment @ SV8 @ SV9 @ SY106 ) )
| ( member @ SY107 @ SY106 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(215,plain,
! [SV24: $i] :
( ( ! [SY124: $i] :
( ~ ( apply @ member_predicate @ SV24 @ SY124 )
| ( member @ SV24 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(216,plain,
! [SV25: $i] :
( ( ! [SY125: $i] :
( ~ ( member @ SV25 @ SY125 )
| ( apply @ member_predicate @ SV25 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(217,plain,
! [SV26: $i] :
( ( ! [SY126: $i] :
( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SY126 @ SV26 ) @ SY126 )
| ~ ( member @ ( sK6_SY60 @ SY126 @ SV26 ) @ SY126 ) )
| ~ ~ ( ~ ( apply @ SV26 @ ( sK5_X @ SY126 @ SV26 ) @ ( sK6_SY60 @ SY126 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SY126 @ SV26 ) @ ( sK5_X @ SY126 @ SV26 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SY126 @ SV26 ) @ SY126 )
| ~ ( member @ ( sK3_SY57 @ SY126 @ SV26 ) @ SY126 ) )
| ~ ( member @ ( sK4_SY59 @ SY126 @ SV26 ) @ SY126 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SY126 @ SV26 ) @ ( sK3_SY57 @ SY126 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SY126 @ SV26 ) @ ( sK4_SY59 @ SY126 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SY126 @ SV26 ) @ ( sK4_SY59 @ SY126 @ SV26 ) ) ) )
| ( strict_order @ SV26 @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(218,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ SX0 @ SX2 @ SX4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(219,plain,
! [SV27: $i] :
( ( ! [SY127: $i] :
( ~ ( member @ SY127 @ ( suc @ SV27 ) )
| ( member @ SY127 @ ( union @ SV27 @ ( singleton @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(220,plain,
! [SV28: $i] :
( ( ! [SY128: $i] :
( ~ ( member @ SY128 @ ( union @ SV28 @ ( singleton @ SV28 ) ) )
| ( member @ SY128 @ ( suc @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(221,plain,
! [SV2: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV2 ) )
= $true )
| ( ( set @ SV10 )
= $true )
| ( ( set @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(222,plain,
! [SV29: $i,SV11: $i] :
( ( ~ ( member @ SV11 @ ( power_set @ SV29 ) )
| ( subset @ SV11 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(223,plain,
! [SV30: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV30 )
| ( member @ SV12 @ ( power_set @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(224,plain,
! [SV13: $i,SV31: $i] :
( ( ~ ( ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV31 ) )
| ( subset @ SV13 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(225,plain,
! [SV32: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV32 )
| ! [SY129: $i] :
( ~ ( member @ SY129 @ SV14 )
| ( member @ SY129 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(226,plain,
! [SV33: $i,SV3: $i] :
( ( ! [SY130: $i] :
( ~ ( member @ SV3 @ ( unordered_pair @ SV33 @ SY130 ) )
| ( SV3 = SV33 )
| ( SV3 = SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(227,plain,
! [SV3: $i] :
( ( ~ ! [SY66: $i] :
( ( SV3 != SY66 )
| ! [SY67: $i] : ( member @ SV3 @ ( unordered_pair @ SY66 @ SY67 ) ) )
| ~ ! [SY68: $i,SY69: $i] :
( ( SV3 != SY69 )
| ( member @ SV3 @ ( unordered_pair @ SY68 @ SY69 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(228,plain,
! [SV15: $i,SV34: $i] :
( ( ! [SY131: $i] :
( ~ ( member @ SY131 @ SV34 )
| ~ ( member @ SV15 @ SY131 ) )
| ( member @ SV15 @ ( sum @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(229,plain,
! [SV35: $i,SV16: $i] :
( ( ~ ( member @ SV16 @ ( sum @ SV35 ) )
| ~ ( ~ ( member @ ( sK13_Y @ SV35 @ SV16 ) @ SV35 )
| ~ ( member @ SV16 @ ( sK13_Y @ SV35 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(230,plain,
! [SV36: $i,SV17: $i] :
( ( ~ ( subset @ SV17 @ SV36 )
| ~ ( subset @ SV36 @ SV17 )
| ( equal_set @ SV17 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(231,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(232,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(233,plain,
! [SV37: $i,SV18: $i] :
( ( ( SV18 != SV37 )
| ( member @ SV18 @ ( singleton @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(234,plain,
! [SV38: $i,SV19: $i] :
( ( ~ ( member @ SV19 @ ( singleton @ SV38 ) )
| ( SV19 = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(235,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( member @ ( sK11_X @ SV20 ) @ SV20 )
| ~ ~ ( subset @ ( sK11_X @ SV20 ) @ SV20 ) )
| ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(236,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(237,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(238,plain,
! [SV21: $i,SV39: $i] :
( ( ~ ( ~ ( member @ ( sK12_Y @ SV39 @ SV21 ) @ SV39 )
| ~ ~ ( member @ SV21 @ ( sK12_Y @ SV39 @ SV21 ) ) )
| ( member @ SV21 @ ( product @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(239,plain,
! [SV40: $i,SV22: $i] :
( ( ~ ( member @ SV22 @ ( product @ SV40 ) )
| ! [SY132: $i] :
( ~ ( member @ SY132 @ SV40 )
| ( member @ SV22 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(240,plain,
! [SV41: $i,SV4: $i] :
( ( ! [SY133: $i] :
( ~ ( member @ SV4 @ SV41 )
| ~ ( member @ SV4 @ SY133 )
| ( member @ SV4 @ ( intersection @ SV41 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV4: $i] :
( ( ~ ! [SY72: $i] :
( ! [SY73: $i] :
~ ( member @ SV4 @ ( intersection @ SY72 @ SY73 ) )
| ( member @ SV4 @ SY72 ) )
| ~ ! [SY74: $i,SY75: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY74 @ SY75 ) )
| ( member @ SV4 @ SY75 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV42: $i,SV5: $i] :
( ( ! [SY134: $i] :
( ~ ( member @ SV5 @ ( union @ SV42 @ SY134 ) )
| ( member @ SV5 @ SV42 )
| ( member @ SV5 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV5: $i] :
( ( ~ ! [SY78: $i] :
( ~ ( member @ SV5 @ SY78 )
| ! [SY79: $i] : ( member @ SV5 @ ( union @ SY78 @ SY79 ) ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV5 @ SY81 )
| ( member @ SV5 @ ( union @ SY80 @ SY81 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV23: $i,SV43: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) )
| ~ ! [SY135: $i] :
~ ( least @ SY135 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) ) )
| ~ ( strict_order @ SV23 @ SV43 )
| ( strict_well_order @ SV23 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(245,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SX2 )
| ~ ( subset @ SX2 @ SX1 )
| ( least @ ( sK8_Y @ SX2 @ SX1 @ SX0 ) @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(246,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ( strict_order @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(247,plain,
! [SV44: $i,SV6: $i] :
( ( ! [SY136: $i] :
( ~ ( member @ SV6 @ SY136 )
| ( member @ SV6 @ SV44 )
| ( member @ SV6 @ ( difference @ SY136 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(248,plain,
! [SV6: $i] :
( ( ~ ! [SY84: $i,SY85: $i] :
( ~ ( member @ SV6 @ ( difference @ SY85 @ SY84 ) )
| ( member @ SV6 @ SY85 ) )
| ~ ! [SY86: $i] :
( ! [SY87: $i] :
~ ( member @ SV6 @ ( difference @ SY87 @ SY86 ) )
| ~ ( member @ SV6 @ SY86 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(249,plain,
! [SV7: $i,SV45: $i] :
( ( ! [SY137: $i] :
( ~ ( ~ ( member @ ( sK7_X @ SY137 @ SV45 @ SV7 ) @ SV45 )
| ~ ~ ( ~ ( ( SY137
!= ( sK7_X @ SY137 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SY137 @ ( sK7_X @ SY137 @ SV45 @ SV7 ) ) ) )
| ~ ( member @ SY137 @ SV45 )
| ( least @ SY137 @ SV7 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(250,plain,
! [SV7: $i] :
( ( ~ ! [SY90: $i,SY91: $i] :
( ~ ( least @ SY91 @ SV7 @ SY90 )
| ! [SY92: $i] :
( ~ ( member @ SY92 @ SY90 )
| ( SY91 = SY92 )
| ( apply @ SV7 @ SY91 @ SY92 ) ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( least @ SY94 @ SV7 @ SY93 )
| ( member @ SY94 @ SY93 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(251,plain,
! [SV8: $i,SV9: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( apply @ SV9 @ SY103 @ SV8 )
| ~ ( member @ SY103 @ SY102 )
| ( member @ SY103 @ ( initial_segment @ SV8 @ SV9 @ SY102 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(252,plain,
! [SV9: $i,SV8: $i] :
( ( ~ ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( initial_segment @ SV8 @ SV9 @ SY104 ) )
| ( apply @ SV9 @ SY105 @ SV8 ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ ( initial_segment @ SV8 @ SV9 @ SY106 ) )
| ( member @ SY107 @ SY106 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(253,plain,
! [SV46: $i,SV24: $i] :
( ( ~ ( apply @ member_predicate @ SV24 @ SV46 )
| ( member @ SV24 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(254,plain,
! [SV47: $i,SV25: $i] :
( ( ~ ( member @ SV25 @ SV47 )
| ( apply @ member_predicate @ SV25 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(255,plain,
! [SV26: $i,SV48: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
| ( strict_order @ SV26 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(256,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(257,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ SX0 @ SX2 @ SX4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(258,plain,
! [SV27: $i,SV49: $i] :
( ( ~ ( member @ SV49 @ ( suc @ SV27 ) )
| ( member @ SV49 @ ( union @ SV27 @ ( singleton @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(259,plain,
! [SV28: $i,SV50: $i] :
( ( ~ ( member @ SV50 @ ( union @ SV28 @ ( singleton @ SV28 ) ) )
| ( member @ SV50 @ ( suc @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(260,plain,
! [SV2: $i,SV10: $i] :
( ( ( member @ SV10 @ SV2 )
= $false )
| ( ( set @ SV10 )
= $true )
| ( ( set @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(261,plain,
! [SV29: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ ( power_set @ SV29 ) ) )
= $true )
| ( ( subset @ SV11 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(262,plain,
! [SV30: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV30 ) )
= $true )
| ( ( member @ SV12 @ ( power_set @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(263,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ( ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV31 ) ) )
= $true )
| ( ( subset @ SV13 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(264,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV32 ) )
= $true )
| ( ( ! [SY129: $i] :
( ~ ( member @ SY129 @ SV14 )
| ( member @ SY129 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(265,plain,
! [SV51: $i,SV33: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ ( unordered_pair @ SV33 @ SV51 ) )
| ( SV3 = SV33 )
| ( SV3 = SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(266,plain,
! [SV3: $i] :
( ( ~ ! [SY66: $i] :
( ( SV3 != SY66 )
| ! [SY67: $i] : ( member @ SV3 @ ( unordered_pair @ SY66 @ SY67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(267,plain,
! [SV3: $i] :
( ( ~ ! [SY68: $i,SY69: $i] :
( ( SV3 != SY69 )
| ( member @ SV3 @ ( unordered_pair @ SY68 @ SY69 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(268,plain,
! [SV15: $i,SV34: $i] :
( ( ( ! [SY131: $i] :
( ~ ( member @ SY131 @ SV34 )
| ~ ( member @ SV15 @ SY131 ) ) )
= $true )
| ( ( member @ SV15 @ ( sum @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(269,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ ( sum @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK13_Y @ SV35 @ SV16 ) @ SV35 )
| ~ ( member @ SV16 @ ( sK13_Y @ SV35 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(270,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV36 )
| ~ ( subset @ SV36 @ SV17 ) )
= $true )
| ( ( equal_set @ SV17 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(271,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(272,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(273,plain,
! [SV37: $i,SV18: $i] :
( ( ( ( SV18 != SV37 ) )
= $true )
| ( ( member @ SV18 @ ( singleton @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(274,plain,
! [SV38: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ ( singleton @ SV38 ) ) )
= $true )
| ( ( SV19 = SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(275,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( member @ ( sK11_X @ SV20 ) @ SV20 )
| ~ ~ ( subset @ ( sK11_X @ SV20 ) @ SV20 ) ) )
= $true )
| ( ( ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(276,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(277,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(278,plain,
! [SV21: $i,SV39: $i] :
( ( ( ~ ( ~ ( member @ ( sK12_Y @ SV39 @ SV21 ) @ SV39 )
| ~ ~ ( member @ SV21 @ ( sK12_Y @ SV39 @ SV21 ) ) ) )
= $true )
| ( ( member @ SV21 @ ( product @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(279,plain,
! [SV40: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ ( product @ SV40 ) ) )
= $true )
| ( ( ! [SY132: $i] :
( ~ ( member @ SY132 @ SV40 )
| ( member @ SV22 @ SY132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(280,plain,
! [SV52: $i,SV41: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ SV41 )
| ~ ( member @ SV4 @ SV52 )
| ( member @ SV4 @ ( intersection @ SV41 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(281,plain,
! [SV4: $i] :
( ( ~ ! [SY72: $i] :
( ! [SY73: $i] :
~ ( member @ SV4 @ ( intersection @ SY72 @ SY73 ) )
| ( member @ SV4 @ SY72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(282,plain,
! [SV4: $i] :
( ( ~ ! [SY74: $i,SY75: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY74 @ SY75 ) )
| ( member @ SV4 @ SY75 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(283,plain,
! [SV53: $i,SV42: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( union @ SV42 @ SV53 ) )
| ( member @ SV5 @ SV42 )
| ( member @ SV5 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(284,plain,
! [SV5: $i] :
( ( ~ ! [SY78: $i] :
( ~ ( member @ SV5 @ SY78 )
| ! [SY79: $i] : ( member @ SV5 @ ( union @ SY78 @ SY79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(285,plain,
! [SV5: $i] :
( ( ~ ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV5 @ SY81 )
| ( member @ SV5 @ ( union @ SY80 @ SY81 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(286,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) )
| ~ ! [SY135: $i] :
~ ( least @ SY135 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) ) )
| ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(287,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ! [SX2: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SX2 )
| ~ ( subset @ SX2 @ SX1 )
| ( least @ ( sK8_Y @ SX2 @ SX1 @ SX0 ) @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(288,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strict_well_order @ SX0 @ SX1 )
| ( strict_order @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(289,plain,
! [SV44: $i,SV54: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ SV54 )
| ( member @ SV6 @ SV44 )
| ( member @ SV6 @ ( difference @ SV54 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(290,plain,
! [SV6: $i] :
( ( ~ ! [SY84: $i,SY85: $i] :
( ~ ( member @ SV6 @ ( difference @ SY85 @ SY84 ) )
| ( member @ SV6 @ SY85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(291,plain,
! [SV6: $i] :
( ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
~ ( member @ SV6 @ ( difference @ SY87 @ SY86 ) )
| ~ ( member @ SV6 @ SY86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(292,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ~ ( ~ ( member @ ( sK7_X @ SV55 @ SV45 @ SV7 ) @ SV45 )
| ~ ~ ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) ) )
| ~ ( member @ SV55 @ SV45 )
| ( least @ SV55 @ SV7 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(293,plain,
! [SV7: $i] :
( ( ~ ! [SY90: $i,SY91: $i] :
( ~ ( least @ SY91 @ SV7 @ SY90 )
| ! [SY92: $i] :
( ~ ( member @ SY92 @ SY90 )
| ( SY91 = SY92 )
| ( apply @ SV7 @ SY91 @ SY92 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(294,plain,
! [SV7: $i] :
( ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( least @ SY94 @ SV7 @ SY93 )
| ( member @ SY94 @ SY93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(295,plain,
! [SV56: $i,SV8: $i,SV9: $i] :
( ( ! [SY138: $i] :
( ~ ( apply @ SV9 @ SY138 @ SV8 )
| ~ ( member @ SY138 @ SV56 )
| ( member @ SY138 @ ( initial_segment @ SV8 @ SV9 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(296,plain,
! [SV9: $i,SV8: $i] :
( ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( initial_segment @ SV8 @ SV9 @ SY104 ) )
| ( apply @ SV9 @ SY105 @ SV8 ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ ( initial_segment @ SV8 @ SV9 @ SY106 ) )
| ( member @ SY107 @ SY106 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(297,plain,
! [SV46: $i,SV24: $i] :
( ( ( ~ ( apply @ member_predicate @ SV24 @ SV46 ) )
= $true )
| ( ( member @ SV24 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(298,plain,
! [SV47: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV47 ) )
= $true )
| ( ( apply @ member_predicate @ SV25 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(299,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strict_order @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ SX0 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(302,plain,
! [SV27: $i,SV49: $i] :
( ( ( ~ ( member @ SV49 @ ( suc @ SV27 ) ) )
= $true )
| ( ( member @ SV49 @ ( union @ SV27 @ ( singleton @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(303,plain,
! [SV28: $i,SV50: $i] :
( ( ( ~ ( member @ SV50 @ ( union @ SV28 @ ( singleton @ SV28 ) ) ) )
= $true )
| ( ( member @ SV50 @ ( suc @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(304,plain,
! [SV29: $i,SV11: $i] :
( ( ( member @ SV11 @ ( power_set @ SV29 ) )
= $false )
| ( ( subset @ SV11 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(305,plain,
! [SV30: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV30 )
= $false )
| ( ( member @ SV12 @ ( power_set @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(306,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV31 ) )
= $false )
| ( ( subset @ SV13 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(307,plain,
! [SV32: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV32 )
= $false )
| ( ( ! [SY129: $i] :
( ~ ( member @ SY129 @ SV14 )
| ( member @ SY129 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(308,plain,
! [SV51: $i,SV33: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( unordered_pair @ SV33 @ SV51 ) ) )
= $true )
| ( ( ( SV3 = SV33 )
| ( SV3 = SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(309,plain,
! [SV3: $i] :
( ( ! [SY66: $i] :
( ( SV3 != SY66 )
| ! [SY67: $i] : ( member @ SV3 @ ( unordered_pair @ SY66 @ SY67 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(310,plain,
! [SV3: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( SV3 != SY69 )
| ( member @ SV3 @ ( unordered_pair @ SY68 @ SY69 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(311,plain,
! [SV15: $i,SV34: $i,SV57: $i] :
( ( ( ~ ( member @ SV57 @ SV34 )
| ~ ( member @ SV15 @ SV57 ) )
= $true )
| ( ( member @ SV15 @ ( sum @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(312,plain,
! [SV35: $i,SV16: $i] :
( ( ( member @ SV16 @ ( sum @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK13_Y @ SV35 @ SV16 ) @ SV35 )
| ~ ( member @ SV16 @ ( sK13_Y @ SV35 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(313,plain,
! [SV36: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV36 ) )
= $true )
| ( ( ~ ( subset @ SV36 @ SV17 ) )
= $true )
| ( ( equal_set @ SV17 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(314,plain,
! [SV58: $i] :
( ( ! [SY139: $i] :
( ~ ( equal_set @ SV58 @ SY139 )
| ( subset @ SV58 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(315,plain,
! [SV59: $i] :
( ( ! [SY140: $i] :
( ~ ( equal_set @ SV59 @ SY140 )
| ( subset @ SY140 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(316,plain,
! [SV37: $i,SV18: $i] :
( ( ( SV18 = SV37 )
= $false )
| ( ( member @ SV18 @ ( singleton @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(317,plain,
! [SV38: $i,SV19: $i] :
( ( ( member @ SV19 @ ( singleton @ SV38 ) )
= $false )
| ( ( SV19 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(318,plain,
! [SV20: $i] :
( ( ( ~ ( member @ ( sK11_X @ SV20 ) @ SV20 )
| ~ ~ ( subset @ ( sK11_X @ SV20 ) @ SV20 ) )
= $false )
| ( ( ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(319,plain,
! [SV60: $i] :
( ( ~ ( member @ SV60 @ on )
| ! [SY141: $i] :
( ~ ( member @ SY141 @ SV60 )
| ( subset @ SY141 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(320,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(321,plain,
! [SV21: $i,SV39: $i] :
( ( ( ~ ( member @ ( sK12_Y @ SV39 @ SV21 ) @ SV39 )
| ~ ~ ( member @ SV21 @ ( sK12_Y @ SV39 @ SV21 ) ) )
= $false )
| ( ( member @ SV21 @ ( product @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(322,plain,
! [SV40: $i,SV22: $i] :
( ( ( member @ SV22 @ ( product @ SV40 ) )
= $false )
| ( ( ! [SY132: $i] :
( ~ ( member @ SY132 @ SV40 )
| ( member @ SV22 @ SY132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(323,plain,
! [SV52: $i,SV41: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ SV41 )
| ~ ( member @ SV4 @ SV52 ) )
= $true )
| ( ( member @ SV4 @ ( intersection @ SV41 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(324,plain,
! [SV4: $i] :
( ( ! [SY72: $i] :
( ! [SY73: $i] :
~ ( member @ SV4 @ ( intersection @ SY72 @ SY73 ) )
| ( member @ SV4 @ SY72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(325,plain,
! [SV4: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY74 @ SY75 ) )
| ( member @ SV4 @ SY75 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(326,plain,
! [SV53: $i,SV42: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( union @ SV42 @ SV53 ) ) )
= $true )
| ( ( ( member @ SV5 @ SV42 )
| ( member @ SV5 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(327,plain,
! [SV5: $i] :
( ( ! [SY78: $i] :
( ~ ( member @ SV5 @ SY78 )
| ! [SY79: $i] : ( member @ SV5 @ ( union @ SY78 @ SY79 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(328,plain,
! [SV5: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( member @ SV5 @ SY81 )
| ( member @ SV5 @ ( union @ SY80 @ SY81 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(329,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) )
| ~ ! [SY135: $i] :
~ ( least @ SY135 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) ) ) )
= $true )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(330,plain,
! [SV61: $i] :
( ( ! [SY142: $i] :
( ~ ( strict_well_order @ SV61 @ SY142 )
| ! [SY143: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SY143 )
| ~ ( subset @ SY143 @ SY142 )
| ( least @ ( sK8_Y @ SY143 @ SY142 @ SV61 ) @ SV61 @ SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(331,plain,
! [SV62: $i] :
( ( ! [SY145: $i] :
( ~ ( strict_well_order @ SV62 @ SY145 )
| ( strict_order @ SV62 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(332,plain,
! [SV44: $i,SV54: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ SV54 )
| ( member @ SV6 @ SV44 ) )
= $true )
| ( ( member @ SV6 @ ( difference @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(333,plain,
! [SV6: $i] :
( ( ! [SY84: $i,SY85: $i] :
( ~ ( member @ SV6 @ ( difference @ SY85 @ SY84 ) )
| ( member @ SV6 @ SY85 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(334,plain,
! [SV6: $i] :
( ( ! [SY86: $i] :
( ! [SY87: $i] :
~ ( member @ SV6 @ ( difference @ SY87 @ SY86 ) )
| ~ ( member @ SV6 @ SY86 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(335,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_X @ SV55 @ SV45 @ SV7 ) @ SV45 )
| ~ ~ ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) ) )
| ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(336,plain,
! [SV7: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( least @ SY91 @ SV7 @ SY90 )
| ! [SY92: $i] :
( ~ ( member @ SY92 @ SY90 )
| ( SY91 = SY92 )
| ( apply @ SV7 @ SY91 @ SY92 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(337,plain,
! [SV7: $i] :
( ( ! [SY93: $i,SY94: $i] :
( ~ ( least @ SY94 @ SV7 @ SY93 )
| ( member @ SY94 @ SY93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(338,plain,
! [SV56: $i,SV8: $i,SV63: $i,SV9: $i] :
( ( ~ ( apply @ SV9 @ SV63 @ SV8 )
| ~ ( member @ SV63 @ SV56 )
| ( member @ SV63 @ ( initial_segment @ SV8 @ SV9 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(339,plain,
! [SV9: $i,SV8: $i] :
( ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( initial_segment @ SV8 @ SV9 @ SY104 ) )
| ( apply @ SV9 @ SY105 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(340,plain,
! [SV9: $i,SV8: $i] :
( ( ~ ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ ( initial_segment @ SV8 @ SV9 @ SY106 ) )
| ( member @ SY107 @ SY106 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(341,plain,
! [SV46: $i,SV24: $i] :
( ( ( apply @ member_predicate @ SV24 @ SV46 )
= $false )
| ( ( member @ SV24 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(342,plain,
! [SV47: $i,SV25: $i] :
( ( ( member @ SV25 @ SV47 )
= $false )
| ( ( apply @ member_predicate @ SV25 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(343,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(344,plain,
! [SV64: $i] :
( ( ! [SY146: $i] :
( ~ ( strict_order @ SV64 @ SY146 )
| ! [SY147: $i,SY148: $i] :
( ~ ( member @ SY147 @ SY146 )
| ~ ( member @ SY148 @ SY146 )
| ~ ( apply @ SV64 @ SY147 @ SY148 )
| ~ ( apply @ SV64 @ SY148 @ SY147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(345,plain,
! [SV65: $i] :
( ( ! [SY149: $i] :
( ~ ( strict_order @ SV65 @ SY149 )
| ! [SY150: $i,SY151: $i,SY152: $i] :
( ~ ( member @ SY150 @ SY149 )
| ~ ( member @ SY151 @ SY149 )
| ~ ( member @ SY152 @ SY149 )
| ~ ( apply @ SV65 @ SY150 @ SY151 )
| ~ ( apply @ SV65 @ SY151 @ SY152 )
| ( apply @ SV65 @ SY150 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(346,plain,
! [SV27: $i,SV49: $i] :
( ( ( member @ SV49 @ ( suc @ SV27 ) )
= $false )
| ( ( member @ SV49 @ ( union @ SV27 @ ( singleton @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(347,plain,
! [SV28: $i,SV50: $i] :
( ( ( member @ SV50 @ ( union @ SV28 @ ( singleton @ SV28 ) ) )
= $false )
| ( ( member @ SV50 @ ( suc @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(348,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV13 ) )
= $false )
| ( ( subset @ SV13 @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(349,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV31 ) )
= $false )
| ( ( subset @ SV13 @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(350,plain,
! [SV32: $i,SV14: $i,SV66: $i] :
( ( ( ~ ( member @ SV66 @ SV14 )
| ( member @ SV66 @ SV32 ) )
= $true )
| ( ( subset @ SV14 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(351,plain,
! [SV51: $i,SV33: $i,SV3: $i] :
( ( ( member @ SV3 @ ( unordered_pair @ SV33 @ SV51 ) )
= $false )
| ( ( ( SV3 = SV33 )
| ( SV3 = SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(352,plain,
! [SV67: $i,SV3: $i] :
( ( ( SV3 != SV67 )
| ! [SY153: $i] : ( member @ SV3 @ ( unordered_pair @ SV67 @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(353,plain,
! [SV68: $i,SV3: $i] :
( ( ! [SY154: $i] :
( ( SV3 != SY154 )
| ( member @ SV3 @ ( unordered_pair @ SV68 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(354,plain,
! [SV15: $i,SV34: $i,SV57: $i] :
( ( ( ~ ( member @ SV57 @ SV34 ) )
= $true )
| ( ( ~ ( member @ SV15 @ SV57 ) )
= $true )
| ( ( member @ SV15 @ ( sum @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(355,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( member @ ( sK13_Y @ SV35 @ SV16 ) @ SV35 )
| ~ ( member @ SV16 @ ( sK13_Y @ SV35 @ SV16 ) ) )
= $false )
| ( ( member @ SV16 @ ( sum @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(356,plain,
! [SV36: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV36 )
= $false )
| ( ( ~ ( subset @ SV36 @ SV17 ) )
= $true )
| ( ( equal_set @ SV17 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(357,plain,
! [SV69: $i,SV58: $i] :
( ( ~ ( equal_set @ SV58 @ SV69 )
| ( subset @ SV58 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(358,plain,
! [SV70: $i,SV59: $i] :
( ( ~ ( equal_set @ SV59 @ SV70 )
| ( subset @ SV70 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(359,plain,
! [SV20: $i] :
( ( ( ~ ( member @ ( sK11_X @ SV20 ) @ SV20 ) )
= $false )
| ( ( ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(360,plain,
! [SV20: $i] :
( ( ( ~ ~ ( subset @ ( sK11_X @ SV20 ) @ SV20 ) )
= $false )
| ( ( ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(361,plain,
! [SV60: $i] :
( ( ( ~ ( member @ SV60 @ on ) )
= $true )
| ( ( ! [SY141: $i] :
( ~ ( member @ SY141 @ SV60 )
| ( subset @ SY141 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(362,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(363,plain,
( ( ~ ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(364,plain,
! [SV21: $i,SV39: $i] :
( ( ( ~ ( member @ ( sK12_Y @ SV39 @ SV21 ) @ SV39 ) )
= $false )
| ( ( member @ SV21 @ ( product @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(365,plain,
! [SV39: $i,SV21: $i] :
( ( ( ~ ~ ( member @ SV21 @ ( sK12_Y @ SV39 @ SV21 ) ) )
= $false )
| ( ( member @ SV21 @ ( product @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(366,plain,
! [SV22: $i,SV40: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV40 )
| ( member @ SV22 @ SV71 ) )
= $true )
| ( ( member @ SV22 @ ( product @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(367,plain,
! [SV52: $i,SV41: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ SV41 ) )
= $true )
| ( ( ~ ( member @ SV4 @ SV52 ) )
= $true )
| ( ( member @ SV4 @ ( intersection @ SV41 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(368,plain,
! [SV72: $i,SV4: $i] :
( ( ! [SY155: $i] :
~ ( member @ SV4 @ ( intersection @ SV72 @ SY155 ) )
| ( member @ SV4 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(369,plain,
! [SV73: $i,SV4: $i] :
( ( ! [SY156: $i] :
( ~ ( member @ SV4 @ ( intersection @ SV73 @ SY156 ) )
| ( member @ SV4 @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(370,plain,
! [SV53: $i,SV42: $i,SV5: $i] :
( ( ( member @ SV5 @ ( union @ SV42 @ SV53 ) )
= $false )
| ( ( ( member @ SV5 @ SV42 )
| ( member @ SV5 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(371,plain,
! [SV74: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ SV74 )
| ! [SY157: $i] : ( member @ SV5 @ ( union @ SV74 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(372,plain,
! [SV75: $i,SV5: $i] :
( ( ! [SY158: $i] :
( ~ ( member @ SV5 @ SY158 )
| ( member @ SV5 @ ( union @ SV75 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(373,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) )
| ~ ! [SY135: $i] :
~ ( least @ SY135 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) ) )
= $false )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(374,plain,
! [SV76: $i,SV61: $i] :
( ( ~ ( strict_well_order @ SV61 @ SV76 )
| ! [SY159: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SY159 )
| ~ ( subset @ SY159 @ SV76 )
| ( least @ ( sK8_Y @ SY159 @ SV76 @ SV61 ) @ SV61 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(375,plain,
! [SV77: $i,SV62: $i] :
( ( ~ ( strict_well_order @ SV62 @ SV77 )
| ( strict_order @ SV62 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(376,plain,
! [SV44: $i,SV54: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ SV54 ) )
= $true )
| ( ( member @ SV6 @ SV44 )
= $true )
| ( ( member @ SV6 @ ( difference @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(377,plain,
! [SV78: $i,SV6: $i] :
( ( ! [SY161: $i] :
( ~ ( member @ SV6 @ ( difference @ SY161 @ SV78 ) )
| ( member @ SV6 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(378,plain,
! [SV79: $i,SV6: $i] :
( ( ! [SY162: $i] :
~ ( member @ SV6 @ ( difference @ SY162 @ SV79 ) )
| ~ ( member @ SV6 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(379,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_X @ SV55 @ SV45 @ SV7 ) @ SV45 )
| ~ ~ ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) ) ) )
= $true )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(380,plain,
! [SV80: $i,SV7: $i] :
( ( ! [SY163: $i] :
( ~ ( least @ SY163 @ SV7 @ SV80 )
| ! [SY164: $i] :
( ~ ( member @ SY164 @ SV80 )
| ( SY163 = SY164 )
| ( apply @ SV7 @ SY163 @ SY164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(381,plain,
! [SV81: $i,SV7: $i] :
( ( ! [SY165: $i] :
( ~ ( least @ SY165 @ SV7 @ SV81 )
| ( member @ SY165 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(382,plain,
! [SV56: $i,SV8: $i,SV63: $i,SV9: $i] :
( ( ( ~ ( apply @ SV9 @ SV63 @ SV8 )
| ~ ( member @ SV63 @ SV56 ) )
= $true )
| ( ( member @ SV63 @ ( initial_segment @ SV8 @ SV9 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(383,plain,
! [SV9: $i,SV8: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( member @ SY105 @ ( initial_segment @ SV8 @ SV9 @ SY104 ) )
| ( apply @ SV9 @ SY105 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(384,plain,
! [SV9: $i,SV8: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( member @ SY107 @ ( initial_segment @ SV8 @ SV9 @ SY106 ) )
| ( member @ SY107 @ SY106 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(385,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(386,plain,
! [SV82: $i,SV64: $i] :
( ( ~ ( strict_order @ SV64 @ SV82 )
| ! [SY166: $i,SY167: $i] :
( ~ ( member @ SY166 @ SV82 )
| ~ ( member @ SY167 @ SV82 )
| ~ ( apply @ SV64 @ SY166 @ SY167 )
| ~ ( apply @ SV64 @ SY167 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(387,plain,
! [SV83: $i,SV65: $i] :
( ( ~ ( strict_order @ SV65 @ SV83 )
| ! [SY168: $i,SY169: $i,SY170: $i] :
( ~ ( member @ SY168 @ SV83 )
| ~ ( member @ SY169 @ SV83 )
| ~ ( member @ SY170 @ SV83 )
| ~ ( apply @ SV65 @ SY168 @ SY169 )
| ~ ( apply @ SV65 @ SY169 @ SY170 )
| ( apply @ SV65 @ SY168 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(388,plain,
! [SV13: $i,SV31: $i] :
( ( ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV13 )
= $true )
| ( ( subset @ SV13 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(389,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV31 ) )
= $true )
| ( ( subset @ SV13 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(390,plain,
! [SV32: $i,SV14: $i,SV66: $i] :
( ( ( ~ ( member @ SV66 @ SV14 ) )
= $true )
| ( ( member @ SV66 @ SV32 )
= $true )
| ( ( subset @ SV14 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(391,plain,
! [SV51: $i,SV33: $i,SV3: $i] :
( ( ( SV3 = SV33 )
= $true )
| ( ( SV3 = SV51 )
= $true )
| ( ( member @ SV3 @ ( unordered_pair @ SV33 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(392,plain,
! [SV67: $i,SV3: $i] :
( ( ( ( SV3 != SV67 ) )
= $true )
| ( ( ! [SY153: $i] : ( member @ SV3 @ ( unordered_pair @ SV67 @ SY153 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(393,plain,
! [SV68: $i,SV84: $i,SV3: $i] :
( ( ( SV3 != SV84 )
| ( member @ SV3 @ ( unordered_pair @ SV68 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(394,plain,
! [SV15: $i,SV34: $i,SV57: $i] :
( ( ( member @ SV57 @ SV34 )
= $false )
| ( ( ~ ( member @ SV15 @ SV57 ) )
= $true )
| ( ( member @ SV15 @ ( sum @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(395,plain,
! [SV16: $i,SV35: $i] :
( ( ( ~ ( member @ ( sK13_Y @ SV35 @ SV16 ) @ SV35 ) )
= $false )
| ( ( member @ SV16 @ ( sum @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(396,plain,
! [SV35: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ ( sK13_Y @ SV35 @ SV16 ) ) )
= $false )
| ( ( member @ SV16 @ ( sum @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(397,plain,
! [SV17: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV17 )
= $false )
| ( ( subset @ SV17 @ SV36 )
= $false )
| ( ( equal_set @ SV17 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(398,plain,
! [SV69: $i,SV58: $i] :
( ( ( ~ ( equal_set @ SV58 @ SV69 ) )
= $true )
| ( ( subset @ SV58 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(399,plain,
! [SV70: $i,SV59: $i] :
( ( ( ~ ( equal_set @ SV59 @ SV70 ) )
= $true )
| ( ( subset @ SV70 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(400,plain,
! [SV20: $i] :
( ( ( member @ ( sK11_X @ SV20 ) @ SV20 )
= $true )
| ( ( ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(401,plain,
! [SV20: $i] :
( ( ( ~ ( subset @ ( sK11_X @ SV20 ) @ SV20 ) )
= $true )
| ( ( ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(402,plain,
! [SV60: $i] :
( ( ( member @ SV60 @ on )
= $false )
| ( ( ! [SY141: $i] :
( ~ ( member @ SY141 @ SV60 )
| ( subset @ SY141 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(403,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( set @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(404,plain,
( ( ! [SX0: $i] :
( ~ ( member @ SX0 @ on )
| ( strict_well_order @ member_predicate @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(405,plain,
! [SV21: $i,SV39: $i] :
( ( ( member @ ( sK12_Y @ SV39 @ SV21 ) @ SV39 )
= $true )
| ( ( member @ SV21 @ ( product @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(406,plain,
! [SV39: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ ( sK12_Y @ SV39 @ SV21 ) ) )
= $true )
| ( ( member @ SV21 @ ( product @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(407,plain,
! [SV22: $i,SV40: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV40 ) )
= $true )
| ( ( member @ SV22 @ SV71 )
= $true )
| ( ( member @ SV22 @ ( product @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(408,plain,
! [SV52: $i,SV41: $i,SV4: $i] :
( ( ( member @ SV4 @ SV41 )
= $false )
| ( ( ~ ( member @ SV4 @ SV52 ) )
= $true )
| ( ( member @ SV4 @ ( intersection @ SV41 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(409,plain,
! [SV72: $i,SV4: $i] :
( ( ( ! [SY155: $i] :
~ ( member @ SV4 @ ( intersection @ SV72 @ SY155 ) ) )
= $true )
| ( ( member @ SV4 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(410,plain,
! [SV85: $i,SV73: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ ( intersection @ SV73 @ SV85 ) )
| ( member @ SV4 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(411,plain,
! [SV53: $i,SV42: $i,SV5: $i] :
( ( ( member @ SV5 @ SV42 )
= $true )
| ( ( member @ SV5 @ SV53 )
= $true )
| ( ( member @ SV5 @ ( union @ SV42 @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(412,plain,
! [SV74: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV74 ) )
= $true )
| ( ( ! [SY157: $i] : ( member @ SV5 @ ( union @ SV74 @ SY157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(413,plain,
! [SV75: $i,SV86: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ SV86 )
| ( member @ SV5 @ ( union @ SV75 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(414,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) ) )
= $false )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(415,plain,
! [SV43: $i,SV23: $i] :
( ( ( ~ ! [SY135: $i] :
~ ( least @ SY135 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) ) )
= $false )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(416,plain,
! [SV76: $i,SV61: $i] :
( ( ( ~ ( strict_well_order @ SV61 @ SV76 ) )
= $true )
| ( ( ! [SY159: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SY159 )
| ~ ( subset @ SY159 @ SV76 )
| ( least @ ( sK8_Y @ SY159 @ SV76 @ SV61 ) @ SV61 @ SY159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(417,plain,
! [SV77: $i,SV62: $i] :
( ( ( ~ ( strict_well_order @ SV62 @ SV77 ) )
= $true )
| ( ( strict_order @ SV62 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(418,plain,
! [SV44: $i,SV54: $i,SV6: $i] :
( ( ( member @ SV6 @ SV54 )
= $false )
| ( ( member @ SV6 @ SV44 )
= $true )
| ( ( member @ SV6 @ ( difference @ SV54 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(419,plain,
! [SV78: $i,SV87: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ ( difference @ SV87 @ SV78 ) )
| ( member @ SV6 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(420,plain,
! [SV79: $i,SV6: $i] :
( ( ( ! [SY162: $i] :
~ ( member @ SV6 @ ( difference @ SY162 @ SV79 ) ) )
= $true )
| ( ( ~ ( member @ SV6 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(421,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK7_X @ SV55 @ SV45 @ SV7 ) @ SV45 )
| ~ ~ ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(422,plain,
! [SV80: $i,SV7: $i,SV88: $i] :
( ( ~ ( least @ SV88 @ SV7 @ SV80 )
| ! [SY171: $i] :
( ~ ( member @ SY171 @ SV80 )
| ( SV88 = SY171 )
| ( apply @ SV7 @ SV88 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(423,plain,
! [SV81: $i,SV7: $i,SV89: $i] :
( ( ~ ( least @ SV89 @ SV7 @ SV81 )
| ( member @ SV89 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(424,plain,
! [SV56: $i,SV8: $i,SV63: $i,SV9: $i] :
( ( ( ~ ( apply @ SV9 @ SV63 @ SV8 ) )
= $true )
| ( ( ~ ( member @ SV63 @ SV56 ) )
= $true )
| ( ( member @ SV63 @ ( initial_segment @ SV8 @ SV9 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(425,plain,
! [SV90: $i,SV9: $i,SV8: $i] :
( ( ! [SY172: $i] :
( ~ ( member @ SY172 @ ( initial_segment @ SV8 @ SV9 @ SV90 ) )
| ( apply @ SV9 @ SY172 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(426,plain,
! [SV91: $i,SV9: $i,SV8: $i] :
( ( ! [SY173: $i] :
( ~ ( member @ SY173 @ ( initial_segment @ SV8 @ SV9 @ SV91 ) )
| ( member @ SY173 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(427,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(428,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(429,plain,
! [SV82: $i,SV64: $i] :
( ( ( ~ ( strict_order @ SV64 @ SV82 ) )
= $true )
| ( ( ! [SY166: $i,SY167: $i] :
( ~ ( member @ SY166 @ SV82 )
| ~ ( member @ SY167 @ SV82 )
| ~ ( apply @ SV64 @ SY166 @ SY167 )
| ~ ( apply @ SV64 @ SY167 @ SY166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(430,plain,
! [SV83: $i,SV65: $i] :
( ( ( ~ ( strict_order @ SV65 @ SV83 ) )
= $true )
| ( ( ! [SY168: $i,SY169: $i,SY170: $i] :
( ~ ( member @ SY168 @ SV83 )
| ~ ( member @ SY169 @ SV83 )
| ~ ( member @ SY170 @ SV83 )
| ~ ( apply @ SV65 @ SY168 @ SY169 )
| ~ ( apply @ SV65 @ SY169 @ SY170 )
| ( apply @ SV65 @ SY168 @ SY170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(431,plain,
! [SV13: $i,SV31: $i] :
( ( ( member @ ( sK14_X @ SV31 @ SV13 ) @ SV31 )
= $false )
| ( ( subset @ SV13 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(432,plain,
! [SV32: $i,SV14: $i,SV66: $i] :
( ( ( member @ SV66 @ SV14 )
= $false )
| ( ( member @ SV66 @ SV32 )
= $true )
| ( ( subset @ SV14 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(433,plain,
! [SV67: $i,SV3: $i] :
( ( ( SV3 = SV67 )
= $false )
| ( ( ! [SY153: $i] : ( member @ SV3 @ ( unordered_pair @ SV67 @ SY153 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(434,plain,
! [SV68: $i,SV84: $i,SV3: $i] :
( ( ( ( SV3 != SV84 ) )
= $true )
| ( ( member @ SV3 @ ( unordered_pair @ SV68 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(435,plain,
! [SV34: $i,SV57: $i,SV15: $i] :
( ( ( member @ SV15 @ SV57 )
= $false )
| ( ( member @ SV57 @ SV34 )
= $false )
| ( ( member @ SV15 @ ( sum @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(436,plain,
! [SV16: $i,SV35: $i] :
( ( ( member @ ( sK13_Y @ SV35 @ SV16 ) @ SV35 )
= $true )
| ( ( member @ SV16 @ ( sum @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(437,plain,
! [SV35: $i,SV16: $i] :
( ( ( member @ SV16 @ ( sK13_Y @ SV35 @ SV16 ) )
= $true )
| ( ( member @ SV16 @ ( sum @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(438,plain,
! [SV69: $i,SV58: $i] :
( ( ( equal_set @ SV58 @ SV69 )
= $false )
| ( ( subset @ SV58 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(439,plain,
! [SV70: $i,SV59: $i] :
( ( ( equal_set @ SV59 @ SV70 )
= $false )
| ( ( subset @ SV70 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(440,plain,
! [SV20: $i] :
( ( ( ~ ( set @ SV20 ) )
= $true )
| ( ( ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ ( sK11_X @ SV20 ) @ SV20 )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(441,plain,
! [SV20: $i] :
( ( ( subset @ ( sK11_X @ SV20 ) @ SV20 )
= $false )
| ( ( ~ ( set @ SV20 )
| ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(442,plain,
! [SV60: $i,SV92: $i] :
( ( ( ~ ( member @ SV92 @ SV60 )
| ( subset @ SV92 @ SV60 ) )
= $true )
| ( ( member @ SV60 @ on )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(443,plain,
! [SV93: $i] :
( ( ~ ( member @ SV93 @ on )
| ( set @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(444,plain,
! [SV94: $i] :
( ( ~ ( member @ SV94 @ on )
| ( strict_well_order @ member_predicate @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(445,plain,
! [SV39: $i,SV21: $i] :
( ( ( member @ SV21 @ ( sK12_Y @ SV39 @ SV21 ) )
= $false )
| ( ( member @ SV21 @ ( product @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(446,plain,
! [SV22: $i,SV40: $i,SV71: $i] :
( ( ( member @ SV71 @ SV40 )
= $false )
| ( ( member @ SV22 @ SV71 )
= $true )
| ( ( member @ SV22 @ ( product @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(447,plain,
! [SV41: $i,SV52: $i,SV4: $i] :
( ( ( member @ SV4 @ SV52 )
= $false )
| ( ( member @ SV4 @ SV41 )
= $false )
| ( ( member @ SV4 @ ( intersection @ SV41 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(448,plain,
! [SV95: $i,SV72: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( intersection @ SV72 @ SV95 ) ) )
= $true )
| ( ( member @ SV4 @ SV72 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(449,plain,
! [SV85: $i,SV73: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( intersection @ SV73 @ SV85 ) ) )
= $true )
| ( ( member @ SV4 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(450,plain,
! [SV74: $i,SV5: $i] :
( ( ( member @ SV5 @ SV74 )
= $false )
| ( ( ! [SY157: $i] : ( member @ SV5 @ ( union @ SV74 @ SY157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(451,plain,
! [SV75: $i,SV86: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV86 ) )
= $true )
| ( ( member @ SV5 @ ( union @ SV75 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(452,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) ) )
= $true )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(453,plain,
! [SV43: $i,SV23: $i] :
( ( ( ! [SY135: $i] :
~ ( least @ SY135 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) ) )
= $true )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(454,plain,
! [SV76: $i,SV61: $i] :
( ( ( strict_well_order @ SV61 @ SV76 )
= $false )
| ( ( ! [SY159: $i] :
( ! [SX3: $i] :
~ ( member @ SX3 @ SY159 )
| ~ ( subset @ SY159 @ SV76 )
| ( least @ ( sK8_Y @ SY159 @ SV76 @ SV61 ) @ SV61 @ SY159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(455,plain,
! [SV77: $i,SV62: $i] :
( ( ( strict_well_order @ SV62 @ SV77 )
= $false )
| ( ( strict_order @ SV62 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(456,plain,
! [SV78: $i,SV87: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ ( difference @ SV87 @ SV78 ) ) )
= $true )
| ( ( member @ SV6 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(457,plain,
! [SV79: $i,SV96: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ ( difference @ SV96 @ SV79 ) ) )
= $true )
| ( ( ~ ( member @ SV6 @ SV79 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(458,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ( member @ ( sK7_X @ SV55 @ SV45 @ SV7 ) @ SV45 ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(459,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(460,plain,
! [SV80: $i,SV7: $i,SV88: $i] :
( ( ( ~ ( least @ SV88 @ SV7 @ SV80 ) )
= $true )
| ( ( ! [SY171: $i] :
( ~ ( member @ SY171 @ SV80 )
| ( SV88 = SY171 )
| ( apply @ SV7 @ SV88 @ SY171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(461,plain,
! [SV81: $i,SV7: $i,SV89: $i] :
( ( ( ~ ( least @ SV89 @ SV7 @ SV81 ) )
= $true )
| ( ( member @ SV89 @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(462,plain,
! [SV56: $i,SV8: $i,SV63: $i,SV9: $i] :
( ( ( apply @ SV9 @ SV63 @ SV8 )
= $false )
| ( ( ~ ( member @ SV63 @ SV56 ) )
= $true )
| ( ( member @ SV63 @ ( initial_segment @ SV8 @ SV9 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(463,plain,
! [SV90: $i,SV9: $i,SV8: $i,SV97: $i] :
( ( ~ ( member @ SV97 @ ( initial_segment @ SV8 @ SV9 @ SV90 ) )
| ( apply @ SV9 @ SV97 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(464,plain,
! [SV91: $i,SV9: $i,SV8: $i,SV98: $i] :
( ( ~ ( member @ SV98 @ ( initial_segment @ SV8 @ SV9 @ SV91 ) )
| ( member @ SV98 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(465,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(466,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(467,plain,
! [SV82: $i,SV64: $i] :
( ( ( strict_order @ SV64 @ SV82 )
= $false )
| ( ( ! [SY166: $i,SY167: $i] :
( ~ ( member @ SY166 @ SV82 )
| ~ ( member @ SY167 @ SV82 )
| ~ ( apply @ SV64 @ SY166 @ SY167 )
| ~ ( apply @ SV64 @ SY167 @ SY166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(468,plain,
! [SV83: $i,SV65: $i] :
( ( ( strict_order @ SV65 @ SV83 )
= $false )
| ( ( ! [SY168: $i,SY169: $i,SY170: $i] :
( ~ ( member @ SY168 @ SV83 )
| ~ ( member @ SY169 @ SV83 )
| ~ ( member @ SY170 @ SV83 )
| ~ ( apply @ SV65 @ SY168 @ SY169 )
| ~ ( apply @ SV65 @ SY169 @ SY170 )
| ( apply @ SV65 @ SY168 @ SY170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(469,plain,
! [SV99: $i,SV67: $i,SV3: $i] :
( ( ( member @ SV3 @ ( unordered_pair @ SV67 @ SV99 ) )
= $true )
| ( ( SV3 = SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(470,plain,
! [SV68: $i,SV84: $i,SV3: $i] :
( ( ( SV3 = SV84 )
= $false )
| ( ( member @ SV3 @ ( unordered_pair @ SV68 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(471,plain,
! [SV20: $i] :
( ( ( set @ SV20 )
= $false )
| ( ( ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( member @ ( sK11_X @ SV20 ) @ SV20 )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(472,plain,
! [SV20: $i] :
( ( ( ~ ( set @ SV20 ) )
= $true )
| ( ( ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( subset @ ( sK11_X @ SV20 ) @ SV20 )
= $false )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(473,plain,
! [SV60: $i,SV92: $i] :
( ( ( ~ ( member @ SV92 @ SV60 ) )
= $true )
| ( ( subset @ SV92 @ SV60 )
= $true )
| ( ( member @ SV60 @ on )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(474,plain,
! [SV93: $i] :
( ( ( ~ ( member @ SV93 @ on ) )
= $true )
| ( ( set @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(475,plain,
! [SV94: $i] :
( ( ( ~ ( member @ SV94 @ on ) )
= $true )
| ( ( strict_well_order @ member_predicate @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(476,plain,
! [SV95: $i,SV72: $i,SV4: $i] :
( ( ( member @ SV4 @ ( intersection @ SV72 @ SV95 ) )
= $false )
| ( ( member @ SV4 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(477,plain,
! [SV85: $i,SV73: $i,SV4: $i] :
( ( ( member @ SV4 @ ( intersection @ SV73 @ SV85 ) )
= $false )
| ( ( member @ SV4 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(478,plain,
! [SV100: $i,SV74: $i,SV5: $i] :
( ( ( member @ SV5 @ ( union @ SV74 @ SV100 ) )
= $true )
| ( ( member @ SV5 @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(479,plain,
! [SV75: $i,SV86: $i,SV5: $i] :
( ( ( member @ SV5 @ SV86 )
= $false )
| ( ( member @ SV5 @ ( union @ SV75 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(480,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
| ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) )
= $false )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(481,plain,
! [SV43: $i,SV23: $i,SV101: $i] :
( ( ( ~ ( least @ SV101 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) ) )
= $true )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(482,plain,
! [SV61: $i,SV76: $i,SV102: $i] :
( ( ( ! [SY174: $i] :
~ ( member @ SY174 @ SV102 )
| ~ ( subset @ SV102 @ SV76 )
| ( least @ ( sK8_Y @ SV102 @ SV76 @ SV61 ) @ SV61 @ SV102 ) )
= $true )
| ( ( strict_well_order @ SV61 @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(483,plain,
! [SV78: $i,SV87: $i,SV6: $i] :
( ( ( member @ SV6 @ ( difference @ SV87 @ SV78 ) )
= $false )
| ( ( member @ SV6 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(484,plain,
! [SV79: $i,SV96: $i,SV6: $i] :
( ( ( member @ SV6 @ ( difference @ SV96 @ SV79 ) )
= $false )
| ( ( ~ ( member @ SV6 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(485,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( member @ ( sK7_X @ SV55 @ SV45 @ SV7 ) @ SV45 )
= $true )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(486,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) ) )
= $true )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(487,plain,
! [SV80: $i,SV7: $i,SV88: $i] :
( ( ( least @ SV88 @ SV7 @ SV80 )
= $false )
| ( ( ! [SY171: $i] :
( ~ ( member @ SY171 @ SV80 )
| ( SV88 = SY171 )
| ( apply @ SV7 @ SV88 @ SY171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(488,plain,
! [SV81: $i,SV7: $i,SV89: $i] :
( ( ( least @ SV89 @ SV7 @ SV81 )
= $false )
| ( ( member @ SV89 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(489,plain,
! [SV8: $i,SV9: $i,SV56: $i,SV63: $i] :
( ( ( member @ SV63 @ SV56 )
= $false )
| ( ( apply @ SV9 @ SV63 @ SV8 )
= $false )
| ( ( member @ SV63 @ ( initial_segment @ SV8 @ SV9 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(490,plain,
! [SV90: $i,SV9: $i,SV8: $i,SV97: $i] :
( ( ( ~ ( member @ SV97 @ ( initial_segment @ SV8 @ SV9 @ SV90 ) ) )
= $true )
| ( ( apply @ SV9 @ SV97 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(491,plain,
! [SV91: $i,SV9: $i,SV8: $i,SV98: $i] :
( ( ( ~ ( member @ SV98 @ ( initial_segment @ SV8 @ SV9 @ SV91 ) ) )
= $true )
| ( ( member @ SV98 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(492,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(493,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(494,plain,
! [SV64: $i,SV82: $i,SV103: $i] :
( ( ( ! [SY175: $i] :
( ~ ( member @ SV103 @ SV82 )
| ~ ( member @ SY175 @ SV82 )
| ~ ( apply @ SV64 @ SV103 @ SY175 )
| ~ ( apply @ SV64 @ SY175 @ SV103 ) ) )
= $true )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(495,plain,
! [SV65: $i,SV83: $i,SV104: $i] :
( ( ( ! [SY176: $i,SY177: $i] :
( ~ ( member @ SV104 @ SV83 )
| ~ ( member @ SY176 @ SV83 )
| ~ ( member @ SY177 @ SV83 )
| ~ ( apply @ SV65 @ SV104 @ SY176 )
| ~ ( apply @ SV65 @ SY176 @ SY177 )
| ( apply @ SV65 @ SV104 @ SY177 ) ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(496,plain,
! [SV20: $i] :
( ( ( strict_well_order @ member_predicate @ SV20 )
= $false )
| ( ( set @ SV20 )
= $false )
| ( ( member @ ( sK11_X @ SV20 ) @ SV20 )
= $true )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(497,plain,
! [SV20: $i] :
( ( ( set @ SV20 )
= $false )
| ( ( ~ ( strict_well_order @ member_predicate @ SV20 ) )
= $true )
| ( ( subset @ ( sK11_X @ SV20 ) @ SV20 )
= $false )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(498,plain,
! [SV60: $i,SV92: $i] :
( ( ( member @ SV92 @ SV60 )
= $false )
| ( ( subset @ SV92 @ SV60 )
= $true )
| ( ( member @ SV60 @ on )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(499,plain,
! [SV93: $i] :
( ( ( member @ SV93 @ on )
= $false )
| ( ( set @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(500,plain,
! [SV94: $i] :
( ( ( member @ SV94 @ on )
= $false )
| ( ( strict_well_order @ member_predicate @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(501,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) ) )
= $false )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(502,plain,
! [SV23: $i,SV43: $i] :
( ( ( ~ ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 ) )
= $false )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(503,plain,
! [SV43: $i,SV23: $i,SV101: $i] :
( ( ( least @ SV101 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) )
= $false )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(504,plain,
! [SV61: $i,SV76: $i,SV102: $i] :
( ( ( ! [SY174: $i] :
~ ( member @ SY174 @ SV102 )
| ~ ( subset @ SV102 @ SV76 ) )
= $true )
| ( ( least @ ( sK8_Y @ SV102 @ SV76 @ SV61 ) @ SV61 @ SV102 )
= $true )
| ( ( strict_well_order @ SV61 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(505,plain,
! [SV96: $i,SV79: $i,SV6: $i] :
( ( ( member @ SV6 @ SV79 )
= $false )
| ( ( member @ SV6 @ ( difference @ SV96 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(506,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( member @ SV55 @ SV45 )
= $false )
| ( ( member @ ( sK7_X @ SV55 @ SV45 @ SV7 ) @ SV45 )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(507,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
| ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(508,plain,
! [SV7: $i,SV88: $i,SV80: $i,SV105: $i] :
( ( ( ~ ( member @ SV105 @ SV80 )
| ( SV88 = SV105 )
| ( apply @ SV7 @ SV88 @ SV105 ) )
= $true )
| ( ( least @ SV88 @ SV7 @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(509,plain,
! [SV90: $i,SV9: $i,SV8: $i,SV97: $i] :
( ( ( member @ SV97 @ ( initial_segment @ SV8 @ SV9 @ SV90 ) )
= $false )
| ( ( apply @ SV9 @ SV97 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(510,plain,
! [SV91: $i,SV9: $i,SV8: $i,SV98: $i] :
( ( ( member @ SV98 @ ( initial_segment @ SV8 @ SV9 @ SV91 ) )
= $false )
| ( ( member @ SV98 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(511,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(512,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(513,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(514,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(515,plain,
! [SV64: $i,SV106: $i,SV82: $i,SV103: $i] :
( ( ( ~ ( member @ SV103 @ SV82 )
| ~ ( member @ SV106 @ SV82 )
| ~ ( apply @ SV64 @ SV103 @ SV106 )
| ~ ( apply @ SV64 @ SV106 @ SV103 ) )
= $true )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(516,plain,
! [SV65: $i,SV107: $i,SV83: $i,SV104: $i] :
( ( ( ! [SY178: $i] :
( ~ ( member @ SV104 @ SV83 )
| ~ ( member @ SV107 @ SV83 )
| ~ ( member @ SY178 @ SV83 )
| ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SY178 )
| ( apply @ SV65 @ SV104 @ SY178 ) ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(517,plain,
! [SV20: $i] :
( ( ( strict_well_order @ member_predicate @ SV20 )
= $false )
| ( ( set @ SV20 )
= $false )
| ( ( subset @ ( sK11_X @ SV20 ) @ SV20 )
= $false )
| ( ( member @ SV20 @ on )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(518,plain,
! [SV23: $i,SV43: $i] :
( ( ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
= $true )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(519,plain,
! [SV23: $i,SV43: $i] :
( ( ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 )
= $true )
| ( ( ~ ( strict_order @ SV23 @ SV43 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(520,plain,
! [SV101: $i,SV43: $i,SV23: $i] :
( ( ( strict_order @ SV23 @ SV43 )
= $false )
| ( ( least @ SV101 @ SV23 @ ( sK9_A @ SV43 @ SV23 ) )
= $false )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(521,plain,
! [SV61: $i,SV76: $i,SV102: $i] :
( ( ( ! [SY174: $i] :
~ ( member @ SY174 @ SV102 ) )
= $true )
| ( ( ~ ( subset @ SV102 @ SV76 ) )
= $true )
| ( ( least @ ( sK8_Y @ SV102 @ SV76 @ SV61 ) @ SV61 @ SV102 )
= $true )
| ( ( strict_well_order @ SV61 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(522,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ~ ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(523,plain,
! [SV45: $i,SV55: $i,SV7: $i] :
( ( ( ~ ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(524,plain,
! [SV7: $i,SV88: $i,SV80: $i,SV105: $i] :
( ( ( ~ ( member @ SV105 @ SV80 ) )
= $true )
| ( ( ( SV88 = SV105 )
| ( apply @ SV7 @ SV88 @ SV105 ) )
= $true )
| ( ( least @ SV88 @ SV7 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(525,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(526,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(527,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(528,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(529,plain,
! [SV64: $i,SV106: $i,SV82: $i,SV103: $i] :
( ( ( ~ ( member @ SV103 @ SV82 )
| ~ ( member @ SV106 @ SV82 ) )
= $true )
| ( ( ~ ( apply @ SV64 @ SV103 @ SV106 )
| ~ ( apply @ SV64 @ SV106 @ SV103 ) )
= $true )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(530,plain,
! [SV65: $i,SV108: $i,SV107: $i,SV83: $i,SV104: $i] :
( ( ( ~ ( member @ SV104 @ SV83 )
| ~ ( member @ SV107 @ SV83 )
| ~ ( member @ SV108 @ SV83 )
| ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 )
| ( apply @ SV65 @ SV104 @ SV108 ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(531,plain,
! [SV43: $i,SV23: $i] :
( ( ( strict_order @ SV23 @ SV43 )
= $false )
| ( ( member @ ( sK10_SY61 @ SV43 @ SV23 ) @ ( sK9_A @ SV43 @ SV23 ) )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(532,plain,
! [SV43: $i,SV23: $i] :
( ( ( strict_order @ SV23 @ SV43 )
= $false )
| ( ( subset @ ( sK9_A @ SV43 @ SV23 ) @ SV43 )
= $true )
| ( ( strict_well_order @ SV23 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(533,plain,
! [SV61: $i,SV76: $i,SV102: $i,SV109: $i] :
( ( ( ~ ( member @ SV109 @ SV102 ) )
= $true )
| ( ( ~ ( subset @ SV102 @ SV76 ) )
= $true )
| ( ( least @ ( sK8_Y @ SV102 @ SV76 @ SV61 ) @ SV61 @ SV102 )
= $true )
| ( ( strict_well_order @ SV61 @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(534,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( ( SV55
!= ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
= $true )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(535,plain,
! [SV45: $i,SV55: $i,SV7: $i] :
( ( ( ~ ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) ) )
= $true )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(536,plain,
! [SV7: $i,SV88: $i,SV80: $i,SV105: $i] :
( ( ( member @ SV105 @ SV80 )
= $false )
| ( ( ( SV88 = SV105 )
| ( apply @ SV7 @ SV88 @ SV105 ) )
= $true )
| ( ( least @ SV88 @ SV7 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(537,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(538,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(539,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(540,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(541,plain,
! [SV64: $i,SV106: $i,SV82: $i,SV103: $i] :
( ( ( ~ ( member @ SV103 @ SV82 ) )
= $true )
| ( ( ~ ( member @ SV106 @ SV82 ) )
= $true )
| ( ( ~ ( apply @ SV64 @ SV103 @ SV106 )
| ~ ( apply @ SV64 @ SV106 @ SV103 ) )
= $true )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(542,plain,
! [SV65: $i,SV108: $i,SV107: $i,SV83: $i,SV104: $i] :
( ( ( ~ ( member @ SV104 @ SV83 )
| ~ ( member @ SV107 @ SV83 )
| ~ ( member @ SV108 @ SV83 ) )
= $true )
| ( ( ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 )
| ( apply @ SV65 @ SV104 @ SV108 ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(543,plain,
! [SV61: $i,SV76: $i,SV102: $i,SV109: $i] :
( ( ( member @ SV109 @ SV102 )
= $false )
| ( ( ~ ( subset @ SV102 @ SV76 ) )
= $true )
| ( ( least @ ( sK8_Y @ SV102 @ SV76 @ SV61 ) @ SV61 @ SV102 )
= $true )
| ( ( strict_well_order @ SV61 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(544,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( SV55
= ( sK7_X @ SV55 @ SV45 @ SV7 ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(545,plain,
! [SV45: $i,SV55: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) )
= $false )
| ( ( ~ ( member @ SV55 @ SV45 ) )
= $true )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(546,plain,
! [SV80: $i,SV7: $i,SV105: $i,SV88: $i] :
( ( ( SV88 = SV105 )
= $true )
| ( ( apply @ SV7 @ SV88 @ SV105 )
= $true )
| ( ( member @ SV105 @ SV80 )
= $false )
| ( ( least @ SV88 @ SV7 @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(547,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(548,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(549,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(550,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(551,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(552,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(553,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(554,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(555,plain,
! [SV64: $i,SV106: $i,SV82: $i,SV103: $i] :
( ( ( member @ SV103 @ SV82 )
= $false )
| ( ( ~ ( member @ SV106 @ SV82 ) )
= $true )
| ( ( ~ ( apply @ SV64 @ SV103 @ SV106 )
| ~ ( apply @ SV64 @ SV106 @ SV103 ) )
= $true )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(556,plain,
! [SV65: $i,SV108: $i,SV107: $i,SV83: $i,SV104: $i] :
( ( ( ~ ( member @ SV104 @ SV83 )
| ~ ( member @ SV107 @ SV83 ) )
= $true )
| ( ( ~ ( member @ SV108 @ SV83 ) )
= $true )
| ( ( ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 )
| ( apply @ SV65 @ SV104 @ SV108 ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(557,plain,
! [SV61: $i,SV109: $i,SV76: $i,SV102: $i] :
( ( ( subset @ SV102 @ SV76 )
= $false )
| ( ( member @ SV109 @ SV102 )
= $false )
| ( ( least @ ( sK8_Y @ SV102 @ SV76 @ SV61 ) @ SV61 @ SV102 )
= $true )
| ( ( strict_well_order @ SV61 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(558,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( member @ SV55 @ SV45 )
= $false )
| ( ( SV55
= ( sK7_X @ SV55 @ SV45 @ SV7 ) )
= $false )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(559,plain,
! [SV7: $i,SV45: $i,SV55: $i] :
( ( ( member @ SV55 @ SV45 )
= $false )
| ( ( apply @ SV7 @ SV55 @ ( sK7_X @ SV55 @ SV45 @ SV7 ) )
= $false )
| ( ( least @ SV55 @ SV7 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(560,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(561,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(562,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(563,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(564,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(565,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(566,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(567,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(568,plain,
! [SV64: $i,SV103: $i,SV82: $i,SV106: $i] :
( ( ( member @ SV106 @ SV82 )
= $false )
| ( ( member @ SV103 @ SV82 )
= $false )
| ( ( ~ ( apply @ SV64 @ SV103 @ SV106 )
| ~ ( apply @ SV64 @ SV106 @ SV103 ) )
= $true )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(569,plain,
! [SV65: $i,SV108: $i,SV107: $i,SV83: $i,SV104: $i] :
( ( ( ~ ( member @ SV104 @ SV83 ) )
= $true )
| ( ( ~ ( member @ SV107 @ SV83 ) )
= $true )
| ( ( ~ ( member @ SV108 @ SV83 ) )
= $true )
| ( ( ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 )
| ( apply @ SV65 @ SV104 @ SV108 ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(570,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(571,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(572,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(573,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(574,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(575,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(576,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
| ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(577,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
| ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(578,plain,
! [SV82: $i,SV106: $i,SV103: $i,SV64: $i] :
( ( ( ~ ( apply @ SV64 @ SV103 @ SV106 ) )
= $true )
| ( ( ~ ( apply @ SV64 @ SV106 @ SV103 ) )
= $true )
| ( ( member @ SV103 @ SV82 )
= $false )
| ( ( member @ SV106 @ SV82 )
= $false )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(579,plain,
! [SV65: $i,SV108: $i,SV107: $i,SV83: $i,SV104: $i] :
( ( ( member @ SV104 @ SV83 )
= $false )
| ( ( ~ ( member @ SV107 @ SV83 ) )
= $true )
| ( ( ~ ( member @ SV108 @ SV83 ) )
= $true )
| ( ( ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 )
| ( apply @ SV65 @ SV104 @ SV108 ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(580,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(581,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(582,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(583,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(584,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(585,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(586,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(587,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(588,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(589,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(590,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(591,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(592,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(593,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(594,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(595,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(596,plain,
! [SV82: $i,SV106: $i,SV103: $i,SV64: $i] :
( ( ( apply @ SV64 @ SV103 @ SV106 )
= $false )
| ( ( ~ ( apply @ SV64 @ SV106 @ SV103 ) )
= $true )
| ( ( member @ SV103 @ SV82 )
= $false )
| ( ( member @ SV106 @ SV82 )
= $false )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(597,plain,
! [SV65: $i,SV108: $i,SV104: $i,SV83: $i,SV107: $i] :
( ( ( member @ SV107 @ SV83 )
= $false )
| ( ( member @ SV104 @ SV83 )
= $false )
| ( ( ~ ( member @ SV108 @ SV83 ) )
= $true )
| ( ( ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 )
| ( apply @ SV65 @ SV104 @ SV108 ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(598,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(599,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(600,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(601,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(602,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(603,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(604,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(605,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(606,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(607,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(608,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(609,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(610,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(611,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK4_SY59 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(612,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(613,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(614,plain,
! [SV82: $i,SV103: $i,SV106: $i,SV64: $i] :
( ( ( apply @ SV64 @ SV106 @ SV103 )
= $false )
| ( ( apply @ SV64 @ SV103 @ SV106 )
= $false )
| ( ( member @ SV103 @ SV82 )
= $false )
| ( ( member @ SV106 @ SV82 )
= $false )
| ( ( strict_order @ SV64 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(615,plain,
! [SV65: $i,SV107: $i,SV104: $i,SV83: $i,SV108: $i] :
( ( ( member @ SV108 @ SV83 )
= $false )
| ( ( member @ SV104 @ SV83 )
= $false )
| ( ( member @ SV107 @ SV83 )
= $false )
| ( ( ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 )
| ( apply @ SV65 @ SV104 @ SV108 ) )
= $true )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(616,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(617,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(618,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(619,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(620,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(621,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(622,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(623,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(624,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(625,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
| ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(626,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
| ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(627,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(628,plain,
! [SV83: $i,SV108: $i,SV107: $i,SV104: $i,SV65: $i] :
( ( ( ~ ( apply @ SV65 @ SV104 @ SV107 )
| ~ ( apply @ SV65 @ SV107 @ SV108 ) )
= $true )
| ( ( apply @ SV65 @ SV104 @ SV108 )
= $true )
| ( ( member @ SV107 @ SV83 )
= $false )
| ( ( member @ SV104 @ SV83 )
= $false )
| ( ( member @ SV108 @ SV83 )
= $false )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(629,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(630,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(631,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(632,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[617]) ).
thf(633,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(634,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(635,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(636,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(637,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[622]) ).
thf(638,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[622]) ).
thf(639,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(640,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(641,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(642,plain,
! [SV26: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[625]) ).
thf(643,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(644,plain,
! [SV48: $i,SV26: $i] :
( ( ( ~ ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) ) )
= $false )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(645,plain,
! [SV83: $i,SV108: $i,SV107: $i,SV104: $i,SV65: $i] :
( ( ( ~ ( apply @ SV65 @ SV104 @ SV107 ) )
= $true )
| ( ( ~ ( apply @ SV65 @ SV107 @ SV108 ) )
= $true )
| ( ( apply @ SV65 @ SV104 @ SV108 )
= $true )
| ( ( member @ SV107 @ SV83 )
= $false )
| ( ( member @ SV104 @ SV83 )
= $false )
| ( ( member @ SV108 @ SV83 )
= $false )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(646,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(647,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(648,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(649,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $true )
| ( ( member @ ( sK5_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(650,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(651,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(652,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(653,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $true )
| ( ( member @ ( sK6_SY60 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(654,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(655,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(656,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[639]) ).
thf(657,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $true )
| ( ( apply @ SV26 @ ( sK5_X @ SV48 @ SV26 ) @ ( sK6_SY60 @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(658,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK2_X @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(659,plain,
! [SV26: $i,SV48: $i] :
( ( ( member @ ( sK3_SY57 @ SV48 @ SV26 ) @ SV48 )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(660,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK2_X @ SV48 @ SV26 ) @ ( sK3_SY57 @ SV48 @ SV26 ) )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(661,plain,
! [SV48: $i,SV26: $i] :
( ( ( apply @ SV26 @ ( sK3_SY57 @ SV48 @ SV26 ) @ ( sK4_SY59 @ SV48 @ SV26 ) )
= $true )
| ( ( apply @ SV26 @ ( sK6_SY60 @ SV48 @ SV26 ) @ ( sK5_X @ SV48 @ SV26 ) )
= $true )
| ( ( strict_order @ SV26 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(662,plain,
! [SV83: $i,SV108: $i,SV107: $i,SV104: $i,SV65: $i] :
( ( ( apply @ SV65 @ SV104 @ SV107 )
= $false )
| ( ( ~ ( apply @ SV65 @ SV107 @ SV108 ) )
= $true )
| ( ( apply @ SV65 @ SV104 @ SV108 )
= $true )
| ( ( member @ SV107 @ SV83 )
= $false )
| ( ( member @ SV104 @ SV83 )
= $false )
| ( ( member @ SV108 @ SV83 )
= $false )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(663,plain,
! [SV83: $i,SV104: $i,SV108: $i,SV107: $i,SV65: $i] :
( ( ( apply @ SV65 @ SV107 @ SV108 )
= $false )
| ( ( apply @ SV65 @ SV104 @ SV107 )
= $false )
| ( ( apply @ SV65 @ SV104 @ SV108 )
= $true )
| ( ( member @ SV107 @ SV83 )
= $false )
| ( ( member @ SV104 @ SV83 )
= $false )
| ( ( member @ SV108 @ SV83 )
= $false )
| ( ( strict_order @ SV65 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(664,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[83,663,661,660,659,658,657,656,655,654,653,652,651,650,649,648,647,646,627,624,621,618,614,611,607,603,599,559,558,557,546,532,531,520,517,510,509,506,505,500,499,498,496,489,488,483,479,478,477,476,470,469,455,447,446,445,439,438,437,436,435,432,431,418,411,405,397,391,388,347,346,342,341,317,316,305,304,260,122,104]) ).
thf(665,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 16:30:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36
% 0.12/0.36 No.of.Axioms: 19
% 0.12/0.36
% 0.12/0.36 Length.of.Defs: 0
% 0.12/0.36
% 0.12/0.36 Contains.Choice.Funs: false
% 0.12/0.37 .
% 0.12/0.38 (rf:0,axioms:19,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:0,translation:fof_full).............................................
% 0.43/0.67
% 0.43/0.67 ********************************
% 0.43/0.67 * All subproblems solved! *
% 0.43/0.67 ********************************
% 0.43/0.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:664,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.61/0.82
% 0.61/0.82 %**** Beginning of derivation protocol ****
% 0.61/0.82 % SZS output start CNFRefutation
% See solution above
% 0.61/0.82
% 0.61/0.82 %**** End of derivation protocol ****
% 0.61/0.82 %**** no. of clauses in derivation: 665 ****
% 0.61/0.82 %**** clause counter: 664 ****
% 0.61/0.82
% 0.61/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:664,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------