%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:41:07 AM UTC 2026
% Result : Theorem 1.26s 0.55s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 17
% Syntax : Number of formulae : 483 ( 167 unt; 0 typ; 0 def)
% Number of atoms : 4064 (1087 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 9729 (2139 ~;1504 |; 33 &;5983 @)
% ( 42 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 6 con; 0-3 aty)
% Number of variables : 1501 ( 0 ^;1498 !; 3 ?;1501 :)
% 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_SY107,type,
sK10_SY107: $i > $i > $i ).
thf(tp_sK11_SY107,type,
sK11_SY107: $i > $i > $i ).
thf(tp_sK12_SY121,type,
sK12_SY121: $i > $i > $i ).
thf(tp_sK13_SY123,type,
sK13_SY123: $i > $i > $i ).
thf(tp_sK14_SY125,type,
sK14_SY125: $i > $i > $i ).
thf(tp_sK15_SY127,type,
sK15_SY127: $i > $i > $i ).
thf(tp_sK16_SY129,type,
sK16_SY129: $i > $i > $i ).
thf(tp_sK17_SY130,type,
sK17_SY130: $i > $i > $i ).
thf(tp_sK18_SY131,type,
sK18_SY131: $i > $i > $i ).
thf(tp_sK19_SY132,type,
sK19_SY132: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY89,type,
sK2_SY89: $i > $i > $i ).
thf(tp_sK3_SY111,type,
sK3_SY111: $i > $i > $i ).
thf(tp_sK4_SY90,type,
sK4_SY90: $i > $i > $i ).
thf(tp_sK5_SY105,type,
sK5_SY105: $i > $i > $i ).
thf(tp_sK6_SY119,type,
sK6_SY119: $i > $i > $i ).
thf(tp_sK7_SY115,type,
sK7_SY115: $i > $i > $i > $i ).
thf(tp_sK8_SY107,type,
sK8_SY107: $i > $i > $i ).
thf(tp_sK9_SY107,type,
sK9_SY107: $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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',initial_segment) ).
thf(3,axiom,
! [X: $i] :
( ( set @ X )
=> ! [Y: $i] :
( ( member @ Y @ X )
=> ( set @ Y ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',strict_order) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( apply @ member_predicate @ X @ Y )
<=> ( member @ X @ Y ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',least) ).
thf(9,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(12,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(14,axiom,
! [X: $i] :
~ ( member @ X @ empty_set ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(17,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(20,conjecture,
! [A: $i] :
( ( member @ A @ on )
=> ( member @ A @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/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,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(30,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(31,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(32,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(33,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(34,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(35,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(36,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(37,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(39,plain,
( ( ( member @ sK1_A @ on )
=> ( member @ sK1_A @ ( suc @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(40,plain,
( ( member @ sK1_A @ on )
= $true ),
inference(standard_cnf,[status(thm)],[39]) ).
thf(41,plain,
( ( member @ sK1_A @ ( suc @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[39]) ).
thf(42,plain,
( ( ~ ( member @ sK1_A @ ( suc @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(44,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(45,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(46,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(47,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(48,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(49,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(50,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(51,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(52,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(53,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(copy,[status(thm)],[28]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ( apply @ member_predicate @ X @ Y )
<=> ( member @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(55,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(copy,[status(thm)],[26]) ).
thf(56,plain,
( ( ! [X: $i] :
( ( set @ X )
=> ! [Y: $i] :
( ( member @ Y @ X )
=> ( set @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(57,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(copy,[status(thm)],[24]) ).
thf(58,plain,
( ( ! [A: $i,X: $i] :
( ( member @ X @ ( suc @ A ) )
<=> ( member @ X @ ( union @ A @ ( singleton @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(59,plain,
( ( member @ sK1_A @ on )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( ~ ( member @ sK1_A @ ( suc @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(63,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ( ~ ( ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( member @ SX3 @ ( initial_segment @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX3 @ SX2 )
| ~ ( apply @ SX1 @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX3 @ SX2 )
| ~ ( apply @ SX1 @ SX3 @ SX0 ) )
| ( member @ SX3 @ ( initial_segment @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( least @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( member @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ( SX2 = SX3 )
| ( apply @ SX0 @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ( SX2 = SX3 )
| ( apply @ SX0 @ SX2 @ SX3 ) ) )
| ( least @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( apply @ member_predicate @ SX0 @ SX1 )
| ( member @ SX0 @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ SX1 )
| ( apply @ member_predicate @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX1 @ ( suc @ SX0 ) )
| ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) ) )
| ~ ( ~ ( member @ SX1 @ ( union @ SX0 @ ( singleton @ SX0 ) ) )
| ( member @ SX1 @ ( suc @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(71,plain,
( ( ! [SX0: $i] :
( ~ ( set @ SX0 )
| ! [SX1: $i] :
( ~ ( member @ SX1 @ SX0 )
| ( set @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(72,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 ) ) )
| ~ ! [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 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX3 @ SX1 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX2 @ SX3 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ! [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 ) ) )
| ( strict_order @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ~ ( ~ ( ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(76,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(77,plain,
( ( member @ sK1_A @ ( suc @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(78,plain,
! [SV2: $i] :
( ( ! [SY48: $i] :
~ ( ~ ( ~ ( subset @ SV2 @ SY48 )
| ! [SY49: $i] :
( ~ ( member @ SY49 @ SV2 )
| ( member @ SY49 @ SY48 ) ) )
| ~ ( ~ ! [SY50: $i] :
( ~ ( member @ SY50 @ SV2 )
| ( member @ SY50 @ SY48 ) )
| ( subset @ SV2 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(79,plain,
! [SV3: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ~ ( member @ SV3 @ ( sum @ SY51 ) )
| ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SY52 @ SY51 )
| ~ ( member @ SV3 @ SY52 ) ) )
| ~ ( ~ ~ ! [SY53: $i] :
~ ~ ( ~ ( member @ SY53 @ SY51 )
| ~ ( member @ SV3 @ SY53 ) )
| ( member @ SV3 @ ( sum @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(80,plain,
! [SV4: $i] :
( ( ! [SY54: $i,SY55: $i] :
~ ( ~ ( ~ ( member @ SV4 @ ( union @ SY54 @ SY55 ) )
| ( member @ SV4 @ SY54 )
| ( member @ SV4 @ SY55 ) )
| ~ ( ~ ( ( member @ SV4 @ SY54 )
| ( member @ SV4 @ SY55 ) )
| ( member @ SV4 @ ( union @ SY54 @ SY55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(81,plain,
! [SV5: $i] :
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
~ ( ~ ( ~ ( member @ SY58 @ ( initial_segment @ SV5 @ SY56 @ SY57 ) )
| ~ ( ~ ( member @ SY58 @ SY57 )
| ~ ( apply @ SY56 @ SY58 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY58 @ SY57 )
| ~ ( apply @ SY56 @ SY58 @ SV5 ) )
| ( member @ SY58 @ ( initial_segment @ SV5 @ SY56 @ SY57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(82,plain,
! [SV6: $i] :
( ( ! [SY59: $i] :
~ ( ~ ( ~ ( member @ SV6 @ ( power_set @ SY59 ) )
| ( subset @ SV6 @ SY59 ) )
| ~ ( ~ ( subset @ SV6 @ SY59 )
| ( member @ SV6 @ ( power_set @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(83,plain,
! [SV7: $i] :
( ( ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( least @ SY61 @ SV7 @ SY60 )
| ~ ( ~ ( member @ SY61 @ SY60 )
| ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SY60 )
| ( SY61 = SY62 )
| ( apply @ SV7 @ SY61 @ SY62 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY61 @ SY60 )
| ~ ! [SY63: $i] :
( ~ ( member @ SY63 @ SY60 )
| ( SY61 = SY63 )
| ( apply @ SV7 @ SY61 @ SY63 ) ) )
| ( least @ SY61 @ SV7 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(84,plain,
! [SV8: $i] :
( ( ! [SY64: $i] :
~ ( ~ ( ~ ( apply @ member_predicate @ SV8 @ SY64 )
| ( member @ SV8 @ SY64 ) )
| ~ ( ~ ( member @ SV8 @ SY64 )
| ( apply @ member_predicate @ SV8 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY65: $i,SY66: $i] :
~ ( ~ ( ~ ( member @ SV9 @ ( intersection @ SY65 @ SY66 ) )
| ~ ( ~ ( member @ SV9 @ SY65 )
| ~ ( member @ SV9 @ SY66 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV9 @ SY65 )
| ~ ( member @ SV9 @ SY66 ) )
| ( member @ SV9 @ ( intersection @ SY65 @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(86,plain,
! [SV10: $i] :
( ( ! [SY67: $i,SY68: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( difference @ SY68 @ SY67 ) )
| ~ ( ~ ( member @ SV10 @ SY68 )
| ~ ~ ( member @ SV10 @ SY67 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ SY68 )
| ~ ~ ( member @ SV10 @ SY67 ) )
| ( member @ SV10 @ ( difference @ SY68 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(87,plain,
! [SV11: $i] :
( ( ! [SY69: $i] :
~ ( ~ ( ~ ( member @ SY69 @ ( suc @ SV11 ) )
| ( member @ SY69 @ ( union @ SV11 @ ( singleton @ SV11 ) ) ) )
| ~ ( ~ ( member @ SY69 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
| ( member @ SY69 @ ( suc @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(88,plain,
! [SV12: $i] :
( ( ~ ( set @ SV12 )
| ! [SY70: $i] :
( ~ ( member @ SY70 @ SV12 )
| ( set @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(89,plain,
! [SV13: $i] :
( ( ! [SY71: $i] :
~ ( ~ ( ~ ( strict_order @ SV13 @ SY71 )
| ~ ( ~ ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( member @ SY72 @ SY71 )
| ~ ( member @ SY73 @ SY71 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY72 @ SY73 )
| ~ ( apply @ SV13 @ SY73 @ SY72 ) ) )
| ~ ! [SY74: $i,SY75: $i,SY76: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY74 @ SY71 )
| ~ ( member @ SY75 @ SY71 ) )
| ~ ( member @ SY76 @ SY71 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY74 @ SY75 )
| ~ ( apply @ SV13 @ SY75 @ SY76 ) )
| ( apply @ SV13 @ SY74 @ SY76 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ~ ( ~ ( member @ SY77 @ SY71 )
| ~ ( member @ SY78 @ SY71 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY77 @ SY78 )
| ~ ( apply @ SV13 @ SY78 @ SY77 ) ) )
| ~ ! [SY79: $i,SY80: $i,SY81: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY79 @ SY71 )
| ~ ( member @ SY80 @ SY71 ) )
| ~ ( member @ SY81 @ SY71 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY79 @ SY80 )
| ~ ( apply @ SV13 @ SY80 @ SY81 ) )
| ( apply @ SV13 @ SY79 @ SY81 ) ) )
| ( strict_order @ SV13 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(90,plain,
! [SV14: $i] :
( ( ! [SY82: $i] :
~ ( ~ ( ~ ( member @ SV14 @ ( product @ SY82 ) )
| ! [SY83: $i] :
( ~ ( member @ SY83 @ SY82 )
| ( member @ SV14 @ SY83 ) ) )
| ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SY82 )
| ( member @ SV14 @ SY84 ) )
| ( member @ SV14 @ ( product @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(91,plain,
! [SV15: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ~ ( member @ SV15 @ ( singleton @ SY85 ) )
| ( SV15 = SY85 ) )
| ~ ( ( SV15 != SY85 )
| ( member @ SV15 @ ( singleton @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(92,plain,
! [SV16: $i] :
( ( ! [SY86: $i,SY87: $i] :
~ ( ~ ( ~ ( member @ SV16 @ ( unordered_pair @ SY86 @ SY87 ) )
| ( SV16 = SY86 )
| ( SV16 = SY87 ) )
| ~ ( ~ ( ( SV16 = SY86 )
| ( SV16 = SY87 ) )
| ( member @ SV16 @ ( unordered_pair @ SY86 @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(93,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(94,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV2 @ SV17 )
| ! [SY88: $i] :
( ~ ( member @ SY88 @ SV2 )
| ( member @ SY88 @ SV17 ) ) )
| ~ ( ~ ! [SY89: $i] :
( ~ ( member @ SY89 @ SV2 )
| ( member @ SY89 @ SV17 ) )
| ( subset @ SV2 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(95,plain,
! [SV18: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( member @ SV3 @ ( sum @ SV18 ) )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV18 )
| ~ ( member @ SV3 @ SY90 ) ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV18 )
| ~ ( member @ SV3 @ SY91 ) )
| ( member @ SV3 @ ( sum @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(96,plain,
! [SV19: $i,SV4: $i] :
( ( ! [SY92: $i] :
~ ( ~ ( ~ ( member @ SV4 @ ( union @ SV19 @ SY92 ) )
| ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SY92 ) )
| ~ ( ~ ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SY92 ) )
| ( member @ SV4 @ ( union @ SV19 @ SY92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV20: $i,SV5: $i] :
( ( ! [SY93: $i,SY94: $i] :
~ ( ~ ( ~ ( member @ SY94 @ ( initial_segment @ SV5 @ SV20 @ SY93 ) )
| ~ ( ~ ( member @ SY94 @ SY93 )
| ~ ( apply @ SV20 @ SY94 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY94 @ SY93 )
| ~ ( apply @ SV20 @ SY94 @ SV5 ) )
| ( member @ SY94 @ ( initial_segment @ SV5 @ SV20 @ SY93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( member @ SV6 @ ( power_set @ SV21 ) )
| ( subset @ SV6 @ SV21 ) )
| ~ ( ~ ( subset @ SV6 @ SV21 )
| ( member @ SV6 @ ( power_set @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV22: $i,SV7: $i] :
( ( ! [SY95: $i] :
~ ( ~ ( ~ ( least @ SY95 @ SV7 @ SV22 )
| ~ ( ~ ( member @ SY95 @ SV22 )
| ~ ! [SY96: $i] :
( ~ ( member @ SY96 @ SV22 )
| ( SY95 = SY96 )
| ( apply @ SV7 @ SY95 @ SY96 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY95 @ SV22 )
| ~ ! [SY97: $i] :
( ~ ( member @ SY97 @ SV22 )
| ( SY95 = SY97 )
| ( apply @ SV7 @ SY95 @ SY97 ) ) )
| ( least @ SY95 @ SV7 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( apply @ member_predicate @ SV8 @ SV23 )
| ( member @ SV8 @ SV23 ) )
| ~ ( ~ ( member @ SV8 @ SV23 )
| ( apply @ member_predicate @ SV8 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV24: $i,SV9: $i] :
( ( ! [SY98: $i] :
~ ( ~ ( ~ ( member @ SV9 @ ( intersection @ SV24 @ SY98 ) )
| ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SY98 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SY98 ) )
| ( member @ SV9 @ ( intersection @ SV24 @ SY98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV25: $i,SV10: $i] :
( ( ! [SY99: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( difference @ SY99 @ SV25 ) )
| ~ ( ~ ( member @ SV10 @ SY99 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ SY99 )
| ~ ~ ( member @ SV10 @ SV25 ) )
| ( member @ SV10 @ ( difference @ SY99 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV11: $i,SV26: $i] :
( ( ~ ( ~ ( ~ ( member @ SV26 @ ( suc @ SV11 ) )
| ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) ) )
| ~ ( ~ ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
| ( member @ SV26 @ ( suc @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV12: $i] :
( ( ( ~ ( set @ SV12 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( member @ SY70 @ SV12 )
| ( set @ SY70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( strict_order @ SV13 @ SV27 )
| ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) )
| ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) )
| ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
| ( strict_order @ SV13 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( member @ SV14 @ ( product @ SV28 ) )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV28 )
| ( member @ SV14 @ SY110 ) ) )
| ~ ( ~ ! [SY111: $i] :
( ~ ( member @ SY111 @ SV28 )
| ( member @ SV14 @ SY111 ) )
| ( member @ SV14 @ ( product @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( member @ SV15 @ ( singleton @ SV29 ) )
| ( SV15 = SV29 ) )
| ~ ( ( SV15 != SV29 )
| ( member @ SV15 @ ( singleton @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY112: $i] :
~ ( ~ ( ~ ( member @ SV16 @ ( unordered_pair @ SV30 @ SY112 ) )
| ( SV16 = SV30 )
| ( SV16 = SY112 ) )
| ~ ( ~ ( ( SV16 = SV30 )
| ( SV16 = SY112 ) )
| ( member @ SV16 @ ( unordered_pair @ SV30 @ SY112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(109,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV17 )
| ! [SY88: $i] :
( ~ ( member @ SY88 @ SV2 )
| ( member @ SY88 @ SV17 ) ) )
| ~ ( ~ ! [SY89: $i] :
( ~ ( member @ SY89 @ SV2 )
| ( member @ SY89 @ SV17 ) )
| ( subset @ SV2 @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV18: $i,SV3: $i] :
( ( ~ ( ~ ( member @ SV3 @ ( sum @ SV18 ) )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV18 )
| ~ ( member @ SV3 @ SY90 ) ) )
| ~ ( ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV18 )
| ~ ( member @ SV3 @ SY91 ) )
| ( member @ SV3 @ ( sum @ SV18 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
| ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
| ~ ( ~ ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
| ( member @ SV4 @ ( union @ SV19 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV32: $i,SV20: $i,SV5: $i] :
( ( ! [SY113: $i] :
~ ( ~ ( ~ ( member @ SY113 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
| ~ ( ~ ( member @ SY113 @ SV32 )
| ~ ( apply @ SV20 @ SY113 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY113 @ SV32 )
| ~ ( apply @ SV20 @ SY113 @ SV5 ) )
| ( member @ SY113 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( ~ ( member @ SV6 @ ( power_set @ SV21 ) )
| ( subset @ SV6 @ SV21 ) )
| ~ ( ~ ( subset @ SV6 @ SV21 )
| ( member @ SV6 @ ( power_set @ SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ~ ( ~ ( ~ ( least @ SV33 @ SV7 @ SV22 )
| ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
| ( least @ SV33 @ SV7 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( ~ ( apply @ member_predicate @ SV8 @ SV23 )
| ( member @ SV8 @ SV23 ) )
| ~ ( ~ ( member @ SV8 @ SV23 )
| ( apply @ member_predicate @ SV8 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
| ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) )
| ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
| ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) )
| ( member @ SV10 @ ( difference @ SV35 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV11: $i,SV26: $i] :
( ( ~ ( ~ ( member @ SV26 @ ( suc @ SV11 ) )
| ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) ) )
| ~ ( ~ ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
| ( member @ SV26 @ ( suc @ SV11 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV12: $i] :
( ( ( set @ SV12 )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( member @ SY70 @ SV12 )
| ( set @ SY70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( ~ ( strict_order @ SV13 @ SV27 )
| ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) )
| ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) )
| ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
| ( strict_order @ SV13 @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ( ~ ( member @ SV14 @ ( product @ SV28 ) )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV28 )
| ( member @ SV14 @ SY110 ) ) )
| ~ ( ~ ! [SY111: $i] :
( ~ ( member @ SY111 @ SV28 )
| ( member @ SV14 @ SY111 ) )
| ( member @ SV14 @ ( product @ SV28 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( singleton @ SV29 ) )
| ( SV15 = SV29 ) )
| ~ ( ( SV15 != SV29 )
| ( member @ SV15 @ ( singleton @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
| ( SV16 = SV30 )
| ( SV16 = SV36 ) )
| ~ ( ~ ( ( SV16 = SV30 )
| ( SV16 = SV36 ) )
| ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV17 )
| ! [SY88: $i] :
( ~ ( member @ SY88 @ SV2 )
| ( member @ SY88 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(125,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( ~ ! [SY89: $i] :
( ~ ( member @ SY89 @ SV2 )
| ( member @ SY89 @ SV17 ) )
| ( subset @ SV2 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(126,plain,
! [SV18: $i,SV3: $i] :
( ( ~ ( ~ ( member @ SV3 @ ( sum @ SV18 ) )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV18 )
| ~ ( member @ SV3 @ SY90 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(127,plain,
! [SV3: $i,SV18: $i] :
( ( ~ ( ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV18 )
| ~ ( member @ SV3 @ SY91 ) )
| ( member @ SV3 @ ( sum @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(128,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ~ ( ~ ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
| ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
| ~ ( ~ ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
| ( member @ SV4 @ ( union @ SV19 @ SV31 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(129,plain,
! [SV32: $i,SV20: $i,SV5: $i,SV37: $i] :
( ( ~ ( ~ ( ~ ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
| ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) )
| ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(130,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( ~ ( member @ SV6 @ ( power_set @ SV21 ) )
| ( subset @ SV6 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(131,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( ~ ( subset @ SV6 @ SV21 )
| ( member @ SV6 @ ( power_set @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(132,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ~ ( ~ ( least @ SV33 @ SV7 @ SV22 )
| ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
| ( least @ SV33 @ SV7 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( ~ ( apply @ member_predicate @ SV8 @ SV23 )
| ( member @ SV8 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(134,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( ~ ( member @ SV8 @ SV23 )
| ( apply @ member_predicate @ SV8 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(135,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
| ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) )
| ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(136,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
| ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) )
| ( member @ SV10 @ ( difference @ SV35 @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(137,plain,
! [SV11: $i,SV26: $i] :
( ( ~ ( ~ ( member @ SV26 @ ( suc @ SV11 ) )
| ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(138,plain,
! [SV11: $i,SV26: $i] :
( ( ~ ( ~ ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
| ( member @ SV26 @ ( suc @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(139,plain,
! [SV12: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ SV12 )
| ( set @ SV38 ) )
= $true )
| ( ( set @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(140,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( ~ ( strict_order @ SV13 @ SV27 )
| ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) )
| ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(141,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) )
| ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
| ( strict_order @ SV13 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(142,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ( ~ ( member @ SV14 @ ( product @ SV28 ) )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV28 )
| ( member @ SV14 @ SY110 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(143,plain,
! [SV14: $i,SV28: $i] :
( ( ~ ( ~ ! [SY111: $i] :
( ~ ( member @ SY111 @ SV28 )
| ( member @ SV14 @ SY111 ) )
| ( member @ SV14 @ ( product @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(144,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( singleton @ SV29 ) )
| ( SV15 = SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(145,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ( SV15 != SV29 )
| ( member @ SV15 @ ( singleton @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(146,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ( ~ ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
| ( SV16 = SV30 )
| ( SV16 = SV36 ) )
| ~ ( ~ ( ( SV16 = SV30 )
| ( SV16 = SV36 ) )
| ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV17 )
| ! [SY88: $i] :
( ~ ( member @ SY88 @ SV2 )
| ( member @ SY88 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(148,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ! [SY89: $i] :
( ~ ( member @ SY89 @ SV2 )
| ( member @ SY89 @ SV17 ) )
| ( subset @ SV2 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(149,plain,
! [SV18: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ ( sum @ SV18 ) )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV18 )
| ~ ( member @ SV3 @ SY90 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(150,plain,
! [SV3: $i,SV18: $i] :
( ( ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV18 )
| ~ ( member @ SV3 @ SY91 ) )
| ( member @ SV3 @ ( sum @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(151,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ~ ( ~ ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
| ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(152,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ~ ( ~ ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
| ( member @ SV4 @ ( union @ SV19 @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(153,plain,
! [SV32: $i,SV20: $i,SV5: $i,SV37: $i] :
( ( ~ ( ~ ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
| ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) )
| ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(154,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ ( power_set @ SV21 ) )
| ( subset @ SV6 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(155,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV21 )
| ( member @ SV6 @ ( power_set @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(156,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ~ ( ~ ( least @ SV33 @ SV7 @ SV22 )
| ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(157,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
| ( least @ SV33 @ SV7 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(158,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( apply @ member_predicate @ SV8 @ SV23 )
| ( member @ SV8 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(159,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( member @ SV8 @ SV23 )
| ( apply @ member_predicate @ SV8 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(160,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
| ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(161,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) )
| ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(162,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
| ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(163,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) )
| ( member @ SV10 @ ( difference @ SV35 @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(164,plain,
! [SV11: $i,SV26: $i] :
( ( ~ ( member @ SV26 @ ( suc @ SV11 ) )
| ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(165,plain,
! [SV11: $i,SV26: $i] :
( ( ~ ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
| ( member @ SV26 @ ( suc @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(166,plain,
! [SV12: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ SV12 ) )
= $true )
| ( ( set @ SV38 )
= $true )
| ( ( set @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(167,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( strict_order @ SV13 @ SV27 )
| ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) )
| ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(168,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) )
| ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
| ( strict_order @ SV13 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(169,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ( member @ SV14 @ ( product @ SV28 ) )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV28 )
| ( member @ SV14 @ SY110 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(170,plain,
! [SV14: $i,SV28: $i] :
( ( ~ ! [SY111: $i] :
( ~ ( member @ SY111 @ SV28 )
| ( member @ SV14 @ SY111 ) )
| ( member @ SV14 @ ( product @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(171,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( singleton @ SV29 ) )
| ( SV15 = SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(172,plain,
! [SV29: $i,SV15: $i] :
( ( ( SV15 != SV29 )
| ( member @ SV15 @ ( singleton @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(173,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ( ~ ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
| ( SV16 = SV30 )
| ( SV16 = SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(174,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ( ~ ( ( SV16 = SV30 )
| ( SV16 = SV36 ) )
| ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(175,plain,
! [SV17: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV17 ) )
= $true )
| ( ( ! [SY88: $i] :
( ~ ( member @ SY88 @ SV2 )
| ( member @ SY88 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(176,plain,
! [SV17: $i,SV2: $i] :
( ( ( ~ ! [SY89: $i] :
( ~ ( member @ SY89 @ SV2 )
| ( member @ SY89 @ SV17 ) ) )
= $true )
| ( ( subset @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(177,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( sum @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV18 )
| ~ ( member @ SV3 @ SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(178,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV18 )
| ~ ( member @ SV3 @ SY91 ) ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(179,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
| ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(180,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ~ ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
| ( member @ SV4 @ ( union @ SV19 @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(181,plain,
! [SV32: $i,SV20: $i,SV5: $i,SV37: $i] :
( ( ~ ( ~ ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
| ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(182,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) )
| ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(183,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ ( power_set @ SV21 ) ) )
= $true )
| ( ( subset @ SV6 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(184,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV21 ) )
= $true )
| ( ( member @ SV6 @ ( power_set @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(185,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ~ ( least @ SV33 @ SV7 @ SV22 )
| ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(186,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ~ ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
| ( least @ SV33 @ SV7 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(187,plain,
! [SV23: $i,SV8: $i] :
( ( ( ~ ( apply @ member_predicate @ SV8 @ SV23 ) )
= $true )
| ( ( member @ SV8 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(188,plain,
! [SV23: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV23 ) )
= $true )
| ( ( apply @ member_predicate @ SV8 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(189,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ~ ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
| ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(190,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ~ ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) )
| ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(191,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ~ ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
| ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(192,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ~ ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) )
| ( member @ SV10 @ ( difference @ SV35 @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(193,plain,
! [SV11: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( suc @ SV11 ) ) )
= $true )
| ( ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(194,plain,
! [SV11: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) ) )
= $true )
| ( ( member @ SV26 @ ( suc @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(195,plain,
! [SV12: $i,SV38: $i] :
( ( ( member @ SV38 @ SV12 )
= $false )
| ( ( set @ SV38 )
= $true )
| ( ( set @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(196,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( strict_order @ SV13 @ SV27 ) )
= $true )
| ( ( ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) )
| ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(197,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) )
| ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(198,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ ( product @ SV28 ) ) )
= $true )
| ( ( ! [SY110: $i] :
( ~ ( member @ SY110 @ SV28 )
| ( member @ SV14 @ SY110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(199,plain,
! [SV14: $i,SV28: $i] :
( ( ( ~ ! [SY111: $i] :
( ~ ( member @ SY111 @ SV28 )
| ( member @ SV14 @ SY111 ) ) )
= $true )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(200,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( singleton @ SV29 ) ) )
= $true )
| ( ( SV15 = SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(201,plain,
! [SV29: $i,SV15: $i] :
( ( ( SV15 != SV29 )
= $true )
| ( ( member @ SV15 @ ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(202,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
| ( SV16 = SV30 )
| ( SV16 = SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(203,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ~ ( ( SV16 = SV30 )
| ( SV16 = SV36 ) )
| ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(204,plain,
! [SV17: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV17 )
= $false )
| ( ( ! [SY88: $i] :
( ~ ( member @ SY88 @ SV2 )
| ( member @ SY88 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(205,plain,
! [SV17: $i,SV2: $i] :
( ( ( ! [SY89: $i] :
( ~ ( member @ SY89 @ SV2 )
| ( member @ SY89 @ SV17 ) ) )
= $false )
| ( ( subset @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(206,plain,
! [SV18: $i,SV3: $i] :
( ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false )
| ( ( ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV18 )
| ~ ( member @ SV3 @ SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(207,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV18 )
| ~ ( member @ SV3 @ SY91 ) ) )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(208,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( union @ SV19 @ SV31 ) ) )
= $true )
| ( ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(209,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ( ~ ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) ) )
= $true )
| ( ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(210,plain,
! [SV32: $i,SV20: $i,SV5: $i,SV37: $i] :
( ( ~ ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
| ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(211,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ~ ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) )
| ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(212,plain,
! [SV21: $i,SV6: $i] :
( ( ( member @ SV6 @ ( power_set @ SV21 ) )
= $false )
| ( ( subset @ SV6 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(213,plain,
! [SV21: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV21 )
= $false )
| ( ( member @ SV6 @ ( power_set @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(214,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ( ~ ( least @ SV33 @ SV7 @ SV22 ) )
= $true )
| ( ( ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(215,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(216,plain,
! [SV23: $i,SV8: $i] :
( ( ( apply @ member_predicate @ SV8 @ SV23 )
= $false )
| ( ( member @ SV8 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(217,plain,
! [SV23: $i,SV8: $i] :
( ( ( member @ SV8 @ SV23 )
= $false )
| ( ( apply @ member_predicate @ SV8 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(218,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(219,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) )
= $true )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(220,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( difference @ SV35 @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(221,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
= $true )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(222,plain,
! [SV11: $i,SV26: $i] :
( ( ( member @ SV26 @ ( suc @ SV11 ) )
= $false )
| ( ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(223,plain,
! [SV11: $i,SV26: $i] :
( ( ( member @ SV26 @ ( union @ SV11 @ ( singleton @ SV11 ) ) )
= $false )
| ( ( member @ SV26 @ ( suc @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(224,plain,
! [SV27: $i,SV13: $i] :
( ( ( strict_order @ SV13 @ SV27 )
= $false )
| ( ( ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) )
| ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(225,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) )
| ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) ) )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(226,plain,
! [SV28: $i,SV14: $i] :
( ( ( member @ SV14 @ ( product @ SV28 ) )
= $false )
| ( ( ! [SY110: $i] :
( ~ ( member @ SY110 @ SV28 )
| ( member @ SV14 @ SY110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(227,plain,
! [SV14: $i,SV28: $i] :
( ( ( ! [SY111: $i] :
( ~ ( member @ SY111 @ SV28 )
| ( member @ SV14 @ SY111 ) ) )
= $false )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(228,plain,
! [SV29: $i,SV15: $i] :
( ( ( member @ SV15 @ ( singleton @ SV29 ) )
= $false )
| ( ( SV15 = SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(229,plain,
! [SV29: $i,SV15: $i] :
( ( ( SV15 = SV29 )
= $false )
| ( ( member @ SV15 @ ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(230,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) ) )
= $true )
| ( ( ( SV16 = SV30 )
| ( SV16 = SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(231,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( ( SV16 = SV30 )
| ( SV16 = SV36 ) ) )
= $true )
| ( ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(232,plain,
! [SV17: $i,SV2: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV2 )
| ( member @ SV39 @ SV17 ) )
= $true )
| ( ( subset @ SV2 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(233,plain,
! [SV2: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK2_SY89 @ SV17 @ SV2 ) @ SV2 )
| ( member @ ( sK2_SY89 @ SV17 @ SV2 ) @ SV17 ) )
= $false )
| ( ( subset @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[205]) ).
thf(234,plain,
! [SV3: $i,SV18: $i] :
( ( ( ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV18 )
| ~ ( member @ SV3 @ SY90 ) ) )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(235,plain,
! [SV3: $i,SV18: $i] :
( ( ( ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV18 )
| ~ ( member @ SV3 @ SY91 ) ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(236,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
= $false )
| ( ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(237,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ( ( member @ SV4 @ SV19 )
| ( member @ SV4 @ SV31 ) )
= $false )
| ( ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(238,plain,
! [SV32: $i,SV20: $i,SV5: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(239,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) )
= $true )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(240,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ( least @ SV33 @ SV7 @ SV22 )
= $false )
| ( ( ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(241,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) ) )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(242,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(243,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) ) )
= $false )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(244,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(245,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) ) )
= $false )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(246,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) )
| ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(247,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) )
| ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(248,plain,
! [SV14: $i,SV28: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV28 )
| ( member @ SV14 @ SV40 ) )
= $true )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(249,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK3_SY111 @ SV14 @ SV28 ) @ SV28 )
| ( member @ SV14 @ ( sK3_SY111 @ SV14 @ SV28 ) ) )
= $false )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[227]) ).
thf(250,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
= $false )
| ( ( ( SV16 = SV30 )
| ( SV16 = SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(251,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ( ( SV16 = SV30 )
| ( SV16 = SV36 ) )
= $false )
| ( ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(252,plain,
! [SV17: $i,SV2: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV2 ) )
= $true )
| ( ( member @ SV39 @ SV17 )
= $true )
| ( ( subset @ SV2 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(253,plain,
! [SV2: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK2_SY89 @ SV17 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(254,plain,
! [SV2: $i,SV17: $i] :
( ( ( member @ ( sK2_SY89 @ SV17 @ SV2 ) @ SV17 )
= $false )
| ( ( subset @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(255,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY90 @ SV3 @ SV18 ) @ SV18 )
| ~ ( member @ SV3 @ ( sK4_SY90 @ SV3 @ SV18 ) ) ) )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[234]) ).
thf(256,plain,
! [SV3: $i,SV18: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ( member @ SV41 @ SV18 )
| ~ ( member @ SV3 @ SV41 ) ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(257,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ( member @ SV4 @ SV19 )
= $true )
| ( ( member @ SV4 @ SV31 )
= $true )
| ( ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(258,plain,
! [SV31: $i,SV19: $i,SV4: $i] :
( ( ( member @ SV4 @ SV19 )
= $false )
| ( ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(259,plain,
! [SV19: $i,SV31: $i,SV4: $i] :
( ( ( member @ SV4 @ SV31 )
= $false )
| ( ( member @ SV4 @ ( union @ SV19 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(260,plain,
! [SV32: $i,SV20: $i,SV5: $i,SV37: $i] :
( ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(261,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ( ~ ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) ) )
= $false )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(262,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(263,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV22 )
| ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(264,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) )
= $false )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(265,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV24 )
| ~ ( member @ SV9 @ SV34 ) )
= $true )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(266,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) )
= $false )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(267,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV35 )
| ~ ~ ( member @ SV10 @ SV25 ) )
= $true )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(268,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) ) )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(269,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(270,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) ) )
= $true )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(271,plain,
! [SV14: $i,SV28: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV28 ) )
= $true )
| ( ( member @ SV14 @ SV40 )
= $true )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(272,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK3_SY111 @ SV14 @ SV28 ) @ SV28 ) )
= $false )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(273,plain,
! [SV28: $i,SV14: $i] :
( ( ( member @ SV14 @ ( sK3_SY111 @ SV14 @ SV28 ) )
= $false )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(274,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ( SV16 = SV30 )
= $true )
| ( ( SV16 = SV36 )
= $true )
| ( ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(275,plain,
! [SV36: $i,SV30: $i,SV16: $i] :
( ( ( SV16 = SV30 )
= $false )
| ( ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(276,plain,
! [SV30: $i,SV36: $i,SV16: $i] :
( ( ( SV16 = SV36 )
= $false )
| ( ( member @ SV16 @ ( unordered_pair @ SV30 @ SV36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(277,plain,
! [SV17: $i,SV2: $i,SV39: $i] :
( ( ( member @ SV39 @ SV2 )
= $false )
| ( ( member @ SV39 @ SV17 )
= $true )
| ( ( subset @ SV2 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(278,plain,
! [SV2: $i,SV17: $i] :
( ( ( member @ ( sK2_SY89 @ SV17 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(279,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY90 @ SV3 @ SV18 ) @ SV18 )
| ~ ( member @ SV3 @ ( sK4_SY90 @ SV3 @ SV18 ) ) ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(280,plain,
! [SV3: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( ~ ( member @ SV41 @ SV18 )
| ~ ( member @ SV3 @ SV41 ) ) )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(281,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) )
= $false )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(282,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV32 )
| ~ ( apply @ SV20 @ SV37 @ SV5 ) )
= $true )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(283,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV22 ) )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(284,plain,
! [SV7: $i,SV33: $i,SV22: $i] :
( ( ( ~ ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(285,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ SV22 ) )
= $true )
| ( ( ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(286,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV24 ) )
= $false )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(287,plain,
! [SV24: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV34 ) )
= $false )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(288,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV9 @ SV34 ) )
= $true )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(289,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV35 ) )
= $false )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(290,plain,
! [SV35: $i,SV25: $i,SV10: $i] :
( ( ( ~ ~ ( member @ SV10 @ SV25 ) )
= $false )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(291,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV35 ) )
= $true )
| ( ( ~ ~ ( member @ SV10 @ SV25 ) )
= $true )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(292,plain,
! [SV13: $i,SV27: $i] :
( ( ( ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( member @ SY100 @ SV27 )
| ~ ( member @ SY101 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY100 @ SY101 )
| ~ ( apply @ SV13 @ SY101 @ SY100 ) ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(293,plain,
! [SV13: $i,SV27: $i] :
( ( ( ! [SY102: $i,SY103: $i,SY104: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY102 @ SV27 )
| ~ ( member @ SY103 @ SV27 ) )
| ~ ( member @ SY104 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY102 @ SY103 )
| ~ ( apply @ SV13 @ SY103 @ SY104 ) )
| ( apply @ SV13 @ SY102 @ SY104 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(294,plain,
! [SV13: $i,SV27: $i] :
( ( ( ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV27 )
| ~ ( member @ SY106 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY105 @ SY106 )
| ~ ( apply @ SV13 @ SY106 @ SY105 ) ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(295,plain,
! [SV14: $i,SV28: $i,SV40: $i] :
( ( ( member @ SV40 @ SV28 )
= $false )
| ( ( member @ SV14 @ SV40 )
= $true )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(296,plain,
! [SV28: $i,SV14: $i] :
( ( ( member @ ( sK3_SY111 @ SV14 @ SV28 ) @ SV28 )
= $true )
| ( ( member @ SV14 @ ( product @ SV28 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(297,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK4_SY90 @ SV3 @ SV18 ) @ SV18 )
| ~ ( member @ SV3 @ ( sK4_SY90 @ SV3 @ SV18 ) ) )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(298,plain,
! [SV3: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV18 )
| ~ ( member @ SV3 @ SV41 ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(299,plain,
! [SV20: $i,SV5: $i,SV32: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV32 ) )
= $false )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(300,plain,
! [SV32: $i,SV5: $i,SV37: $i,SV20: $i] :
( ( ( ~ ( apply @ SV20 @ SV37 @ SV5 ) )
= $false )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(301,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV32 ) )
= $true )
| ( ( ~ ( apply @ SV20 @ SV37 @ SV5 ) )
= $true )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(302,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( member @ SV33 @ SV22 )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(303,plain,
! [SV7: $i,SV33: $i,SV22: $i] :
( ( ( ! [SY114: $i] :
( ~ ( member @ SY114 @ SV22 )
| ( SV33 = SY114 )
| ( apply @ SV7 @ SV33 @ SY114 ) ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(304,plain,
! [SV7: $i,SV22: $i,SV33: $i] :
( ( ( member @ SV33 @ SV22 )
= $false )
| ( ( ~ ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(305,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( member @ SV9 @ SV24 )
= $true )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(306,plain,
! [SV24: $i,SV34: $i,SV9: $i] :
( ( ( member @ SV9 @ SV34 )
= $true )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(307,plain,
! [SV34: $i,SV24: $i,SV9: $i] :
( ( ( member @ SV9 @ SV24 )
= $false )
| ( ( ~ ( member @ SV9 @ SV34 ) )
= $true )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(308,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( member @ SV10 @ SV35 )
= $true )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(309,plain,
! [SV35: $i,SV25: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV25 ) )
= $true )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(310,plain,
! [SV25: $i,SV35: $i,SV10: $i] :
( ( ( member @ SV10 @ SV35 )
= $false )
| ( ( ~ ~ ( member @ SV10 @ SV25 ) )
= $true )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(311,plain,
! [SV13: $i,SV27: $i,SV42: $i] :
( ( ( ! [SY116: $i] :
( ~ ~ ( ~ ( member @ SV42 @ SV27 )
| ~ ( member @ SY116 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SY116 )
| ~ ( apply @ SV13 @ SY116 @ SV42 ) ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(312,plain,
! [SV13: $i,SV27: $i,SV43: $i] :
( ( ( ! [SY117: $i,SY118: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SY117 @ SV27 ) )
| ~ ( member @ SY118 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SY117 )
| ~ ( apply @ SV13 @ SY117 @ SY118 ) )
| ( apply @ SV13 @ SV43 @ SY118 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(313,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY119: $i] :
( ~ ~ ( ~ ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ SY119 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ SY119 )
| ~ ( apply @ SV13 @ SY119 @ ( sK5_SY105 @ SV13 @ SV27 ) ) ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[294]) ).
thf(314,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK4_SY90 @ SV3 @ SV18 ) @ SV18 ) )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(315,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( sK4_SY90 @ SV3 @ SV18 ) ) )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(316,plain,
! [SV3: $i,SV18: $i,SV41: $i] :
( ( ( ~ ( member @ SV41 @ SV18 ) )
= $true )
| ( ( ~ ( member @ SV3 @ SV41 ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(317,plain,
! [SV20: $i,SV5: $i,SV32: $i,SV37: $i] :
( ( ( member @ SV37 @ SV32 )
= $true )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(318,plain,
! [SV32: $i,SV5: $i,SV37: $i,SV20: $i] :
( ( ( apply @ SV20 @ SV37 @ SV5 )
= $true )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(319,plain,
! [SV5: $i,SV20: $i,SV32: $i,SV37: $i] :
( ( ( member @ SV37 @ SV32 )
= $false )
| ( ( ~ ( apply @ SV20 @ SV37 @ SV5 ) )
= $true )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(320,plain,
! [SV7: $i,SV33: $i,SV22: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV22 )
| ( SV33 = SV44 )
| ( apply @ SV7 @ SV33 @ SV44 ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(321,plain,
! [SV7: $i,SV33: $i,SV22: $i] :
( ( ( ! [SY115: $i] :
( ~ ( member @ SY115 @ SV22 )
| ( SV33 = SY115 )
| ( apply @ SV7 @ SV33 @ SY115 ) ) )
= $false )
| ( ( member @ SV33 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(322,plain,
! [SV24: $i,SV34: $i,SV9: $i] :
( ( ( member @ SV9 @ SV34 )
= $false )
| ( ( member @ SV9 @ SV24 )
= $false )
| ( ( member @ SV9 @ ( intersection @ SV24 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(323,plain,
! [SV35: $i,SV25: $i,SV10: $i] :
( ( ( member @ SV10 @ SV25 )
= $false )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(324,plain,
! [SV35: $i,SV25: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ SV25 ) )
= $false )
| ( ( member @ SV10 @ SV35 )
= $false )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(325,plain,
! [SV13: $i,SV45: $i,SV27: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( member @ SV42 @ SV27 )
| ~ ( member @ SV45 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(326,plain,
! [SV13: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ! [SY120: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) )
| ~ ( member @ SY120 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SY120 ) )
| ( apply @ SV13 @ SV43 @ SY120 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(327,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[313]) ).
thf(328,plain,
! [SV18: $i,SV3: $i] :
( ( ( member @ ( sK4_SY90 @ SV3 @ SV18 ) @ SV18 )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(329,plain,
! [SV18: $i,SV3: $i] :
( ( ( member @ SV3 @ ( sK4_SY90 @ SV3 @ SV18 ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(330,plain,
! [SV3: $i,SV18: $i,SV41: $i] :
( ( ( member @ SV41 @ SV18 )
= $false )
| ( ( ~ ( member @ SV3 @ SV41 ) )
= $true )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(331,plain,
! [SV32: $i,SV5: $i,SV37: $i,SV20: $i] :
( ( ( apply @ SV20 @ SV37 @ SV5 )
= $false )
| ( ( member @ SV37 @ SV32 )
= $false )
| ( ( member @ SV37 @ ( initial_segment @ SV5 @ SV20 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(332,plain,
! [SV7: $i,SV33: $i,SV22: $i,SV44: $i] :
( ( ( ~ ( member @ SV44 @ SV22 ) )
= $true )
| ( ( ( SV33 = SV44 )
| ( apply @ SV7 @ SV33 @ SV44 ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(333,plain,
! [SV22: $i,SV33: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) @ SV22 )
| ( SV33
= ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) )
| ( apply @ SV7 @ SV33 @ ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) ) )
= $false )
| ( ( member @ SV33 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[321]) ).
thf(334,plain,
! [SV35: $i,SV25: $i,SV10: $i] :
( ( ( member @ SV10 @ SV25 )
= $true )
| ( ( member @ SV10 @ SV35 )
= $false )
| ( ( member @ SV10 @ ( difference @ SV35 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(335,plain,
! [SV13: $i,SV45: $i,SV27: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( member @ SV42 @ SV27 )
| ~ ( member @ SV45 @ SV27 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(336,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) )
| ~ ( member @ SV47 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(337,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(338,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(339,plain,
! [SV18: $i,SV41: $i,SV3: $i] :
( ( ( member @ SV3 @ SV41 )
= $false )
| ( ( member @ SV41 @ SV18 )
= $false )
| ( ( member @ SV3 @ ( sum @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(340,plain,
! [SV7: $i,SV33: $i,SV22: $i,SV44: $i] :
( ( ( member @ SV44 @ SV22 )
= $false )
| ( ( ( SV33 = SV44 )
| ( apply @ SV7 @ SV33 @ SV44 ) )
= $true )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(341,plain,
! [SV22: $i,SV33: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) @ SV22 ) )
= $false )
| ( ( member @ SV33 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(342,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ( ( SV33
= ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) )
| ( apply @ SV7 @ SV33 @ ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) ) )
= $false )
| ( ( member @ SV33 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(343,plain,
! [SV13: $i,SV45: $i,SV27: $i,SV42: $i] :
( ( ( ~ ( ~ ( member @ SV42 @ SV27 )
| ~ ( member @ SV45 @ SV27 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(344,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) )
| ~ ( member @ SV47 @ SV27 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(345,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(346,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) ) ) )
= $true )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(347,plain,
! [SV22: $i,SV7: $i,SV44: $i,SV33: $i] :
( ( ( SV33 = SV44 )
= $true )
| ( ( apply @ SV7 @ SV33 @ SV44 )
= $true )
| ( ( member @ SV44 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(348,plain,
! [SV22: $i,SV33: $i,SV7: $i] :
( ( ( member @ ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) @ SV22 )
= $true )
| ( ( member @ SV33 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(349,plain,
! [SV22: $i,SV7: $i,SV33: $i] :
( ( ( SV33
= ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) )
= $false )
| ( ( member @ SV33 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(350,plain,
! [SV22: $i,SV33: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV33 @ ( sK7_SY115 @ SV7 @ SV33 @ SV22 ) )
= $false )
| ( ( member @ SV33 @ SV22 )
= $false )
| ( ( least @ SV33 @ SV7 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(351,plain,
! [SV13: $i,SV45: $i,SV27: $i,SV42: $i] :
( ( ( ~ ( member @ SV42 @ SV27 )
| ~ ( member @ SV45 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(352,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) )
| ~ ( member @ SV47 @ SV27 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(353,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(354,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(355,plain,
! [SV13: $i,SV45: $i,SV27: $i,SV42: $i] :
( ( ( ~ ( member @ SV42 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV45 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(356,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) )
| ~ ( member @ SV47 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(357,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(358,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(359,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(360,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) ) )
= $false )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(361,plain,
! [SV13: $i,SV45: $i,SV27: $i,SV42: $i] :
( ( ( member @ SV42 @ SV27 )
= $false )
| ( ( ~ ( member @ SV45 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(362,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) ) )
= $true )
| ( ( ~ ( member @ SV47 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(363,plain,
! [SV27: $i,SV13: $i] :
( ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(364,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(365,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(366,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(367,plain,
! [SV13: $i,SV42: $i,SV27: $i,SV45: $i] :
( ( ( member @ SV45 @ SV27 )
= $false )
| ( ( member @ SV42 @ SV27 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(368,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) ) )
= $false )
| ( ( ~ ( member @ SV47 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(369,plain,
! [SV13: $i,SV27: $i] :
( ( ( ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(370,plain,
! [SV13: $i,SV27: $i] :
( ( ( ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(371,plain,
! [SV13: $i,SV27: $i] :
( ( ( ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(372,plain,
! [SV13: $i,SV27: $i] :
( ( ( ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SV27 )
| ~ ( member @ SY108 @ SV27 ) )
| ~ ( member @ SY109 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ SY107 @ SY108 )
| ~ ( apply @ SV13 @ SY108 @ SY109 ) )
| ( apply @ SV13 @ SY107 @ SY109 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(373,plain,
! [SV27: $i,SV45: $i,SV42: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) ) )
= $false )
| ( ( member @ SV42 @ SV27 )
= $false )
| ( ( member @ SV45 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(374,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV27 )
| ~ ( member @ SV46 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV47 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(375,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY121: $i,SY122: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ SY121 @ SV27 ) )
| ~ ( member @ SY122 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ SY121 )
| ~ ( apply @ SV13 @ SY121 @ SY122 ) )
| ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ SY122 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[369]) ).
thf(376,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY123: $i,SY124: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ SY123 @ SV27 ) )
| ~ ( member @ SY124 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ SY123 )
| ~ ( apply @ SV13 @ SY123 @ SY124 ) )
| ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ SY124 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[370]) ).
thf(377,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ SY125 @ SV27 ) )
| ~ ( member @ SY126 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ SY125 )
| ~ ( apply @ SV13 @ SY125 @ SY126 ) )
| ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ SY126 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[371]) ).
thf(378,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ SY127 @ SV27 ) )
| ~ ( member @ SY128 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ SY127 )
| ~ ( apply @ SV13 @ SY127 @ SY128 ) )
| ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ SY128 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[372]) ).
thf(379,plain,
! [SV27: $i,SV45: $i,SV42: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ SV42 @ SV45 )
| ~ ( apply @ SV13 @ SV45 @ SV42 ) )
= $true )
| ( ( member @ SV42 @ SV27 )
= $false )
| ( ( member @ SV45 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(380,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV46 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV47 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(381,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY129: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ SY129 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ SY129 ) )
| ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ SY129 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[375]) ).
thf(382,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY130: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ SY130 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ SY130 ) )
| ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ SY130 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[376]) ).
thf(383,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY131: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ SY131 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ SY131 ) )
| ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ SY131 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[377]) ).
thf(384,plain,
! [SV27: $i,SV13: $i] :
( ( ( ! [SY132: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ SY132 @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ SY132 ) )
| ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ SY132 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[378]) ).
thf(385,plain,
! [SV27: $i,SV45: $i,SV42: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ SV42 @ SV45 ) )
= $true )
| ( ( ~ ( apply @ SV13 @ SV45 @ SV42 ) )
= $true )
| ( ( member @ SV42 @ SV27 )
= $false )
| ( ( member @ SV45 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(386,plain,
! [SV13: $i,SV47: $i,SV46: $i,SV27: $i,SV43: $i] :
( ( ( member @ SV43 @ SV27 )
= $false )
| ( ( ~ ( member @ SV46 @ SV27 ) )
= $true )
| ( ( ~ ( member @ SV47 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(387,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK16_SY129 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[381]) ).
thf(388,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK17_SY130 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[382]) ).
thf(389,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK18_SY131 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[383]) ).
thf(390,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK19_SY132 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ~ ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[384]) ).
thf(391,plain,
! [SV27: $i,SV45: $i,SV42: $i,SV13: $i] :
( ( ( apply @ SV13 @ SV42 @ SV45 )
= $false )
| ( ( ~ ( apply @ SV13 @ SV45 @ SV42 ) )
= $true )
| ( ( member @ SV42 @ SV27 )
= $false )
| ( ( member @ SV45 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(392,plain,
! [SV13: $i,SV47: $i,SV43: $i,SV27: $i,SV46: $i] :
( ( ( member @ SV46 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( ~ ( member @ SV47 @ SV27 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(393,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK16_SY129 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(394,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(395,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK17_SY130 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(396,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(397,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK18_SY131 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(398,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(399,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK19_SY132 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(400,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) )
| ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(401,plain,
! [SV27: $i,SV42: $i,SV45: $i,SV13: $i] :
( ( ( apply @ SV13 @ SV45 @ SV42 )
= $false )
| ( ( apply @ SV13 @ SV42 @ SV45 )
= $false )
| ( ( member @ SV42 @ SV27 )
= $false )
| ( ( member @ SV45 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(402,plain,
! [SV13: $i,SV46: $i,SV43: $i,SV27: $i,SV47: $i] :
( ( ( member @ SV47 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( member @ SV46 @ SV27 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
| ( apply @ SV13 @ SV43 @ SV47 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(403,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK16_SY129 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(404,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(405,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK16_SY129 @ SV27 @ SV13 ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(406,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK17_SY130 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(407,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(408,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK17_SY130 @ SV27 @ SV13 ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(409,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK18_SY131 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(410,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(411,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK18_SY131 @ SV27 @ SV13 ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(412,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK19_SY132 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(413,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(414,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK19_SY132 @ SV27 @ SV13 ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(415,plain,
! [SV27: $i,SV47: $i,SV46: $i,SV43: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) ) )
= $true )
| ( ( apply @ SV13 @ SV43 @ SV47 )
= $true )
| ( ( member @ SV46 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( member @ SV47 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(416,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK16_SY129 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(417,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) ) )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(418,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK17_SY130 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(419,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) ) )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(420,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK18_SY131 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(421,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) ) )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(422,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) )
| ~ ( member @ ( sK19_SY132 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(423,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) ) )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(424,plain,
! [SV27: $i,SV47: $i,SV46: $i,SV43: $i,SV13: $i] :
( ( ( ~ ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) ) )
= $false )
| ( ( apply @ SV13 @ SV43 @ SV47 )
= $true )
| ( ( member @ SV46 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( member @ SV47 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(425,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(426,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK16_SY129 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(427,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(428,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(429,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK17_SY130 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(430,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(431,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(432,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK18_SY131 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(433,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(434,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(435,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK19_SY132 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(436,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) )
| ~ ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(437,plain,
! [SV27: $i,SV47: $i,SV46: $i,SV43: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ SV43 @ SV46 )
| ~ ( apply @ SV13 @ SV46 @ SV47 ) )
= $true )
| ( ( apply @ SV13 @ SV43 @ SV47 )
= $true )
| ( ( member @ SV46 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( member @ SV47 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(438,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(439,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK16_SY129 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(440,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(441,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ ( sK16_SY129 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(442,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(443,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK17_SY130 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(444,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(445,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ ( sK17_SY130 @ SV27 @ SV13 ) ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(446,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(447,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK18_SY131 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(448,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(449,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ ( sK18_SY131 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(450,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) ) )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(451,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK19_SY132 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(452,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(453,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ ( sK19_SY132 @ SV27 @ SV13 ) ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(454,plain,
! [SV27: $i,SV47: $i,SV46: $i,SV43: $i,SV13: $i] :
( ( ( ~ ( apply @ SV13 @ SV43 @ SV46 ) )
= $true )
| ( ( ~ ( apply @ SV13 @ SV46 @ SV47 ) )
= $true )
| ( ( apply @ SV13 @ SV43 @ SV47 )
= $true )
| ( ( member @ SV46 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( member @ SV47 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(455,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(456,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK8_SY107 @ SV13 @ SV27 ) @ ( sK12_SY121 @ SV27 @ SV13 ) )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(457,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK12_SY121 @ SV27 @ SV13 ) @ ( sK16_SY129 @ SV27 @ SV13 ) )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(458,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(459,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK9_SY107 @ SV13 @ SV27 ) @ ( sK13_SY123 @ SV27 @ SV13 ) )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(460,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK13_SY123 @ SV27 @ SV13 ) @ ( sK17_SY130 @ SV27 @ SV13 ) )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(461,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(462,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK10_SY107 @ SV13 @ SV27 ) @ ( sK14_SY125 @ SV27 @ SV13 ) )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(463,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK14_SY125 @ SV27 @ SV13 ) @ ( sK18_SY131 @ SV27 @ SV13 ) )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(464,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
| ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(465,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK11_SY107 @ SV13 @ SV27 ) @ ( sK15_SY127 @ SV27 @ SV13 ) )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(466,plain,
! [SV27: $i,SV13: $i] :
( ( ( apply @ SV13 @ ( sK15_SY127 @ SV27 @ SV13 ) @ ( sK19_SY132 @ SV27 @ SV13 ) )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(467,plain,
! [SV27: $i,SV47: $i,SV46: $i,SV43: $i,SV13: $i] :
( ( ( apply @ SV13 @ SV43 @ SV46 )
= $false )
| ( ( ~ ( apply @ SV13 @ SV46 @ SV47 ) )
= $true )
| ( ( apply @ SV13 @ SV43 @ SV47 )
= $true )
| ( ( member @ SV46 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( member @ SV47 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(468,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(469,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(470,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(471,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(472,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(473,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(474,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(475,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 ) )
= $false )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(476,plain,
! [SV27: $i,SV43: $i,SV47: $i,SV46: $i,SV13: $i] :
( ( ( apply @ SV13 @ SV46 @ SV47 )
= $false )
| ( ( apply @ SV13 @ SV43 @ SV46 )
= $false )
| ( ( apply @ SV13 @ SV43 @ SV47 )
= $true )
| ( ( member @ SV46 @ SV27 )
= $false )
| ( ( member @ SV43 @ SV27 )
= $false )
| ( ( member @ SV47 @ SV27 )
= $false )
| ( ( strict_order @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(477,plain,
! [SV27: $i,SV13: $i] :
( ( ( member @ ( sK8_SY107 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(478,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK12_SY121 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( member @ ( sK5_SY105 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(479,plain,
! [SV27: $i,SV13: $i] :
( ( ( member @ ( sK9_SY107 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(480,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK13_SY123 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( member @ ( sK6_SY119 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(481,plain,
! [SV27: $i,SV13: $i] :
( ( ( member @ ( sK10_SY107 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(482,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK14_SY125 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( apply @ SV13 @ ( sK5_SY105 @ SV13 @ SV27 ) @ ( sK6_SY119 @ SV27 @ SV13 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(483,plain,
! [SV27: $i,SV13: $i] :
( ( ( member @ ( sK11_SY107 @ SV13 @ SV27 ) @ SV27 )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(484,plain,
! [SV13: $i,SV27: $i] :
( ( ( member @ ( sK15_SY127 @ SV27 @ SV13 ) @ SV27 )
= $true )
| ( ( apply @ SV13 @ ( sK6_SY119 @ SV27 @ SV13 ) @ ( sK5_SY105 @ SV13 @ SV27 ) )
= $true )
| ( ( strict_order @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(485,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,484,483,482,481,480,479,478,477,476,466,465,463,462,460,459,457,456,451,447,443,439,414,411,408,405,401,350,349,348,347,339,334,331,329,328,323,322,318,317,308,306,305,302,296,295,278,277,276,275,274,273,259,258,257,254,229,228,223,222,217,216,213,212,195,93,77]) ).
thf(486,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 14:53:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.26/0.55
% 1.26/0.55 No.of.Axioms: 16
% 1.26/0.55
% 1.26/0.55 Length.of.Defs: 0
% 1.26/0.55
% 1.26/0.55 Contains.Choice.Funs: false
% 1.26/0.55 ................
% 1.26/0.55
% 1.26/0.55 ********************************
% 1.26/0.55 * All subproblems solved! *
% 1.26/0.55 ********************************
% 1.26/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:485,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.26/0.55
% 1.26/0.55 %**** Beginning of derivation protocol ****
% 1.26/0.55 % SZS output start CNFRefutation
% See solution above
% 0.67/0.56
% 0.67/0.56 %**** End of derivation protocol ****
% 0.67/0.56 %**** no. of clauses in derivation: 483 ****
% 0.67/0.56 %**** clause counter: 485 ****
% 0.67/0.56
% 0.67/0.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:485,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------