%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET714+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:40:54 AM UTC 2026
% Result : Theorem 158.45s 26.69s
% Output : CNFRefutation 158.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 7
% Syntax : Number of formulae : 369 ( 78 unt; 0 typ; 0 def)
% Number of atoms : 4881 (1220 equ; 0 cnn)
% Maximal formula atoms : 11 ( 13 avg)
% Number of connectives : 14714 (3307 ~;2105 |; 57 &;9197 @)
% ( 21 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 6 con; 0-7 aty)
% Number of variables : 2182 ( 0 ^;2176 !; 6 ?;2182 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i > $o ).
thf(tp_compose_function,type,
compose_function: $i > $i > $i > $i > $i > $i ).
thf(tp_compose_predicate,type,
compose_predicate: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_decreasing,type,
decreasing: $i > $i > $i > $i > $i > $o ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_maps,type,
equal_maps: $i > $i > $i > $i > $o ).
thf(tp_equal_set,type,
equal_set: $i > $i > $o ).
thf(tp_identity,type,
identity: $i > $i > $o ).
thf(tp_image2,type,
image2: $i > $i > $i ).
thf(tp_image3,type,
image3: $i > $i > $i > $i ).
thf(tp_increasing,type,
increasing: $i > $i > $i > $i > $i > $o ).
thf(tp_injective,type,
injective: $i > $i > $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_inverse_function,type,
inverse_function: $i > $i > $i > $i ).
thf(tp_inverse_image2,type,
inverse_image2: $i > $i > $i ).
thf(tp_inverse_image3,type,
inverse_image3: $i > $i > $i > $i ).
thf(tp_inverse_predicate,type,
inverse_predicate: $i > $i > $i > $i > $o ).
thf(tp_isomorphism,type,
isomorphism: $i > $i > $i > $i > $i > $o ).
thf(tp_maps,type,
maps: $i > $i > $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $i > $i > $o ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_sK10_SY169,type,
sK10_SY169: $i > $i > $i > $i > $i > $i ).
thf(tp_sK11_SY176,type,
sK11_SY176: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_SY192,type,
sK12_SY192: $i > $i > $i > $i > $i > $i ).
thf(tp_sK13_SY195,type,
sK13_SY195: $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_SY131,type,
sK14_SY131: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY197,type,
sK15_SY197: $i > $i > $i > $i > $i > $i ).
thf(tp_sK16_SY198,type,
sK16_SY198: $i > $i > $i > $i > $i ).
thf(tp_sK17_SY200,type,
sK17_SY200: $i > $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK2_SY39,type,
sK2_SY39: $i ).
thf(tp_sK3_SY41,type,
sK3_SY41: $i ).
thf(tp_sK4_SY91,type,
sK4_SY91: $i > $i > $i ).
thf(tp_sK5_SY129,type,
sK5_SY129: $i > $i > $i > $i ).
thf(tp_sK6_SY178,type,
sK6_SY178: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY131,type,
sK7_SY131: $i > $i > $i > $i ).
thf(tp_sK8_SY188,type,
sK8_SY188: $i > $i > $i > $i ).
thf(tp_sK9_SY191,type,
sK9_SY191: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_surjective,type,
surjective: $i > $i > $i > $o ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( isomorphism @ F @ A @ R @ B @ S )
<=> ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B )
& ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( ( apply @ R @ X1 @ X2 )
<=> ( apply @ S @ Y1 @ Y2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isomorphism) ).
thf(8,axiom,
! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function) ).
thf(10,axiom,
! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
thf(13,axiom,
! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
thf(15,axiom,
! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
thf(17,axiom,
! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
thf(29,conjecture,
! [F: $i,A: $i,B: $i] :
( ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B ) )
=> ( identity @ ( compose_function @ ( inverse_function @ F @ A @ B ) @ F @ A @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII05) ).
thf(30,negated_conjecture,
( ( ! [F: $i,A: $i,B: $i] :
( ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B ) )
=> ( identity @ ( compose_function @ ( inverse_function @ F @ A @ B ) @ F @ A @ B @ A ) @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B ) )
=> ( identity @ ( compose_function @ ( inverse_function @ F @ A @ B ) @ F @ A @ B @ A ) @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( isomorphism @ F @ A @ R @ B @ S )
<=> ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B )
& ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( ( apply @ R @ X1 @ X2 )
<=> ( apply @ S @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( ! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(34,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(37,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(38,plain,
( ( ! [SY39: $i,SY40: $i] :
( ( ( maps @ sK1_F @ SY39 @ SY40 )
& ( one_to_one @ sK1_F @ SY39 @ SY40 ) )
=> ( identity @ ( compose_function @ ( inverse_function @ sK1_F @ SY39 @ SY40 ) @ sK1_F @ SY39 @ SY40 @ SY39 ) @ SY39 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(39,plain,
( ( ! [SY41: $i] :
( ( ( maps @ sK1_F @ sK2_SY39 @ SY41 )
& ( one_to_one @ sK1_F @ sK2_SY39 @ SY41 ) )
=> ( identity @ ( compose_function @ ( inverse_function @ sK1_F @ sK2_SY39 @ SY41 ) @ sK1_F @ sK2_SY39 @ SY41 @ sK2_SY39 ) @ sK2_SY39 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ( ( maps @ sK1_F @ sK2_SY39 @ sK3_SY41 )
& ( one_to_one @ sK1_F @ sK2_SY39 @ sK3_SY41 ) )
=> ( identity @ ( compose_function @ ( inverse_function @ sK1_F @ sK2_SY39 @ sK3_SY41 ) @ sK1_F @ sK2_SY39 @ sK3_SY41 @ sK2_SY39 ) @ sK2_SY39 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( maps @ sK1_F @ sK2_SY39 @ sK3_SY41 )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(42,plain,
( ( one_to_one @ sK1_F @ sK2_SY39 @ sK3_SY41 )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(43,plain,
( ( identity @ ( compose_function @ ( inverse_function @ sK1_F @ sK2_SY39 @ sK3_SY41 ) @ sK1_F @ sK2_SY39 @ sK3_SY41 @ sK2_SY39 ) @ sK2_SY39 )
= $false ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ( identity @ ( compose_function @ ( inverse_function @ sK1_F @ sK2_SY39 @ sK3_SY41 ) @ sK1_F @ sK2_SY39 @ sK3_SY41 @ sK2_SY39 ) @ sK2_SY39 ) )
= $true ),
inference(polarity_switch,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(46,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(47,plain,
( ( ! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(48,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(49,plain,
( ( ! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( member @ X @ A )
& ( member @ Y @ B ) )
=> ( ( apply @ F @ X @ Y )
<=> ( apply @ ( inverse_function @ F @ A @ B ) @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(50,plain,
( ( ! [F: $i,A: $i,R: $i,B: $i,S: $i] :
( ( isomorphism @ F @ A @ R @ B @ S )
<=> ( ( maps @ F @ A @ B )
& ( one_to_one @ F @ A @ B )
& ! [X1: $i,Y1: $i,X2: $i,Y2: $i] :
( ( ( member @ X1 @ A )
& ( member @ Y1 @ B )
& ( member @ X2 @ A )
& ( member @ Y2 @ B )
& ( apply @ F @ X1 @ Y1 )
& ( apply @ F @ X2 @ Y2 ) )
=> ( ( apply @ R @ X1 @ X2 )
<=> ( apply @ S @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(51,plain,
( ( one_to_one @ sK1_F @ sK2_SY39 @ sK3_SY41 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(52,plain,
( ( maps @ sK1_F @ sK2_SY39 @ sK3_SY41 )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(53,plain,
( ( ~ ( identity @ ( compose_function @ ( inverse_function @ sK1_F @ sK2_SY39 @ sK3_SY41 ) @ sK1_F @ sK2_SY39 @ sK3_SY41 @ sK2_SY39 ) @ sK2_SY39 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( member @ SX5 @ SX2 )
| ~ ( member @ SX6 @ SX4 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 )
| ~ ! [SX7: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX7 @ SX3 )
| ~ ( apply @ SX1 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX7 @ SX6 ) ) )
| ~ ( ~ ~ ! [SX7: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX7 @ SX3 )
| ~ ( apply @ SX1 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX7 @ SX6 ) )
| ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( identity @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) )
| ( identity @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( maps @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ~ ( apply @ SX0 @ SX3 @ SX5 ) )
| ( SX4 = SX5 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ~ ( apply @ SX0 @ SX3 @ SX5 ) )
| ( SX4 = SX5 ) ) )
| ( maps @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( one_to_one @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ~ ( surjective @ SX0 @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ~ ( surjective @ SX0 @ SX1 @ SX2 ) )
| ( one_to_one @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ( apply @ ( inverse_function @ SX0 @ SX1 @ SX2 ) @ SX4 @ SX3 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SX0 @ SX1 @ SX2 ) @ SX4 @ SX3 )
| ( apply @ SX0 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( isomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
| ~ ( ~ ~ ( ~ ( maps @ SX0 @ SX1 @ SX3 )
| ~ ( one_to_one @ SX0 @ SX1 @ SX3 ) )
| ~ ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ~ ( ~ ( ~ ( apply @ SX2 @ SX5 @ SX7 )
| ( apply @ SX4 @ SX6 @ SX8 ) )
| ~ ( ~ ( apply @ SX4 @ SX6 @ SX8 )
| ( apply @ SX2 @ SX5 @ SX7 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SX0 @ SX1 @ SX3 )
| ~ ( one_to_one @ SX0 @ SX1 @ SX3 ) )
| ~ ! [SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SX5 @ SX1 )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ( member @ SX7 @ SX1 ) )
| ~ ( member @ SX8 @ SX3 ) )
| ~ ( apply @ SX0 @ SX5 @ SX6 ) )
| ~ ( apply @ SX0 @ SX7 @ SX8 ) )
| ~ ( ~ ( ~ ( apply @ SX2 @ SX5 @ SX7 )
| ( apply @ SX4 @ SX6 @ SX8 ) )
| ~ ( ~ ( apply @ SX4 @ SX6 @ SX8 )
| ( apply @ SX2 @ SX5 @ SX7 ) ) ) ) )
| ( isomorphism @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(60,plain,
( ( identity @ ( compose_function @ ( inverse_function @ sK1_F @ sK2_SY39 @ sK3_SY41 ) @ sK1_F @ sK2_SY39 @ sK3_SY41 @ sK2_SY39 ) @ sK2_SY39 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(61,plain,
! [SV1: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i,SY45: $i,SY46: $i,SY47: $i] :
( ~ ~ ( ~ ( member @ SY46 @ SY43 )
| ~ ( member @ SY47 @ SY45 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SY42 @ SY43 @ SY44 @ SY45 ) @ SY46 @ SY47 )
| ~ ! [SY48: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY48 @ SY44 )
| ~ ( apply @ SY42 @ SY46 @ SY48 ) )
| ~ ( apply @ SV1 @ SY48 @ SY47 ) ) )
| ~ ( ~ ~ ! [SY49: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY49 @ SY44 )
| ~ ( apply @ SY42 @ SY46 @ SY49 ) )
| ~ ( apply @ SV1 @ SY49 @ SY47 ) )
| ( apply @ ( compose_function @ SV1 @ SY42 @ SY43 @ SY44 @ SY45 ) @ SY46 @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV2: $i] :
( ( ! [SY50: $i] :
~ ( ~ ( ~ ( identity @ SV2 @ SY50 )
| ! [SY51: $i] :
( ~ ( member @ SY51 @ SY50 )
| ( apply @ SV2 @ SY51 @ SY51 ) ) )
| ~ ( ~ ! [SY52: $i] :
( ~ ( member @ SY52 @ SY50 )
| ( apply @ SV2 @ SY52 @ SY52 ) )
| ( identity @ SV2 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV3: $i] :
( ( ! [SY53: $i,SY54: $i] :
~ ( ~ ( ~ ( maps @ SV3 @ SY53 @ SY54 )
| ~ ( ~ ! [SY55: $i] :
( ~ ( member @ SY55 @ SY53 )
| ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SY54 )
| ~ ( apply @ SV3 @ SY55 @ SY56 ) ) )
| ~ ! [SY57: $i,SY58: $i,SY59: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY57 @ SY53 )
| ~ ( member @ SY58 @ SY54 ) )
| ~ ( member @ SY59 @ SY54 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY57 @ SY58 )
| ~ ( apply @ SV3 @ SY57 @ SY59 ) )
| ( SY58 = SY59 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY60: $i] :
( ~ ( member @ SY60 @ SY53 )
| ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ SY54 )
| ~ ( apply @ SV3 @ SY60 @ SY61 ) ) )
| ~ ! [SY62: $i,SY63: $i,SY64: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY62 @ SY53 )
| ~ ( member @ SY63 @ SY54 ) )
| ~ ( member @ SY64 @ SY54 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY62 @ SY63 )
| ~ ( apply @ SV3 @ SY62 @ SY64 ) )
| ( SY63 = SY64 ) ) )
| ( maps @ SV3 @ SY53 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV4: $i] :
( ( ! [SY65: $i,SY66: $i] :
~ ( ~ ( ~ ( one_to_one @ SV4 @ SY65 @ SY66 )
| ~ ( ~ ( injective @ SV4 @ SY65 @ SY66 )
| ~ ( surjective @ SV4 @ SY65 @ SY66 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV4 @ SY65 @ SY66 )
| ~ ( surjective @ SV4 @ SY65 @ SY66 ) )
| ( one_to_one @ SV4 @ SY65 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV5: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i,SY70: $i] :
( ~ ~ ( ~ ( member @ SY69 @ SY67 )
| ~ ( member @ SY70 @ SY68 ) )
| ~ ( ~ ( ~ ( apply @ SV5 @ SY69 @ SY70 )
| ( apply @ ( inverse_function @ SV5 @ SY67 @ SY68 ) @ SY70 @ SY69 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SY67 @ SY68 ) @ SY70 @ SY69 )
| ( apply @ SV5 @ SY69 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV6: $i] :
( ( ! [SY71: $i,SY72: $i,SY73: $i,SY74: $i] :
~ ( ~ ( ~ ( isomorphism @ SV6 @ SY71 @ SY72 @ SY73 @ SY74 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SY71 @ SY73 )
| ~ ( one_to_one @ SV6 @ SY71 @ SY73 ) )
| ~ ! [SY75: $i,SY76: $i,SY77: $i,SY78: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY75 @ SY71 )
| ~ ( member @ SY76 @ SY73 ) )
| ~ ( member @ SY77 @ SY71 ) )
| ~ ( member @ SY78 @ SY73 ) )
| ~ ( apply @ SV6 @ SY75 @ SY76 ) )
| ~ ( apply @ SV6 @ SY77 @ SY78 ) )
| ~ ( ~ ( ~ ( apply @ SY72 @ SY75 @ SY77 )
| ( apply @ SY74 @ SY76 @ SY78 ) )
| ~ ( ~ ( apply @ SY74 @ SY76 @ SY78 )
| ( apply @ SY72 @ SY75 @ SY77 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SY71 @ SY73 )
| ~ ( one_to_one @ SV6 @ SY71 @ SY73 ) )
| ~ ! [SY79: $i,SY80: $i,SY81: $i,SY82: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY79 @ SY71 )
| ~ ( member @ SY80 @ SY73 ) )
| ~ ( member @ SY81 @ SY71 ) )
| ~ ( member @ SY82 @ SY73 ) )
| ~ ( apply @ SV6 @ SY79 @ SY80 ) )
| ~ ( apply @ SV6 @ SY81 @ SY82 ) )
| ~ ( ~ ( ~ ( apply @ SY72 @ SY79 @ SY81 )
| ( apply @ SY74 @ SY80 @ SY82 ) )
| ~ ( ~ ( apply @ SY74 @ SY80 @ SY82 )
| ( apply @ SY72 @ SY79 @ SY81 ) ) ) ) )
| ( isomorphism @ SV6 @ SY71 @ SY72 @ SY73 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ( member @ SY86 @ SY83 )
| ~ ( member @ SY87 @ SY85 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SY83 @ SY84 @ SY85 ) @ SY86 @ SY87 )
| ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY88 @ SY84 )
| ~ ( apply @ SV7 @ SY86 @ SY88 ) )
| ~ ( apply @ SV1 @ SY88 @ SY87 ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY89 @ SY84 )
| ~ ( apply @ SV7 @ SY86 @ SY89 ) )
| ~ ( apply @ SV1 @ SY89 @ SY87 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SY83 @ SY84 @ SY85 ) @ SY86 @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( identity @ SV2 @ SV8 )
| ! [SY90: $i] :
( ~ ( member @ SY90 @ SV8 )
| ( apply @ SV2 @ SY90 @ SY90 ) ) )
| ~ ( ~ ! [SY91: $i] :
( ~ ( member @ SY91 @ SV8 )
| ( apply @ SV2 @ SY91 @ SY91 ) )
| ( identity @ SV2 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY92: $i] :
~ ( ~ ( ~ ( maps @ SV3 @ SV9 @ SY92 )
| ~ ( ~ ! [SY93: $i] :
( ~ ( member @ SY93 @ SV9 )
| ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SY92 )
| ~ ( apply @ SV3 @ SY93 @ SY56 ) ) )
| ~ ! [SY95: $i,SY96: $i,SY97: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY95 @ SV9 )
| ~ ( member @ SY96 @ SY92 ) )
| ~ ( member @ SY97 @ SY92 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY95 @ SY96 )
| ~ ( apply @ SV3 @ SY95 @ SY97 ) )
| ( SY96 = SY97 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY98: $i] :
( ~ ( member @ SY98 @ SV9 )
| ~ ! [SY61: $i] :
~ ~ ( ~ ( member @ SY61 @ SY92 )
| ~ ( apply @ SV3 @ SY98 @ SY61 ) ) )
| ~ ! [SY100: $i,SY101: $i,SY102: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY100 @ SV9 )
| ~ ( member @ SY101 @ SY92 ) )
| ~ ( member @ SY102 @ SY92 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY100 @ SY101 )
| ~ ( apply @ SV3 @ SY100 @ SY102 ) )
| ( SY101 = SY102 ) ) )
| ( maps @ SV3 @ SV9 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY103: $i] :
~ ( ~ ( ~ ( one_to_one @ SV4 @ SV10 @ SY103 )
| ~ ( ~ ( injective @ SV4 @ SV10 @ SY103 )
| ~ ( surjective @ SV4 @ SV10 @ SY103 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV4 @ SV10 @ SY103 )
| ~ ( surjective @ SV4 @ SV10 @ SY103 ) )
| ( one_to_one @ SV4 @ SV10 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV5: $i,SV11: $i] :
( ( ! [SY104: $i,SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SV11 )
| ~ ( member @ SY106 @ SY104 ) )
| ~ ( ~ ( ~ ( apply @ SV5 @ SY105 @ SY106 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SY104 ) @ SY106 @ SY105 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SY104 ) @ SY106 @ SY105 )
| ( apply @ SV5 @ SY105 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY107: $i,SY108: $i,SY109: $i] :
~ ( ~ ( ~ ( isomorphism @ SV6 @ SV12 @ SY107 @ SY108 @ SY109 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SY108 )
| ~ ( one_to_one @ SV6 @ SV12 @ SY108 ) )
| ~ ! [SY110: $i,SY111: $i,SY112: $i,SY113: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY110 @ SV12 )
| ~ ( member @ SY111 @ SY108 ) )
| ~ ( member @ SY112 @ SV12 ) )
| ~ ( member @ SY113 @ SY108 ) )
| ~ ( apply @ SV6 @ SY110 @ SY111 ) )
| ~ ( apply @ SV6 @ SY112 @ SY113 ) )
| ~ ( ~ ( ~ ( apply @ SY107 @ SY110 @ SY112 )
| ( apply @ SY109 @ SY111 @ SY113 ) )
| ~ ( ~ ( apply @ SY109 @ SY111 @ SY113 )
| ( apply @ SY107 @ SY110 @ SY112 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SY108 )
| ~ ( one_to_one @ SV6 @ SV12 @ SY108 ) )
| ~ ! [SY114: $i,SY115: $i,SY116: $i,SY117: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY114 @ SV12 )
| ~ ( member @ SY115 @ SY108 ) )
| ~ ( member @ SY116 @ SV12 ) )
| ~ ( member @ SY117 @ SY108 ) )
| ~ ( apply @ SV6 @ SY114 @ SY115 ) )
| ~ ( apply @ SV6 @ SY116 @ SY117 ) )
| ~ ( ~ ( ~ ( apply @ SY107 @ SY114 @ SY116 )
| ( apply @ SY109 @ SY115 @ SY117 ) )
| ~ ( ~ ( apply @ SY109 @ SY115 @ SY117 )
| ( apply @ SY107 @ SY114 @ SY116 ) ) ) ) )
| ( isomorphism @ SV6 @ SV12 @ SY107 @ SY108 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ! [SY118: $i,SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ( member @ SY120 @ SV13 )
| ~ ( member @ SY121 @ SY119 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SY118 @ SY119 ) @ SY120 @ SY121 )
| ~ ! [SY88: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY88 @ SY118 )
| ~ ( apply @ SV7 @ SY120 @ SY88 ) )
| ~ ( apply @ SV1 @ SY88 @ SY121 ) ) )
| ~ ( ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY89 @ SY118 )
| ~ ( apply @ SV7 @ SY120 @ SY89 ) )
| ~ ( apply @ SV1 @ SY89 @ SY121 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SY118 @ SY119 ) @ SY120 @ SY121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( identity @ SV2 @ SV8 )
| ! [SY90: $i] :
( ~ ( member @ SY90 @ SV8 )
| ( apply @ SV2 @ SY90 @ SY90 ) ) )
| ~ ( ~ ! [SY91: $i] :
( ~ ( member @ SY91 @ SV8 )
| ( apply @ SV2 @ SY91 @ SY91 ) )
| ( identity @ SV2 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV14: $i,SV9: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( maps @ SV3 @ SV9 @ SV14 )
| ~ ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) )
| ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) )
| ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
| ( maps @ SV3 @ SV9 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( one_to_one @ SV4 @ SV10 @ SV15 )
| ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
| ( one_to_one @ SV4 @ SV10 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV5: $i,SV16: $i,SV11: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ~ ( ~ ( member @ SY134 @ SV11 )
| ~ ( member @ SY135 @ SV16 ) )
| ~ ( ~ ( ~ ( apply @ SV5 @ SY134 @ SY135 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SY135 @ SY134 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SY135 @ SY134 )
| ( apply @ SV5 @ SY134 @ SY135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ! [SY136: $i,SY137: $i] :
~ ( ~ ( ~ ( isomorphism @ SV6 @ SV12 @ SV17 @ SY136 @ SY137 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SY136 )
| ~ ( one_to_one @ SV6 @ SV12 @ SY136 ) )
| ~ ! [SY138: $i,SY139: $i,SY140: $i,SY141: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY138 @ SV12 )
| ~ ( member @ SY139 @ SY136 ) )
| ~ ( member @ SY140 @ SV12 ) )
| ~ ( member @ SY141 @ SY136 ) )
| ~ ( apply @ SV6 @ SY138 @ SY139 ) )
| ~ ( apply @ SV6 @ SY140 @ SY141 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY138 @ SY140 )
| ( apply @ SY137 @ SY139 @ SY141 ) )
| ~ ( ~ ( apply @ SY137 @ SY139 @ SY141 )
| ( apply @ SV17 @ SY138 @ SY140 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SY136 )
| ~ ( one_to_one @ SV6 @ SV12 @ SY136 ) )
| ~ ! [SY142: $i,SY143: $i,SY144: $i,SY145: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY142 @ SV12 )
| ~ ( member @ SY143 @ SY136 ) )
| ~ ( member @ SY144 @ SV12 ) )
| ~ ( member @ SY145 @ SY136 ) )
| ~ ( apply @ SV6 @ SY142 @ SY143 ) )
| ~ ( apply @ SV6 @ SY144 @ SY145 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY142 @ SY144 )
| ( apply @ SY137 @ SY143 @ SY145 ) )
| ~ ( ~ ( apply @ SY137 @ SY143 @ SY145 )
| ( apply @ SV17 @ SY142 @ SY144 ) ) ) ) )
| ( isomorphism @ SV6 @ SV12 @ SV17 @ SY136 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV13: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i] :
( ~ ~ ( ~ ( member @ SY147 @ SV13 )
| ~ ( member @ SY148 @ SY146 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SY146 ) @ SY147 @ SY148 )
| ~ ! [SY149: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY149 @ SV18 )
| ~ ( apply @ SV7 @ SY147 @ SY149 ) )
| ~ ( apply @ SV1 @ SY149 @ SY148 ) ) )
| ~ ( ~ ~ ! [SY150: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY150 @ SV18 )
| ~ ( apply @ SV7 @ SY147 @ SY150 ) )
| ~ ( apply @ SV1 @ SY150 @ SY148 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SY146 ) @ SY147 @ SY148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( identity @ SV2 @ SV8 )
| ! [SY90: $i] :
( ~ ( member @ SY90 @ SV8 )
| ( apply @ SV2 @ SY90 @ SY90 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(81,plain,
! [SV2: $i,SV8: $i] :
( ( ~ ( ~ ! [SY91: $i] :
( ~ ( member @ SY91 @ SV8 )
| ( apply @ SV2 @ SY91 @ SY91 ) )
| ( identity @ SV2 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(82,plain,
! [SV14: $i,SV9: $i,SV3: $i] :
( ( ~ ( ~ ( maps @ SV3 @ SV9 @ SV14 )
| ~ ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) )
| ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) )
| ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
| ( maps @ SV3 @ SV9 @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ( ~ ( one_to_one @ SV4 @ SV10 @ SV15 )
| ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
| ( one_to_one @ SV4 @ SV10 @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV5: $i,SV16: $i,SV11: $i,SV19: $i] :
( ( ! [SY151: $i] :
( ~ ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SY151 @ SV16 ) )
| ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SY151 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SY151 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SY151 @ SV19 )
| ( apply @ SV5 @ SV19 @ SY151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV20: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ! [SY152: $i] :
~ ( ~ ( ~ ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SY152 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY153: $i,SY154: $i,SY155: $i,SY156: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY153 @ SV12 )
| ~ ( member @ SY154 @ SV20 ) )
| ~ ( member @ SY155 @ SV12 ) )
| ~ ( member @ SY156 @ SV20 ) )
| ~ ( apply @ SV6 @ SY153 @ SY154 ) )
| ~ ( apply @ SV6 @ SY155 @ SY156 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY153 @ SY155 )
| ( apply @ SY152 @ SY154 @ SY156 ) )
| ~ ( ~ ( apply @ SY152 @ SY154 @ SY156 )
| ( apply @ SV17 @ SY153 @ SY155 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY157: $i,SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY157 @ SV12 )
| ~ ( member @ SY158 @ SV20 ) )
| ~ ( member @ SY159 @ SV12 ) )
| ~ ( member @ SY160 @ SV20 ) )
| ~ ( apply @ SV6 @ SY157 @ SY158 ) )
| ~ ( apply @ SV6 @ SY159 @ SY160 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY157 @ SY159 )
| ( apply @ SY152 @ SY158 @ SY160 ) )
| ~ ( ~ ( apply @ SY152 @ SY158 @ SY160 )
| ( apply @ SV17 @ SY157 @ SY159 ) ) ) ) )
| ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV13: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ~ ~ ( ~ ( member @ SY161 @ SV13 )
| ~ ( member @ SY162 @ SV21 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SY161 @ SY162 )
| ~ ! [SY149: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY149 @ SV18 )
| ~ ( apply @ SV7 @ SY161 @ SY149 ) )
| ~ ( apply @ SV1 @ SY149 @ SY162 ) ) )
| ~ ( ~ ~ ! [SY150: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY150 @ SV18 )
| ~ ( apply @ SV7 @ SY161 @ SY150 ) )
| ~ ( apply @ SV1 @ SY150 @ SY162 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SY161 @ SY162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( identity @ SV2 @ SV8 )
| ! [SY90: $i] :
( ~ ( member @ SY90 @ SV8 )
| ( apply @ SV2 @ SY90 @ SY90 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV2: $i,SV8: $i] :
( ( ~ ! [SY91: $i] :
( ~ ( member @ SY91 @ SV8 )
| ( apply @ SV2 @ SY91 @ SY91 ) )
| ( identity @ SV2 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV14: $i,SV9: $i,SV3: $i] :
( ( ~ ( ~ ( maps @ SV3 @ SV9 @ SV14 )
| ~ ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) )
| ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) )
| ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
| ( maps @ SV3 @ SV9 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(91,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ( ~ ( one_to_one @ SV4 @ SV10 @ SV15 )
| ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(92,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
| ( one_to_one @ SV4 @ SV10 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(93,plain,
! [SV5: $i,SV16: $i,SV22: $i,SV11: $i,SV19: $i] :
( ( ~ ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV22 @ SV16 ) )
| ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
| ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV13: $i,SV24: $i] :
( ( ! [SY173: $i] :
( ~ ~ ( ~ ( member @ SV24 @ SV13 )
| ~ ( member @ SY173 @ SV21 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SY173 )
| ~ ! [SY174: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY174 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY174 ) )
| ~ ( apply @ SV1 @ SY174 @ SY173 ) ) )
| ~ ( ~ ~ ! [SY175: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY175 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY175 ) )
| ~ ( apply @ SV1 @ SY175 @ SY173 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( identity @ SV2 @ SV8 ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( member @ SY90 @ SV8 )
| ( apply @ SV2 @ SY90 @ SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ! [SY91: $i] :
( ~ ( member @ SY91 @ SV8 )
| ( apply @ SV2 @ SY91 @ SY91 ) ) )
= $true )
| ( ( identity @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV14: $i,SV9: $i,SV3: $i] :
( ( ~ ( maps @ SV3 @ SV9 @ SV14 )
| ~ ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) )
| ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(99,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ~ ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) )
| ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
| ( maps @ SV3 @ SV9 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(100,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ( one_to_one @ SV4 @ SV10 @ SV15 )
| ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(101,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ~ ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
| ( one_to_one @ SV4 @ SV10 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(102,plain,
! [SV5: $i,SV16: $i,SV22: $i,SV11: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV22 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
| ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV25: $i,SV13: $i,SV24: $i] :
( ( ~ ~ ( ~ ( member @ SV24 @ SV13 )
| ~ ( member @ SV25 @ SV21 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV8: $i,SV2: $i] :
( ( ( identity @ SV2 @ SV8 )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( member @ SY90 @ SV8 )
| ( apply @ SV2 @ SY90 @ SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV2: $i,SV8: $i] :
( ( ( ! [SY91: $i] :
( ~ ( member @ SY91 @ SV8 )
| ( apply @ SV2 @ SY91 @ SY91 ) ) )
= $false )
| ( ( identity @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV14: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( maps @ SV3 @ SV9 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) )
| ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) )
| ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( one_to_one @ SV4 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) )
= $true )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV5: $i,SV16: $i,SV22: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV22 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(113,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
| ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(114,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV25: $i,SV13: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ SV24 @ SV13 )
| ~ ( member @ SV25 @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV2: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV8 )
| ( apply @ SV2 @ SV26 @ SV26 ) )
= $true )
| ( ( identity @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( member @ ( sK4_SY91 @ SV2 @ SV8 ) @ SV8 )
| ( apply @ SV2 @ ( sK4_SY91 @ SV2 @ SV8 ) @ ( sK4_SY91 @ SV2 @ SV8 ) ) )
= $false )
| ( ( identity @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(117,plain,
! [SV14: $i,SV9: $i,SV3: $i] :
( ( ( maps @ SV3 @ SV9 @ SV14 )
= $false )
| ( ( ~ ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) )
| ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) )
| ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) ) )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) ) )
= $false )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV5: $i,SV16: $i,SV22: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV22 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
| ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(123,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
| ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(124,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV25: $i,SV13: $i,SV24: $i] :
( ( ( ~ ( ~ ( member @ SV24 @ SV13 )
| ~ ( member @ SV25 @ SV21 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV2: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV8 ) )
= $true )
| ( ( apply @ SV2 @ SV26 @ SV26 )
= $true )
| ( ( identity @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( member @ ( sK4_SY91 @ SV2 @ SV8 ) @ SV8 ) )
= $false )
| ( ( identity @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(127,plain,
! [SV8: $i,SV2: $i] :
( ( ( apply @ SV2 @ ( sK4_SY91 @ SV2 @ SV8 ) @ ( sK4_SY91 @ SV2 @ SV8 ) )
= $false )
| ( ( identity @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(128,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) )
| ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(129,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) )
| ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(130,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
= $false )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( injective @ SV4 @ SV10 @ SV15 )
| ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
= $true )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(132,plain,
! [SV5: $i,SV16: $i,SV22: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV25: $i,SV13: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV13 )
| ~ ( member @ SV25 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV2: $i,SV8: $i,SV26: $i] :
( ( ( member @ SV26 @ SV8 )
= $false )
| ( ( apply @ SV2 @ SV26 @ SV26 )
= $true )
| ( ( identity @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV8: $i,SV2: $i] :
( ( ( member @ ( sK4_SY91 @ SV2 @ SV8 ) @ SV8 )
= $true )
| ( ( identity @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(138,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) ) )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(139,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(140,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) ) )
= $true )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( injective @ SV4 @ SV10 @ SV15 ) )
= $false )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(142,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
= $false )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(143,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( injective @ SV4 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
= $true )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV5: $i,SV16: $i,SV22: $i,SV11: $i,SV19: $i] :
( ( ( member @ SV19 @ SV11 )
= $false )
| ( ( ~ ( member @ SV22 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV12: $i,SV6: $i] :
( ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) ) )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV25: $i,SV13: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV13 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ! [SY124: $i] :
( ~ ( member @ SY124 @ SV9 )
| ~ ! [SY125: $i] :
~ ~ ( ~ ( member @ SY125 @ SV14 )
| ~ ( apply @ SV3 @ SY124 @ SY125 ) ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(149,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV9 )
| ~ ( member @ SY127 @ SV14 ) )
| ~ ( member @ SY128 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY126 @ SY127 )
| ~ ( apply @ SV3 @ SY126 @ SY128 ) )
| ( SY127 = SY128 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(150,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ! [SY129: $i] :
( ~ ( member @ SY129 @ SV9 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV14 )
| ~ ( apply @ SV3 @ SY129 @ SY130 ) ) ) )
= $false )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( injective @ SV4 @ SV10 @ SV15 )
= $true )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(152,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( surjective @ SV4 @ SV10 @ SV15 )
= $true )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(153,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( injective @ SV4 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( surjective @ SV4 @ SV10 @ SV15 ) )
= $true )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV5: $i,SV11: $i,SV19: $i,SV16: $i,SV22: $i] :
( ( ( member @ SV22 @ SV16 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
| ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(157,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV21: $i,SV25: $i,SV13: $i,SV24: $i] :
( ( ( member @ SV24 @ SV13 )
= $false )
| ( ( ~ ( member @ SV25 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV3: $i,SV14: $i,SV9: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV9 )
| ~ ! [SY178: $i] :
~ ~ ( ~ ( member @ SY178 @ SV14 )
| ~ ( apply @ SV3 @ SV27 @ SY178 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV3: $i,SV14: $i,SV9: $i,SV28: $i] :
( ( ( ! [SY179: $i,SY180: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SY179 @ SV14 ) )
| ~ ( member @ SY180 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SY179 )
| ~ ( apply @ SV3 @ SV28 @ SY180 ) )
| ( SY179 = SY180 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ! [SY181: $i] :
~ ~ ( ~ ( member @ SY181 @ SV14 )
| ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SY181 ) ) )
= $false )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(161,plain,
! [SV15: $i,SV10: $i,SV4: $i] :
( ( ( surjective @ SV4 @ SV10 @ SV15 )
= $false )
| ( ( injective @ SV4 @ SV10 @ SV15 )
= $false )
| ( ( one_to_one @ SV4 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV16: $i,SV11: $i,SV22: $i,SV19: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
| ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(163,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) ) )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(164,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( ~ ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(165,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) ) )
= $true )
| ( ( ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV18: $i,SV7: $i,SV1: $i,SV13: $i,SV24: $i,SV21: $i,SV25: $i] :
( ( ( member @ SV25 @ SV21 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV3: $i,SV14: $i,SV9: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV9 ) )
= $true )
| ( ( ~ ! [SY178: $i] :
~ ~ ( ~ ( member @ SY178 @ SV14 )
| ~ ( apply @ SV3 @ SV27 @ SY178 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(168,plain,
! [SV3: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ! [SY182: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) )
| ~ ( member @ SY182 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SY182 ) )
| ( SV29 = SY182 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(169,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 ) )
= $false )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(170,plain,
! [SV9: $i,SV3: $i,SV14: $i] :
( ( ( ~ ! [SY181: $i] :
~ ~ ( ~ ( member @ SY181 @ SV14 )
| ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SY181 ) ) )
= $false )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(171,plain,
! [SV16: $i,SV11: $i,SV22: $i,SV19: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(172,plain,
! [SV19: $i,SV22: $i,SV16: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(173,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(174,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( member @ SY166 @ SV20 ) )
| ~ ( member @ SY167 @ SV12 ) )
| ~ ( member @ SY168 @ SV20 ) )
| ~ ( apply @ SV6 @ SY165 @ SY166 ) )
| ~ ( apply @ SV6 @ SY167 @ SY168 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY165 @ SY167 )
| ( apply @ SV23 @ SY166 @ SY168 ) )
| ~ ( ~ ( apply @ SV23 @ SY166 @ SY168 )
| ( apply @ SV17 @ SY165 @ SY167 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(175,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV25: $i,SV24: $i,SV21: $i,SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
| ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV3: $i,SV14: $i,SV9: $i,SV27: $i] :
( ( ( member @ SV27 @ SV9 )
= $false )
| ( ( ~ ! [SY178: $i] :
~ ~ ( ~ ( member @ SY178 @ SV14 )
| ~ ( apply @ SV3 @ SV27 @ SY178 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) )
| ~ ( member @ SV30 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(180,plain,
! [SV9: $i,SV3: $i,SV14: $i] :
( ( ( ! [SY181: $i] :
~ ~ ( ~ ( member @ SY181 @ SV14 )
| ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SY181 ) ) )
= $true )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(181,plain,
! [SV16: $i,SV11: $i,SV22: $i,SV19: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV19 @ SV22 )
| ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(182,plain,
! [SV19: $i,SV22: $i,SV16: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
| ( apply @ SV5 @ SV19 @ SV22 ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV31: $i] :
( ( ( ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SY183 @ SV20 ) )
| ~ ( member @ SY184 @ SV12 ) )
| ~ ( member @ SY185 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SY183 ) )
| ~ ( apply @ SV6 @ SY184 @ SY185 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SY184 )
| ( apply @ SV23 @ SY183 @ SY185 ) )
| ~ ( ~ ( apply @ SV23 @ SY183 @ SY185 )
| ( apply @ SV17 @ SV31 @ SY184 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( maps @ SV6 @ SV12 @ SV20 )
| ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
= $true )
| ( ( ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(186,plain,
! [SV25: $i,SV24: $i,SV21: $i,SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) ) )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(187,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) ) )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(188,plain,
! [SV9: $i,SV27: $i,SV3: $i,SV14: $i] :
( ( ( ! [SY178: $i] :
~ ~ ( ~ ( member @ SY178 @ SV14 )
| ~ ( apply @ SV3 @ SV27 @ SY178 ) ) )
= $false )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) )
| ~ ( member @ SV30 @ SV14 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(190,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(191,plain,
! [SV9: $i,SV3: $i,SV14: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( member @ SV32 @ SV14 )
| ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 ) ) )
= $true )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV16: $i,SV11: $i,SV22: $i,SV19: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV19 @ SV22 ) )
= $true )
| ( ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV19: $i,SV22: $i,SV16: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 ) )
= $true )
| ( ( apply @ SV5 @ SV19 @ SV22 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( maps @ SV6 @ SV12 @ SV20 ) )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(195,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(196,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ! [SY186: $i,SY187: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SY186 @ SV12 ) )
| ~ ( member @ SY187 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) )
| ~ ( apply @ SV6 @ SY186 @ SY187 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SY186 )
| ( apply @ SV23 @ SV33 @ SY187 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SY187 )
| ( apply @ SV17 @ SV31 @ SY186 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( maps @ SV6 @ SV12 @ SV20 ) )
= $true )
| ( ( ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
= $true )
| ( ( ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(198,plain,
! [SV25: $i,SV24: $i,SV21: $i,SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(199,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) )
| ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(200,plain,
! [SV14: $i,SV3: $i,SV27: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) @ SV14 )
| ~ ( apply @ SV3 @ SV27 @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) ) ) )
= $false )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[188]) ).
thf(201,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) )
| ~ ( member @ SV30 @ SV14 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ! [SY188: $i,SY189: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ SY188 @ SV14 ) )
| ~ ( member @ SY189 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SY188 )
| ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SY189 ) )
| ( SY188 = SY189 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[190]) ).
thf(203,plain,
! [SV9: $i,SV3: $i,SV14: $i,SV32: $i] :
( ( ( ~ ( ~ ( member @ SV32 @ SV14 )
| ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(204,plain,
! [SV16: $i,SV11: $i,SV22: $i,SV19: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV19 @ SV22 )
= $false )
| ( ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(205,plain,
! [SV19: $i,SV22: $i,SV16: $i,SV11: $i,SV5: $i] :
( ( ( apply @ ( inverse_function @ SV5 @ SV11 @ SV16 ) @ SV22 @ SV19 )
= $false )
| ( ( apply @ SV5 @ SV19 @ SV22 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(206,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( maps @ SV6 @ SV12 @ SV20 )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(207,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(208,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ! [SY190: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SY190 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) )
| ~ ( apply @ SV6 @ SV34 @ SY190 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SY190 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SY190 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( ~ ( one_to_one @ SV6 @ SV12 @ SV20 ) )
= $true )
| ( ( ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV25: $i,SV24: $i,SV21: $i,SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 ) )
= $true )
| ( ( ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(211,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(212,plain,
! [SV14: $i,SV3: $i,SV27: $i,SV9: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) @ SV14 )
| ~ ( apply @ SV3 @ SV27 @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) ) ) )
= $true )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(213,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) )
| ~ ( member @ SV30 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(214,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ! [SY191: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
| ~ ( member @ SY191 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) )
| ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SY191 ) )
| ( ( sK8_SY188 @ SV9 @ SV14 @ SV3 )
= SY191 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[202]) ).
thf(215,plain,
! [SV9: $i,SV3: $i,SV14: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV14 )
| ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 ) )
= $true )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(216,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) )
| ~ ( apply @ SV6 @ SV34 @ SV35 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(217,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( ~ ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(218,plain,
! [SV25: $i,SV24: $i,SV21: $i,SV18: $i,SV13: $i,SV7: $i,SV1: $i] :
( ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( ~ ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(219,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i] :
( ( ( ~ ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV14: $i,SV3: $i,SV27: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) @ SV14 )
| ~ ( apply @ SV3 @ SV27 @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) ) )
= $false )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) ) )
= $true )
| ( ( ~ ( member @ SV30 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(222,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
| ~ ( member @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) )
| ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) )
| ( ( sK8_SY188 @ SV9 @ SV14 @ SV3 )
= ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[214]) ).
thf(223,plain,
! [SV9: $i,SV3: $i,SV14: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV14 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 ) )
= $true )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(224,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) )
| ~ ( apply @ SV6 @ SV34 @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(225,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( ! [SY169: $i,SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( member @ SY170 @ SV20 ) )
| ~ ( member @ SY171 @ SV12 ) )
| ~ ( member @ SY172 @ SV20 ) )
| ~ ( apply @ SV6 @ SY169 @ SY170 ) )
| ~ ( apply @ SV6 @ SY171 @ SY172 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ SY169 @ SY171 )
| ( apply @ SV23 @ SY170 @ SY172 ) )
| ~ ( ~ ( apply @ SV23 @ SY170 @ SY172 )
| ( apply @ SV17 @ SY169 @ SY171 ) ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(226,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i] :
( ( ( ! [SY176: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY176 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY176 ) )
| ~ ( apply @ SV1 @ SY176 @ SV25 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i] :
( ( ( ! [SY177: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY177 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SY177 ) )
| ~ ( apply @ SV1 @ SY177 @ SV25 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(228,plain,
! [SV14: $i,SV3: $i,SV27: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) @ SV14 ) )
= $false )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(229,plain,
! [SV14: $i,SV9: $i,SV27: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ SV27 @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) ) )
= $false )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(230,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) ) )
= $false )
| ( ( ~ ( member @ SV30 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(231,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
| ~ ( member @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) @ SV14 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(232,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) )
| ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) )
| ( ( sK8_SY188 @ SV9 @ SV14 @ SV3 )
= ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(233,plain,
! [SV9: $i,SV3: $i,SV14: $i,SV32: $i] :
( ( ( member @ SV32 @ SV14 )
= $false )
| ( ( ~ ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 ) )
= $true )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(234,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) )
| ~ ( apply @ SV6 @ SV34 @ SV35 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(235,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ! [SY192: $i,SY193: $i,SY194: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ SY192 @ SV20 ) )
| ~ ( member @ SY193 @ SV12 ) )
| ~ ( member @ SY194 @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SY192 ) )
| ~ ( apply @ SV6 @ SY193 @ SY194 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SY193 )
| ( apply @ SV23 @ SY192 @ SY194 ) )
| ~ ( ~ ( apply @ SV23 @ SY192 @ SY194 )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SY193 ) ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[225]) ).
thf(236,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) ) )
| ~ ( apply @ SV1 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV25 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[226]) ).
thf(237,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV36 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SV36 ) )
| ~ ( apply @ SV1 @ SV36 @ SV25 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(238,plain,
! [SV14: $i,SV3: $i,SV27: $i,SV9: $i] :
( ( ( member @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(239,plain,
! [SV14: $i,SV9: $i,SV27: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV27 @ ( sK6_SY178 @ SV9 @ SV27 @ SV3 @ SV14 ) )
= $true )
| ( ( member @ SV27 @ SV9 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(240,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ SV9 )
| ~ ( member @ SV29 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV30 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(241,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
| ~ ( member @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) @ SV14 ) ) )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(242,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) )
| ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(243,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ( sK8_SY188 @ SV9 @ SV14 @ SV3 )
= ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(244,plain,
! [SV32: $i,SV9: $i,SV14: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( ~ ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(245,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) )
| ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(246,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ! [SY195: $i,SY196: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ SY195 @ SV12 ) )
| ~ ( member @ SY196 @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( apply @ SV6 @ SY195 @ SY196 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SY195 )
| ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SY196 ) )
| ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SY196 )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SY195 ) ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[235]) ).
thf(247,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) ) )
| ~ ( apply @ SV1 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV25 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(248,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV36 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SV36 ) )
| ~ ( apply @ SV1 @ SV36 @ SV25 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(249,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( ~ ( member @ SV28 @ SV9 ) )
= $true )
| ( ( ~ ( member @ SV29 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV30 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(250,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
| ~ ( member @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(251,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) )
| ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) ) )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(252,plain,
! [SV32: $i,SV3: $i,SV14: $i,SV9: $i] :
( ( ( ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY131 @ SV9 )
| ~ ( member @ SY132 @ SV14 ) )
| ~ ( member @ SY133 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY131 @ SY132 )
| ~ ( apply @ SV3 @ SY131 @ SY133 ) )
| ( SY132 = SY133 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(253,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ! [SY197: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ SY197 @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( apply @ SV6 @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SY197 ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SY197 ) )
| ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SY197 )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[246]) ).
thf(255,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) ) )
| ~ ( apply @ SV1 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV25 ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(256,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( member @ SV36 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SV36 ) )
| ~ ( apply @ SV1 @ SV36 @ SV25 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(257,plain,
! [SV3: $i,SV30: $i,SV14: $i,SV29: $i,SV9: $i,SV28: $i] :
( ( ( member @ SV28 @ SV9 )
= $false )
| ( ( ~ ( member @ SV29 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV30 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(258,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(259,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(260,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) )
| ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(261,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ! [SY198: $i,SY199: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ SY198 @ SV14 ) )
| ~ ( member @ SY199 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SY198 )
| ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SY199 ) )
| ( SY198 = SY199 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[252]) ).
thf(262,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) ) )
= $false )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(263,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( apply @ SV6 @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( ~ ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[254]) ).
thf(264,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(265,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV25: $i,SV13: $i,SV21: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV25 ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(266,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( member @ SV36 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SV36 ) ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV36 @ SV25 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(267,plain,
! [SV3: $i,SV30: $i,SV9: $i,SV28: $i,SV14: $i,SV29: $i] :
( ( ( member @ SV29 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( ~ ( member @ SV30 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(268,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) ) )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(269,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( member @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) @ SV14 )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(270,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(271,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(272,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ! [SY200: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
| ~ ( member @ SY200 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) )
| ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SY200 ) )
| ( ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 )
= SY200 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[261]) ).
thf(273,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
| ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(274,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( apply @ SV6 @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(275,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(276,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( ~ ( ~ ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(277,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV25: $i,SV13: $i,SV21: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV25 )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(278,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( ~ ( ~ ( member @ SV36 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SV36 ) ) )
= $false )
| ( ( ~ ( apply @ SV1 @ SV36 @ SV25 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(279,plain,
! [SV3: $i,SV29: $i,SV9: $i,SV28: $i,SV14: $i,SV30: $i] :
( ( ( member @ SV30 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( member @ SV29 @ SV14 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
| ( SV29 = SV30 ) )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(280,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(281,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(282,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ ( sK9_SY191 @ SV9 @ SV14 @ SV3 ) )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(283,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
| ~ ( member @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) )
| ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) )
| ( ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 )
= ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[272]) ).
thf(284,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(285,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( apply @ SV6 @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(286,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(287,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(288,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV18 )
| ~ ( apply @ SV7 @ SV24 @ SV36 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV36 @ SV25 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(289,plain,
! [SV9: $i,SV14: $i,SV30: $i,SV29: $i,SV28: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) ) )
= $true )
| ( ( SV29 = SV30 )
= $true )
| ( ( member @ SV29 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( member @ SV30 @ SV14 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(290,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(291,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(292,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
| ~ ( member @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(293,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) )
| ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) )
| ( ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 )
= ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(294,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) ) )
= $false )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(295,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
| ~ ( apply @ SV6 @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(296,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(297,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( ~ ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(298,plain,
! [SV18: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(299,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV18 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV24 @ SV36 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV36 @ SV25 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(300,plain,
! [SV9: $i,SV14: $i,SV30: $i,SV29: $i,SV28: $i,SV3: $i] :
( ( ( ~ ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) ) )
= $false )
| ( ( SV29 = SV30 )
= $true )
| ( ( member @ SV29 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( member @ SV30 @ SV14 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(301,plain,
! [SV9: $i,SV14: $i,SV3: $i] :
( ( ( member @ ( sK7_SY131 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(302,plain,
! [SV3: $i,SV14: $i,SV9: $i] :
( ( ( member @ ( sK8_SY188 @ SV9 @ SV14 @ SV3 ) @ SV14 )
= $true )
| ( ( member @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(303,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
| ~ ( member @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) ) )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(304,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) )
| ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(305,plain,
! [SV32: $i,SV3: $i,SV14: $i,SV9: $i] :
( ( ( ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 )
= ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(306,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
| ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(307,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(308,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( apply @ SV6 @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(309,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(310,plain,
! [SV18: $i,SV7: $i,SV24: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i] :
( ( ( member @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) @ SV18 )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(311,plain,
! [SV18: $i,SV1: $i,SV25: $i,SV13: $i,SV21: $i,SV24: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV24 @ ( sK11_SY176 @ SV21 @ SV13 @ SV25 @ SV1 @ SV24 @ SV7 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $false )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(312,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV24: $i,SV7: $i,SV18: $i,SV36: $i] :
( ( ( member @ SV36 @ SV18 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV24 @ SV36 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV36 @ SV25 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(313,plain,
! [SV9: $i,SV14: $i,SV30: $i,SV29: $i,SV28: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ SV28 @ SV29 )
| ~ ( apply @ SV3 @ SV28 @ SV30 ) )
= $true )
| ( ( SV29 = SV30 )
= $true )
| ( ( member @ SV29 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( member @ SV30 @ SV14 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(314,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
| ~ ( member @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(315,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( ~ ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) )
| ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) ) )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(316,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(317,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(318,plain,
! [SV23: $i,SV17: $i,SV20: $i,SV12: $i,SV6: $i] :
( ( ( apply @ SV6 @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(319,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(320,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV23: $i] :
( ( ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $false )
| ( ( ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(321,plain,
! [SV21: $i,SV13: $i,SV25: $i,SV1: $i,SV18: $i,SV36: $i,SV24: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV24 @ SV36 )
= $false )
| ( ( member @ SV36 @ SV18 )
= $false )
| ( ( ~ ( apply @ SV1 @ SV36 @ SV25 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(322,plain,
! [SV9: $i,SV14: $i,SV30: $i,SV29: $i,SV28: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ SV28 @ SV29 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV28 @ SV30 ) )
= $true )
| ( ( SV29 = SV30 )
= $true )
| ( ( member @ SV29 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( member @ SV30 @ SV14 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(323,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(324,plain,
! [SV32: $i,SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(325,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) )
| ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(326,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) ) )
= $false )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(327,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(328,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(329,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(330,plain,
! [SV21: $i,SV13: $i,SV24: $i,SV7: $i,SV18: $i,SV25: $i,SV36: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV36 @ SV25 )
= $false )
| ( ( member @ SV36 @ SV18 )
= $false )
| ( ( apply @ SV7 @ SV24 @ SV36 )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV7 @ SV13 @ SV18 @ SV21 ) @ SV24 @ SV25 )
= $true )
| ( ( member @ SV24 @ SV13 )
= $false )
| ( ( member @ SV25 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(331,plain,
! [SV9: $i,SV14: $i,SV30: $i,SV29: $i,SV28: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV28 @ SV29 )
= $false )
| ( ( ~ ( apply @ SV3 @ SV28 @ SV30 ) )
= $true )
| ( ( SV29 = SV30 )
= $true )
| ( ( member @ SV29 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( member @ SV30 @ SV14 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(332,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) ) )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(333,plain,
! [SV32: $i,SV3: $i,SV14: $i,SV9: $i] :
( ( ( member @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(334,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(335,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(336,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
| ~ ( member @ SV34 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(337,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(338,plain,
! [SV12: $i,SV20: $i,SV17: $i,SV23: $i,SV6: $i] :
( ( ( ~ ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(339,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
| ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(340,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(341,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $false )
| ( ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(342,plain,
! [SV9: $i,SV14: $i,SV29: $i,SV30: $i,SV28: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV28 @ SV30 )
= $false )
| ( ( apply @ SV3 @ SV28 @ SV29 )
= $false )
| ( ( SV29 = SV30 )
= $true )
| ( ( member @ SV29 @ SV14 )
= $false )
| ( ( member @ SV28 @ SV9 )
= $false )
| ( ( member @ SV30 @ SV14 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(343,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(344,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(345,plain,
! [SV9: $i,SV14: $i,SV32: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ ( sK17_SY200 @ SV9 @ SV14 @ SV3 @ SV32 ) )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(346,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) ) )
= $true )
| ( ( ~ ( member @ SV34 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(347,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(348,plain,
! [SV12: $i,SV20: $i,SV17: $i,SV23: $i,SV6: $i] :
( ( ( apply @ SV6 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(349,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) ) )
= $false )
| ( ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(350,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV23: $i,SV17: $i] :
( ( ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $false )
| ( ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(351,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV23: $i] :
( ( ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(352,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( ~ ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(353,plain,
! [SV32: $i,SV3: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 ) )
= $false )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(354,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) ) )
= $false )
| ( ( ~ ( member @ SV34 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(355,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
| ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(356,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV12: $i,SV23: $i] :
( ( ( apply @ SV23 @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( apply @ SV17 @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(357,plain,
! [SV9: $i,SV14: $i,SV3: $i,SV32: $i] :
( ( ( member @ ( sK14_SY131 @ SV32 @ SV3 @ SV14 @ SV9 ) @ SV9 )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(358,plain,
! [SV32: $i,SV3: $i,SV14: $i,SV9: $i] :
( ( ( member @ ( sK16_SY198 @ SV9 @ SV14 @ SV3 @ SV32 ) @ SV14 )
= $true )
| ( ( member @ SV32 @ SV14 )
= $false )
| ( ( apply @ SV3 @ ( sK5_SY129 @ SV3 @ SV14 @ SV9 ) @ SV32 )
= $false )
| ( ( maps @ SV3 @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(359,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV12 )
| ~ ( member @ SV33 @ SV20 ) )
= $true )
| ( ( ~ ( member @ SV34 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(360,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(361,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(362,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV33 @ SV20 ) )
= $true )
| ( ( ~ ( member @ SV34 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(363,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(364,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( member @ ( sK15_SY197 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(365,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV20: $i,SV33: $i,SV12: $i,SV31: $i] :
( ( ( member @ SV31 @ SV12 )
= $false )
| ( ( ~ ( member @ SV33 @ SV20 ) )
= $true )
| ( ( ~ ( member @ SV34 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(366,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
| ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(367,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV34: $i,SV12: $i,SV31: $i,SV20: $i,SV33: $i] :
( ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( ~ ( member @ SV34 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(368,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(369,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(370,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV35: $i,SV20: $i,SV33: $i,SV31: $i,SV12: $i,SV34: $i] :
( ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( ~ ( member @ SV35 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(371,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) ) )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(372,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( member @ ( sK13_SY195 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV12 )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(373,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV34: $i,SV12: $i,SV31: $i,SV33: $i,SV20: $i,SV35: $i] :
( ( ( member @ SV35 @ SV20 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( ~ ( apply @ SV6 @ SV31 @ SV33 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(374,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(375,plain,
! [SV23: $i,SV17: $i,SV35: $i,SV20: $i,SV12: $i,SV34: $i,SV33: $i,SV31: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( ~ ( apply @ SV6 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(376,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(377,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 ) )
= $false )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(378,plain,
! [SV23: $i,SV17: $i,SV12: $i,SV31: $i,SV33: $i,SV20: $i,SV35: $i,SV34: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) ) )
= $true )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(379,plain,
! [SV12: $i,SV20: $i,SV6: $i,SV17: $i,SV23: $i] :
( ( ( member @ ( sK10_SY169 @ SV23 @ SV17 @ SV6 @ SV20 @ SV12 ) @ SV12 )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(380,plain,
! [SV23: $i,SV17: $i,SV6: $i,SV20: $i,SV12: $i] :
( ( ( member @ ( sK12_SY192 @ SV12 @ SV20 @ SV6 @ SV17 @ SV23 ) @ SV20 )
= $true )
| ( ( maps @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( one_to_one @ SV6 @ SV12 @ SV20 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(381,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV35: $i,SV33: $i,SV23: $i,SV34: $i,SV31: $i,SV17: $i] :
( ( ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
| ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) )
= $false )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(382,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV35: $i,SV33: $i,SV23: $i,SV34: $i,SV31: $i,SV17: $i] :
( ( ( ~ ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) ) )
= $false )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(383,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV34: $i,SV31: $i,SV17: $i,SV35: $i,SV33: $i,SV23: $i] :
( ( ( ~ ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) ) )
= $false )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(384,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV35: $i,SV33: $i,SV23: $i,SV34: $i,SV31: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ SV31 @ SV34 )
| ( apply @ SV23 @ SV33 @ SV35 ) )
= $true )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(385,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV34: $i,SV31: $i,SV17: $i,SV35: $i,SV33: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ SV33 @ SV35 )
| ( apply @ SV17 @ SV31 @ SV34 ) )
= $true )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(386,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV35: $i,SV33: $i,SV23: $i,SV34: $i,SV31: $i,SV17: $i] :
( ( ( ~ ( apply @ SV17 @ SV31 @ SV34 ) )
= $true )
| ( ( apply @ SV23 @ SV33 @ SV35 )
= $true )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(387,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV34: $i,SV31: $i,SV17: $i,SV35: $i,SV33: $i,SV23: $i] :
( ( ( ~ ( apply @ SV23 @ SV33 @ SV35 ) )
= $true )
| ( ( apply @ SV17 @ SV31 @ SV34 )
= $true )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(388,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV35: $i,SV33: $i,SV23: $i,SV34: $i,SV31: $i,SV17: $i] :
( ( ( apply @ SV17 @ SV31 @ SV34 )
= $false )
| ( ( apply @ SV23 @ SV33 @ SV35 )
= $true )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(389,plain,
! [SV20: $i,SV12: $i,SV6: $i,SV34: $i,SV31: $i,SV17: $i,SV35: $i,SV33: $i,SV23: $i] :
( ( ( apply @ SV23 @ SV33 @ SV35 )
= $false )
| ( ( apply @ SV17 @ SV31 @ SV34 )
= $true )
| ( ( apply @ SV6 @ SV31 @ SV33 )
= $false )
| ( ( member @ SV34 @ SV12 )
= $false )
| ( ( member @ SV31 @ SV12 )
= $false )
| ( ( member @ SV33 @ SV20 )
= $false )
| ( ( member @ SV35 @ SV20 )
= $false )
| ( ( apply @ SV6 @ SV34 @ SV35 )
= $false )
| ( ( isomorphism @ SV6 @ SV12 @ SV17 @ SV20 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(390,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,389,388,380,379,372,364,358,357,356,351,350,348,345,344,342,341,333,330,318,311,310,305,302,301,282,281,277,269,243,239,238,207,206,205,204,161,152,151,137,136,127,60,52]) ).
thf(391,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET714+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 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
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 14:52:12 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 158.45/26.69
% 158.45/26.69 No.of.Axioms: 6
% 158.45/26.69
% 158.45/26.69 Length.of.Defs: 0
% 158.45/26.69
% 158.45/26.69 Contains.Choice.Funs: false
% 158.45/26.69 ...................
% 158.45/26.69
% 158.45/26.69 ********************************
% 158.45/26.69 * All subproblems solved! *
% 158.45/26.69 ********************************
% 158.45/26.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,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:390,loop_count:0,foatp_calls:1,translation:fof_full)
% 158.45/26.69
% 158.45/26.69 %**** Beginning of derivation protocol ****
% 158.45/26.69 % SZS output start CNFRefutation
% See solution above
% 158.45/26.69
% 158.45/26.69 %**** End of derivation protocol ****
% 158.45/26.69 %**** no. of clauses in derivation: 369 ****
% 158.45/26.69 %**** clause counter: 390 ****
% 158.45/26.69
% 158.45/26.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,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:390,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------