%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET724+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 : n012.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 10:40:56 AM UTC 2026
% Result : Theorem 40.03s 6.84s
% Output : CNFRefutation 40.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 6
% Syntax : Number of formulae : 313 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 3458 ( 938 equ; 0 cnn)
% Maximal formula atoms : 10 ( 11 avg)
% Number of connectives : 9793 (2257 ~;1381 |; 75 &;6035 @)
% ( 15 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 9 con; 0-7 aty)
% Number of variables : 1691 ( 0 ^;1682 !; 9 ?;1691 :)
% 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_SY175,type,
sK10_SY175: $i > $i > $i > $i > $i ).
thf(tp_sK11_SY143,type,
sK11_SY143: $i > $i > $i > $i ).
thf(tp_sK12_SY168,type,
sK12_SY168: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY176,type,
sK13_SY176: $i > $i > $i > $i > $i ).
thf(tp_sK14_SY145,type,
sK14_SY145: $i > $i > $i > $i ).
thf(tp_sK15_SY181,type,
sK15_SY181: $i > $i > $i > $i ).
thf(tp_sK16_SY183,type,
sK16_SY183: $i > $i > $i > $i ).
thf(tp_sK17_SY166,type,
sK17_SY166: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK18_SY145,type,
sK18_SY145: $i > $i > $i > $i > $i ).
thf(tp_sK19_SY184,type,
sK19_SY184: $i > $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK20_SY186,type,
sK20_SY186: $i > $i > $i > $i > $i ).
thf(tp_sK2_SY37,type,
sK2_SY37: $i ).
thf(tp_sK3_SY42,type,
sK3_SY42: $i ).
thf(tp_sK4_SY46,type,
sK4_SY46: $i ).
thf(tp_sK5_SY49,type,
sK5_SY49: $i ).
thf(tp_sK6_SY51,type,
sK6_SY51: $i ).
thf(tp_sK7_SY129,type,
sK7_SY129: $i > $i > $i > $i ).
thf(tp_sK8_SY156,type,
sK8_SY156: $i > $i > $i > $i > $i ).
thf(tp_sK9_SY172,type,
sK9_SY172: $i > $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(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(11,axiom,
! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
thf(14,axiom,
! [F: $i,G: $i,A: $i,B: $i] :
( ( equal_maps @ F @ G @ A @ B )
<=> ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ G @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_maps) ).
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,G: $i,H: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( maps @ G @ B @ C )
& ( maps @ H @ B @ C )
& ( surjective @ F @ A @ B )
& ( equal_maps @ ( compose_function @ G @ F @ A @ B @ C ) @ ( compose_function @ H @ F @ A @ B @ C ) @ A @ C ) )
=> ( equal_maps @ G @ H @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII15) ).
thf(30,negated_conjecture,
( ( ! [F: $i,G: $i,H: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( maps @ G @ B @ C )
& ( maps @ H @ B @ C )
& ( surjective @ F @ A @ B )
& ( equal_maps @ ( compose_function @ G @ F @ A @ B @ C ) @ ( compose_function @ H @ F @ A @ B @ C ) @ A @ C ) )
=> ( equal_maps @ G @ H @ B @ C ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [F: $i,G: $i,H: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( maps @ G @ B @ C )
& ( maps @ H @ B @ C )
& ( surjective @ F @ A @ B )
& ( equal_maps @ ( compose_function @ G @ F @ A @ B @ C ) @ ( compose_function @ H @ F @ A @ B @ C ) @ A @ C ) )
=> ( equal_maps @ G @ H @ B @ C ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,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(33,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [F: $i,G: $i,A: $i,B: $i] :
( ( equal_maps @ F @ G @ A @ B )
<=> ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ G @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(35,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(36,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(37,plain,
( ( ! [SY37: $i,SY38: $i,SY39: $i,SY40: $i,SY41: $i] :
( ( ( maps @ sK1_F @ SY39 @ SY40 )
& ( maps @ SY37 @ SY40 @ SY41 )
& ( maps @ SY38 @ SY40 @ SY41 )
& ( surjective @ sK1_F @ SY39 @ SY40 )
& ( equal_maps @ ( compose_function @ SY37 @ sK1_F @ SY39 @ SY40 @ SY41 ) @ ( compose_function @ SY38 @ sK1_F @ SY39 @ SY40 @ SY41 ) @ SY39 @ SY41 ) )
=> ( equal_maps @ SY37 @ SY38 @ SY40 @ SY41 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(38,plain,
( ( ! [SY42: $i,SY43: $i,SY44: $i,SY45: $i] :
( ( ( maps @ sK1_F @ SY43 @ SY44 )
& ( maps @ sK2_SY37 @ SY44 @ SY45 )
& ( maps @ SY42 @ SY44 @ SY45 )
& ( surjective @ sK1_F @ SY43 @ SY44 )
& ( equal_maps @ ( compose_function @ sK2_SY37 @ sK1_F @ SY43 @ SY44 @ SY45 ) @ ( compose_function @ SY42 @ sK1_F @ SY43 @ SY44 @ SY45 ) @ SY43 @ SY45 ) )
=> ( equal_maps @ sK2_SY37 @ SY42 @ SY44 @ SY45 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(39,plain,
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ( ( maps @ sK1_F @ SY46 @ SY47 )
& ( maps @ sK2_SY37 @ SY47 @ SY48 )
& ( maps @ sK3_SY42 @ SY47 @ SY48 )
& ( surjective @ sK1_F @ SY46 @ SY47 )
& ( equal_maps @ ( compose_function @ sK2_SY37 @ sK1_F @ SY46 @ SY47 @ SY48 ) @ ( compose_function @ sK3_SY42 @ sK1_F @ SY46 @ SY47 @ SY48 ) @ SY46 @ SY48 ) )
=> ( equal_maps @ sK2_SY37 @ sK3_SY42 @ SY47 @ SY48 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ! [SY49: $i,SY50: $i] :
( ( ( maps @ sK1_F @ sK4_SY46 @ SY49 )
& ( maps @ sK2_SY37 @ SY49 @ SY50 )
& ( maps @ sK3_SY42 @ SY49 @ SY50 )
& ( surjective @ sK1_F @ sK4_SY46 @ SY49 )
& ( equal_maps @ ( compose_function @ sK2_SY37 @ sK1_F @ sK4_SY46 @ SY49 @ SY50 ) @ ( compose_function @ sK3_SY42 @ sK1_F @ sK4_SY46 @ SY49 @ SY50 ) @ sK4_SY46 @ SY50 ) )
=> ( equal_maps @ sK2_SY37 @ sK3_SY42 @ SY49 @ SY50 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ! [SY51: $i] :
( ( ( maps @ sK1_F @ sK4_SY46 @ sK5_SY49 )
& ( maps @ sK2_SY37 @ sK5_SY49 @ SY51 )
& ( maps @ sK3_SY42 @ sK5_SY49 @ SY51 )
& ( surjective @ sK1_F @ sK4_SY46 @ sK5_SY49 )
& ( equal_maps @ ( compose_function @ sK2_SY37 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ SY51 ) @ ( compose_function @ sK3_SY42 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ SY51 ) @ sK4_SY46 @ SY51 ) )
=> ( equal_maps @ sK2_SY37 @ sK3_SY42 @ sK5_SY49 @ SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( ( ( maps @ sK1_F @ sK4_SY46 @ sK5_SY49 )
& ( maps @ sK2_SY37 @ sK5_SY49 @ sK6_SY51 )
& ( maps @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 )
& ( surjective @ sK1_F @ sK4_SY46 @ sK5_SY49 )
& ( equal_maps @ ( compose_function @ sK2_SY37 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ sK6_SY51 ) @ ( compose_function @ sK3_SY42 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ sK6_SY51 ) @ sK4_SY46 @ sK6_SY51 ) )
=> ( equal_maps @ sK2_SY37 @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( maps @ sK1_F @ sK4_SY46 @ sK5_SY49 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(44,plain,
( ( maps @ sK2_SY37 @ sK5_SY49 @ sK6_SY51 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(45,plain,
( ( maps @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(46,plain,
( ( surjective @ sK1_F @ sK4_SY46 @ sK5_SY49 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(47,plain,
( ( equal_maps @ ( compose_function @ sK2_SY37 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ sK6_SY51 ) @ ( compose_function @ sK3_SY42 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ sK6_SY51 ) @ sK4_SY46 @ sK6_SY51 )
= $true ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(48,plain,
( ( equal_maps @ sK2_SY37 @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 )
= $false ),
inference(standard_cnf,[status(thm)],[42]) ).
thf(49,plain,
( ( ~ ( equal_maps @ sK2_SY37 @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 ) )
= $true ),
inference(polarity_switch,[status(thm)],[48]) ).
thf(50,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)],[36]) ).
thf(51,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)],[35]) ).
thf(52,plain,
( ( ! [F: $i,G: $i,A: $i,B: $i] :
( ( equal_maps @ F @ G @ A @ B )
<=> ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ G @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(53,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(54,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)],[32]) ).
thf(55,plain,
( ( equal_maps @ ( compose_function @ sK2_SY37 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ sK6_SY51 ) @ ( compose_function @ sK3_SY42 @ sK1_F @ sK4_SY46 @ sK5_SY49 @ sK6_SY51 ) @ sK4_SY46 @ sK6_SY51 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(56,plain,
( ( surjective @ sK1_F @ sK4_SY46 @ sK5_SY49 )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(57,plain,
( ( maps @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(58,plain,
( ( maps @ sK2_SY37 @ sK5_SY49 @ sK6_SY51 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(59,plain,
( ( maps @ sK1_F @ sK4_SY46 @ sK5_SY49 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(60,plain,
( ( ~ ( equal_maps @ sK2_SY37 @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(61,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)],[51]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( surjective @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( member @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) )
| ( surjective @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(63,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)],[54]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( equal_maps @ SX0 @ SX1 @ SX2 @ SX3 )
| ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( member @ SX5 @ SX3 ) )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX4 @ SX5 )
| ~ ( apply @ SX1 @ SX4 @ SX6 ) )
| ( SX5 = SX6 ) ) )
| ~ ( ~ ! [SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( member @ SX5 @ SX3 ) )
| ~ ( member @ SX6 @ SX3 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX4 @ SX5 )
| ~ ( apply @ SX1 @ SX4 @ SX6 ) )
| ( SX5 = SX6 ) )
| ( equal_maps @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(65,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)],[50]) ).
thf(66,plain,
( ( equal_maps @ sK2_SY37 @ sK3_SY42 @ sK5_SY49 @ sK6_SY51 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV1: $i] :
( ( ! [SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i,SY57: $i] :
( ~ ~ ( ~ ( member @ SY56 @ SY53 )
| ~ ( member @ SY57 @ SY55 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SY52 @ SY53 @ SY54 @ SY55 ) @ SY56 @ SY57 )
| ~ ! [SY58: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY58 @ SY54 )
| ~ ( apply @ SY52 @ SY56 @ SY58 ) )
| ~ ( apply @ SV1 @ SY58 @ SY57 ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY59 @ SY54 )
| ~ ( apply @ SY52 @ SY56 @ SY59 ) )
| ~ ( apply @ SV1 @ SY59 @ SY57 ) )
| ( apply @ ( compose_function @ SV1 @ SY52 @ SY53 @ SY54 @ SY55 ) @ SY56 @ SY57 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV2: $i] :
( ( ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( surjective @ SV2 @ SY60 @ SY61 )
| ! [SY62: $i] :
( ~ ( member @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( member @ SY63 @ SY60 )
| ~ ( apply @ SV2 @ SY63 @ SY62 ) ) ) )
| ~ ( ~ ! [SY64: $i] :
( ~ ( member @ SY64 @ SY61 )
| ~ ! [SY65: $i] :
~ ~ ( ~ ( member @ SY65 @ SY60 )
| ~ ( apply @ SV2 @ SY65 @ SY64 ) ) )
| ( surjective @ SV2 @ SY60 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV3: $i] :
( ( ! [SY66: $i,SY67: $i] :
~ ( ~ ( ~ ( one_to_one @ SV3 @ SY66 @ SY67 )
| ~ ( ~ ( injective @ SV3 @ SY66 @ SY67 )
| ~ ( surjective @ SV3 @ SY66 @ SY67 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV3 @ SY66 @ SY67 )
| ~ ( surjective @ SV3 @ SY66 @ SY67 ) )
| ( one_to_one @ SV3 @ SY66 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV4: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i] :
~ ( ~ ( ~ ( equal_maps @ SV4 @ SY68 @ SY69 @ SY70 )
| ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY71 @ SY69 )
| ~ ( member @ SY72 @ SY70 ) )
| ~ ( member @ SY73 @ SY70 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY71 @ SY72 )
| ~ ( apply @ SY68 @ SY71 @ SY73 ) )
| ( SY72 = SY73 ) ) )
| ~ ( ~ ! [SY74: $i,SY75: $i,SY76: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY74 @ SY69 )
| ~ ( member @ SY75 @ SY70 ) )
| ~ ( member @ SY76 @ SY70 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY74 @ SY75 )
| ~ ( apply @ SY68 @ SY74 @ SY76 ) )
| ( SY75 = SY76 ) )
| ( equal_maps @ SV4 @ SY68 @ SY69 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV5: $i] :
( ( ! [SY77: $i,SY78: $i] :
~ ( ~ ( ~ ( maps @ SV5 @ SY77 @ SY78 )
| ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SY77 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SY78 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SY77 )
| ~ ( member @ SY82 @ SY78 ) )
| ~ ( member @ SY83 @ SY78 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SY77 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SY78 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SY77 )
| ~ ( member @ SY87 @ SY78 ) )
| ~ ( member @ SY88 @ SY78 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
| ( maps @ SV5 @ SY77 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i,SY92: $i,SY93: $i] :
( ~ ~ ( ~ ( member @ SY92 @ SY89 )
| ~ ( member @ SY93 @ SY91 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SY89 @ SY90 @ SY91 ) @ SY92 @ SY93 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY94 @ SY90 )
| ~ ( apply @ SV6 @ SY92 @ SY94 ) )
| ~ ( apply @ SV1 @ SY94 @ SY93 ) ) )
| ~ ( ~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY95 @ SY90 )
| ~ ( apply @ SV6 @ SY92 @ SY95 ) )
| ~ ( apply @ SV1 @ SY95 @ SY93 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SY89 @ SY90 @ SY91 ) @ SY92 @ SY93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY96: $i] :
~ ( ~ ( ~ ( surjective @ SV2 @ SV7 @ SY96 )
| ! [SY97: $i] :
( ~ ( member @ SY97 @ SY96 )
| ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ SV7 )
| ~ ( apply @ SV2 @ SY98 @ SY97 ) ) ) )
| ~ ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SY96 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV7 )
| ~ ( apply @ SV2 @ SY100 @ SY99 ) ) )
| ( surjective @ SV2 @ SV7 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY101: $i] :
~ ( ~ ( ~ ( one_to_one @ SV3 @ SV8 @ SY101 )
| ~ ( ~ ( injective @ SV3 @ SV8 @ SY101 )
| ~ ( surjective @ SV3 @ SV8 @ SY101 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV3 @ SV8 @ SY101 )
| ~ ( surjective @ SV3 @ SV8 @ SY101 ) )
| ( one_to_one @ SV3 @ SV8 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY102: $i,SY103: $i] :
~ ( ~ ( ~ ( equal_maps @ SV4 @ SV9 @ SY102 @ SY103 )
| ! [SY104: $i,SY105: $i,SY106: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY104 @ SY102 )
| ~ ( member @ SY105 @ SY103 ) )
| ~ ( member @ SY106 @ SY103 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY104 @ SY105 )
| ~ ( apply @ SV9 @ SY104 @ SY106 ) )
| ( SY105 = SY106 ) ) )
| ~ ( ~ ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SY102 )
| ~ ( member @ SY108 @ SY103 ) )
| ~ ( member @ SY109 @ SY103 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY107 @ SY108 )
| ~ ( apply @ SV9 @ SY107 @ SY109 ) )
| ( SY108 = SY109 ) )
| ( equal_maps @ SV4 @ SV9 @ SY102 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY110: $i] :
~ ( ~ ( ~ ( maps @ SV5 @ SV10 @ SY110 )
| ~ ( ~ ! [SY111: $i] :
( ~ ( member @ SY111 @ SV10 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SY110 )
| ~ ( apply @ SV5 @ SY111 @ SY80 ) ) )
| ~ ! [SY113: $i,SY114: $i,SY115: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY113 @ SV10 )
| ~ ( member @ SY114 @ SY110 ) )
| ~ ( member @ SY115 @ SY110 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY113 @ SY114 )
| ~ ( apply @ SV5 @ SY113 @ SY115 ) )
| ( SY114 = SY115 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY116: $i] :
( ~ ( member @ SY116 @ SV10 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SY110 )
| ~ ( apply @ SV5 @ SY116 @ SY85 ) ) )
| ~ ! [SY118: $i,SY119: $i,SY120: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY118 @ SV10 )
| ~ ( member @ SY119 @ SY110 ) )
| ~ ( member @ SY120 @ SY110 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY118 @ SY119 )
| ~ ( apply @ SV5 @ SY118 @ SY120 ) )
| ( SY119 = SY120 ) ) )
| ( maps @ SV5 @ SV10 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ! [SY121: $i,SY122: $i,SY123: $i,SY124: $i] :
( ~ ~ ( ~ ( member @ SY123 @ SV11 )
| ~ ( member @ SY124 @ SY122 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SY121 @ SY122 ) @ SY123 @ SY124 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY94 @ SY121 )
| ~ ( apply @ SV6 @ SY123 @ SY94 ) )
| ~ ( apply @ SV1 @ SY94 @ SY124 ) ) )
| ~ ( ~ ~ ! [SY95: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY95 @ SY121 )
| ~ ( apply @ SV6 @ SY123 @ SY95 ) )
| ~ ( apply @ SV1 @ SY95 @ SY124 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SY121 @ SY122 ) @ SY123 @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( surjective @ SV2 @ SV7 @ SV12 )
| ! [SY127: $i] :
( ~ ( member @ SY127 @ SV12 )
| ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ SV7 )
| ~ ( apply @ SV2 @ SY98 @ SY127 ) ) ) )
| ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV12 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV7 )
| ~ ( apply @ SV2 @ SY100 @ SY129 ) ) )
| ( surjective @ SV2 @ SV7 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( one_to_one @ SV3 @ SV8 @ SV13 )
| ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
| ( one_to_one @ SV3 @ SV8 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ! [SY131: $i] :
~ ( ~ ( ~ ( equal_maps @ SV4 @ SV9 @ SV14 @ SY131 )
| ! [SY132: $i,SY133: $i,SY134: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY132 @ SV14 )
| ~ ( member @ SY133 @ SY131 ) )
| ~ ( member @ SY134 @ SY131 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY132 @ SY133 )
| ~ ( apply @ SV9 @ SY132 @ SY134 ) )
| ( SY133 = SY134 ) ) )
| ~ ( ~ ! [SY135: $i,SY136: $i,SY137: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY135 @ SV14 )
| ~ ( member @ SY136 @ SY131 ) )
| ~ ( member @ SY137 @ SY131 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY135 @ SY136 )
| ~ ( apply @ SV9 @ SY135 @ SY137 ) )
| ( SY136 = SY137 ) )
| ( equal_maps @ SV4 @ SV9 @ SV14 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( maps @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
| ( maps @ SV5 @ SV10 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV11: $i] :
( ( ! [SY148: $i,SY149: $i,SY150: $i] :
( ~ ~ ( ~ ( member @ SY149 @ SV11 )
| ~ ( member @ SY150 @ SY148 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SY148 ) @ SY149 @ SY150 )
| ~ ! [SY151: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY151 @ SV16 )
| ~ ( apply @ SV6 @ SY149 @ SY151 ) )
| ~ ( apply @ SV1 @ SY151 @ SY150 ) ) )
| ~ ( ~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY152 @ SV16 )
| ~ ( apply @ SV6 @ SY149 @ SY152 ) )
| ~ ( apply @ SV1 @ SY152 @ SY150 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SY148 ) @ SY149 @ SY150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ( surjective @ SV2 @ SV7 @ SV12 )
| ! [SY127: $i] :
( ~ ( member @ SY127 @ SV12 )
| ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ SV7 )
| ~ ( apply @ SV2 @ SY98 @ SY127 ) ) ) )
| ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV12 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV7 )
| ~ ( apply @ SV2 @ SY100 @ SY129 ) ) )
| ( surjective @ SV2 @ SV7 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ~ ( one_to_one @ SV3 @ SV8 @ SV13 )
| ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
| ( one_to_one @ SV3 @ SV8 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
| ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY153 @ SV14 )
| ~ ( member @ SY154 @ SV17 ) )
| ~ ( member @ SY155 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY153 @ SY154 )
| ~ ( apply @ SV9 @ SY153 @ SY155 ) )
| ( SY154 = SY155 ) ) )
| ~ ( ~ ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY156 @ SV14 )
| ~ ( member @ SY157 @ SV17 ) )
| ~ ( member @ SY158 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY156 @ SY157 )
| ~ ( apply @ SV9 @ SY156 @ SY158 ) )
| ( SY157 = SY158 ) )
| ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( maps @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
| ( maps @ SV5 @ SV10 @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV11: $i] :
( ( ! [SY159: $i,SY160: $i] :
( ~ ~ ( ~ ( member @ SY159 @ SV11 )
| ~ ( member @ SY160 @ SV18 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SY159 @ SY160 )
| ~ ! [SY151: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY151 @ SV16 )
| ~ ( apply @ SV6 @ SY159 @ SY151 ) )
| ~ ( apply @ SV1 @ SY151 @ SY160 ) ) )
| ~ ( ~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY152 @ SV16 )
| ~ ( apply @ SV6 @ SY159 @ SY152 ) )
| ~ ( apply @ SV1 @ SY152 @ SY160 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SY159 @ SY160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ( surjective @ SV2 @ SV7 @ SV12 )
| ! [SY127: $i] :
( ~ ( member @ SY127 @ SV12 )
| ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ SV7 )
| ~ ( apply @ SV2 @ SY98 @ SY127 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV2: $i,SV7: $i,SV12: $i] :
( ( ~ ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV12 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV7 )
| ~ ( apply @ SV2 @ SY100 @ SY129 ) ) )
| ( surjective @ SV2 @ SV7 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(90,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ~ ( one_to_one @ SV3 @ SV8 @ SV13 )
| ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(91,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( ~ ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
| ( one_to_one @ SV3 @ SV8 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(92,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ~ ( ~ ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
| ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY153 @ SV14 )
| ~ ( member @ SY154 @ SV17 ) )
| ~ ( member @ SY155 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY153 @ SY154 )
| ~ ( apply @ SV9 @ SY153 @ SY155 ) )
| ( SY154 = SY155 ) ) )
| ~ ( ~ ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY156 @ SV14 )
| ~ ( member @ SY157 @ SV17 ) )
| ~ ( member @ SY158 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY156 @ SY157 )
| ~ ( apply @ SV9 @ SY156 @ SY158 ) )
| ( SY157 = SY158 ) )
| ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( maps @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(94,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
| ( maps @ SV5 @ SV10 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(95,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV11: $i,SV19: $i] :
( ( ! [SY163: $i] :
( ~ ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SY163 @ SV18 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SY163 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY164 ) )
| ~ ( apply @ SV1 @ SY164 @ SY163 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY165 ) )
| ~ ( apply @ SV1 @ SY165 @ SY163 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( surjective @ SV2 @ SV7 @ SV12 )
| ! [SY127: $i] :
( ~ ( member @ SY127 @ SV12 )
| ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ SV7 )
| ~ ( apply @ SV2 @ SY98 @ SY127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(97,plain,
! [SV2: $i,SV7: $i,SV12: $i] :
( ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV12 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV7 )
| ~ ( apply @ SV2 @ SY100 @ SY129 ) ) )
| ( surjective @ SV2 @ SV7 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( one_to_one @ SV3 @ SV8 @ SV13 )
| ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(99,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
| ( one_to_one @ SV3 @ SV8 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(100,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ~ ( ~ ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
| ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY153 @ SV14 )
| ~ ( member @ SY154 @ SV17 ) )
| ~ ( member @ SY155 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY153 @ SY154 )
| ~ ( apply @ SV9 @ SY153 @ SY155 ) )
| ( SY154 = SY155 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(101,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ~ ( ~ ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY156 @ SV14 )
| ~ ( member @ SY157 @ SV17 ) )
| ~ ( member @ SY158 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY156 @ SY157 )
| ~ ( apply @ SV9 @ SY156 @ SY158 ) )
| ( SY157 = SY158 ) )
| ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(102,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( maps @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(103,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ~ ~ ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
| ( maps @ SV5 @ SV10 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(104,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV20: $i,SV11: $i,SV19: $i] :
( ( ~ ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV20 @ SV18 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( surjective @ SV2 @ SV7 @ SV12 ) )
= $true )
| ( ( ! [SY127: $i] :
( ~ ( member @ SY127 @ SV12 )
| ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ SV7 )
| ~ ( apply @ SV2 @ SY98 @ SY127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV2: $i,SV7: $i,SV12: $i] :
( ( ( ~ ! [SY129: $i] :
( ~ ( member @ SY129 @ SV12 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV7 )
| ~ ( apply @ SV2 @ SY100 @ SY129 ) ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( one_to_one @ SV3 @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) )
= $true )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ~ ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
| ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY153 @ SV14 )
| ~ ( member @ SY154 @ SV17 ) )
| ~ ( member @ SY155 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY153 @ SY154 )
| ~ ( apply @ SV9 @ SY153 @ SY155 ) )
| ( SY154 = SY155 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(110,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ~ ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY156 @ SV14 )
| ~ ( member @ SY157 @ SV17 ) )
| ~ ( member @ SY158 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY156 @ SY157 )
| ~ ( apply @ SV9 @ SY156 @ SY158 ) )
| ( SY157 = SY158 ) )
| ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(111,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( maps @ SV5 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV20: $i,SV11: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV20 @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false )
| ( ( ! [SY127: $i] :
( ~ ( member @ SY127 @ SV12 )
| ~ ! [SY98: $i] :
~ ~ ( ~ ( member @ SY98 @ SV7 )
| ~ ( apply @ SV2 @ SY98 @ SY127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV2: $i,SV7: $i,SV12: $i] :
( ( ( ! [SY129: $i] :
( ~ ( member @ SY129 @ SV12 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV7 )
| ~ ( apply @ SV2 @ SY100 @ SY129 ) ) ) )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $false )
| ( ( ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) ) )
= $false )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(118,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 ) )
= $true )
| ( ( ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY153 @ SV14 )
| ~ ( member @ SY154 @ SV17 ) )
| ~ ( member @ SY155 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY153 @ SY154 )
| ~ ( apply @ SV9 @ SY153 @ SY155 ) )
| ( SY154 = SY155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(119,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ( ~ ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY156 @ SV14 )
| ~ ( member @ SY157 @ SV17 ) )
| ~ ( member @ SY158 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY156 @ SY157 )
| ~ ( apply @ SV9 @ SY156 @ SY158 ) )
| ( SY157 = SY158 ) ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(120,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( maps @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) ) )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(122,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV20: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV20 @ SV18 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV2: $i,SV7: $i,SV12: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV12 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ( member @ SY168 @ SV7 )
| ~ ( apply @ SV2 @ SY168 @ SV21 ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( member @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) @ SV12 )
| ~ ! [SY169: $i] :
~ ~ ( ~ ( member @ SY169 @ SV7 )
| ~ ( apply @ SV2 @ SY169 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) ) )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(125,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
= $false )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( injective @ SV3 @ SV8 @ SV13 )
| ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
= $true )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(127,plain,
! [SV17: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false )
| ( ( ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY153 @ SV14 )
| ~ ( member @ SY154 @ SV17 ) )
| ~ ( member @ SY155 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY153 @ SY154 )
| ~ ( apply @ SV9 @ SY153 @ SY155 ) )
| ( SY154 = SY155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(128,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ( ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY156 @ SV14 )
| ~ ( member @ SY157 @ SV17 ) )
| ~ ( member @ SY158 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SY156 @ SY157 )
| ~ ( apply @ SV9 @ SY156 @ SY158 ) )
| ( SY157 = SY158 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) )
| ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) )
| ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(131,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV20: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 )
| ~ ( member @ SV20 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(132,plain,
! [SV2: $i,SV7: $i,SV12: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV12 ) )
= $true )
| ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( member @ SY168 @ SV7 )
| ~ ( apply @ SV2 @ SY168 @ SV21 ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( member @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) @ SV12 ) )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(134,plain,
! [SV12: $i,SV2: $i,SV7: $i] :
( ( ( ~ ! [SY169: $i] :
~ ~ ( ~ ( member @ SY169 @ SV7 )
| ~ ( apply @ SV2 @ SY169 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) ) )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(135,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( injective @ SV3 @ SV8 @ SV13 ) )
= $false )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(136,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
= $false )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(137,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( injective @ SV3 @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
= $true )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i,SV22: $i] :
( ( ( ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SY170 @ SV17 ) )
| ~ ( member @ SY171 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SY170 )
| ~ ( apply @ SV9 @ SV22 @ SY171 ) )
| ( SY170 = SY171 ) ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ! [SY172: $i,SY173: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ SY172 @ SV17 ) )
| ~ ( member @ SY173 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SY172 )
| ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SY173 ) )
| ( SY172 = SY173 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(140,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) ) )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(141,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(142,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) ) )
= $true )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV20: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV20 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV2: $i,SV7: $i,SV12: $i,SV21: $i] :
( ( ( member @ SV21 @ SV12 )
= $false )
| ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( member @ SY168 @ SV7 )
| ~ ( apply @ SV2 @ SY168 @ SV21 ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( member @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) @ SV12 )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(146,plain,
! [SV12: $i,SV2: $i,SV7: $i] :
( ( ( ! [SY169: $i] :
~ ~ ( ~ ( member @ SY169 @ SV7 )
| ~ ( apply @ SV2 @ SY169 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(147,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( injective @ SV3 @ SV8 @ SV13 )
= $true )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(148,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( surjective @ SV3 @ SV8 @ SV13 )
= $true )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(149,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( injective @ SV3 @ SV8 @ SV13 )
= $false )
| ( ( ~ ( surjective @ SV3 @ SV8 @ SV13 ) )
= $true )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ! [SY174: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) )
| ~ ( member @ SY174 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SY174 ) )
| ( SV23 = SY174 ) ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ! [SY175: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
| ~ ( member @ SY175 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) )
| ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SY175 ) )
| ( ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 )
= SY175 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[139]) ).
thf(152,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ! [SY138: $i] :
( ~ ( member @ SY138 @ SV10 )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( member @ SY139 @ SV15 )
| ~ ( apply @ SV5 @ SY138 @ SY139 ) ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(153,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ! [SY140: $i,SY141: $i,SY142: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY140 @ SV10 )
| ~ ( member @ SY141 @ SV15 ) )
| ~ ( member @ SY142 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY140 @ SY141 )
| ~ ( apply @ SV5 @ SY140 @ SY142 ) )
| ( SY141 = SY142 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(154,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ! [SY143: $i] :
( ~ ( member @ SY143 @ SV10 )
| ~ ! [SY144: $i] :
~ ~ ( ~ ( member @ SY144 @ SV15 )
| ~ ( apply @ SV5 @ SY143 @ SY144 ) ) ) )
= $false )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(155,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV18: $i,SV20: $i,SV11: $i,SV19: $i] :
( ( ( member @ SV19 @ SV11 )
= $false )
| ( ( ~ ( member @ SV20 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV12: $i,SV21: $i,SV2: $i,SV7: $i] :
( ( ( ! [SY168: $i] :
~ ~ ( ~ ( member @ SY168 @ SV7 )
| ~ ( apply @ SV2 @ SY168 @ SV21 ) ) )
= $false )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV12: $i,SV2: $i,SV7: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ SV24 @ SV7 )
| ~ ( apply @ SV2 @ SV24 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( surjective @ SV3 @ SV8 @ SV13 )
= $false )
| ( ( injective @ SV3 @ SV8 @ SV13 )
= $false )
| ( ( one_to_one @ SV3 @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(159,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) )
| ~ ( member @ SV25 @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(160,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
| ~ ( member @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
| ~ ~ ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) )
| ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) )
| ( ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 )
= ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[151]) ).
thf(161,plain,
! [SV5: $i,SV15: $i,SV10: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV10 )
| ~ ! [SY176: $i] :
~ ~ ( ~ ( member @ SY176 @ SV15 )
| ~ ( apply @ SV5 @ SV26 @ SY176 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV5: $i,SV15: $i,SV10: $i,SV27: $i] :
( ( ( ! [SY177: $i,SY178: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SY177 @ SV15 ) )
| ~ ( member @ SY178 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SY177 )
| ~ ( apply @ SV5 @ SV27 @ SY178 ) )
| ( SY177 = SY178 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ! [SY179: $i] :
~ ~ ( ~ ( member @ SY179 @ SV15 )
| ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SY179 ) ) )
= $false )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[154]) ).
thf(164,plain,
! [SV16: $i,SV6: $i,SV1: $i,SV11: $i,SV19: $i,SV18: $i,SV20: $i] :
( ( ( member @ SV20 @ SV18 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV7: $i,SV2: $i,SV21: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV7 )
| ~ ( apply @ SV2 @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV21 ) ) )
= $false )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[156]) ).
thf(166,plain,
! [SV12: $i,SV2: $i,SV7: $i,SV24: $i] :
( ( ( ~ ( ~ ( member @ SV24 @ SV7 )
| ~ ( apply @ SV2 @ SV24 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) ) )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) )
| ~ ( member @ SV25 @ SV17 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
| ~ ( member @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(169,plain,
! [SV14: $i,SV17: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) )
| ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) )
| ( ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 )
= ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(170,plain,
! [SV5: $i,SV15: $i,SV10: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV10 ) )
= $true )
| ( ( ~ ! [SY176: $i] :
~ ~ ( ~ ( member @ SY176 @ SV15 )
| ~ ( apply @ SV5 @ SV26 @ SY176 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(171,plain,
! [SV5: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ! [SY180: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) )
| ~ ( member @ SY180 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SY180 ) )
| ( SV28 = SY180 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 ) )
= $false )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(173,plain,
! [SV10: $i,SV5: $i,SV15: $i] :
( ( ( ~ ! [SY179: $i] :
~ ~ ( ~ ( member @ SY179 @ SV15 )
| ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SY179 ) ) )
= $false )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(174,plain,
! [SV20: $i,SV19: $i,SV18: $i,SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
| ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV7: $i,SV2: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( ~ ( member @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV7 )
| ~ ( apply @ SV2 @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV21 ) ) )
= $true )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(176,plain,
! [SV12: $i,SV2: $i,SV7: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV7 )
| ~ ( apply @ SV2 @ SV24 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(177,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) )
| ~ ( member @ SV25 @ SV17 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
| ~ ( member @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(179,plain,
! [SV14: $i,SV17: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) )
| ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(180,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ( ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 )
= ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(181,plain,
! [SV5: $i,SV15: $i,SV10: $i,SV26: $i] :
( ( ( member @ SV26 @ SV10 )
= $false )
| ( ( ~ ! [SY176: $i] :
~ ~ ( ~ ( member @ SY176 @ SV15 )
| ~ ( apply @ SV5 @ SV26 @ SY176 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) )
| ~ ( member @ SV29 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(184,plain,
! [SV10: $i,SV5: $i,SV15: $i] :
( ( ( ! [SY179: $i] :
~ ~ ( ~ ( member @ SY179 @ SV15 )
| ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SY179 ) ) )
= $true )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(185,plain,
! [SV20: $i,SV19: $i,SV18: $i,SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(186,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(187,plain,
! [SV7: $i,SV2: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( member @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV7 )
| ~ ( apply @ SV2 @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV21 ) )
= $false )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV12: $i,SV2: $i,SV7: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV7 ) )
= $true )
| ( ( ~ ( apply @ SV2 @ SV24 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(189,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) )
| ~ ( member @ SV25 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(190,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
| ~ ( member @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV14: $i,SV17: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) )
| ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(192,plain,
! [SV10: $i,SV26: $i,SV5: $i,SV15: $i] :
( ( ( ! [SY176: $i] :
~ ~ ( ~ ( member @ SY176 @ SV15 )
| ~ ( apply @ SV5 @ SV26 @ SY176 ) ) )
= $false )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) )
| ~ ( member @ SV29 @ SV15 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV10: $i,SV5: $i,SV15: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( member @ SV30 @ SV15 )
| ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 ) ) )
= $true )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV20: $i,SV19: $i,SV18: $i,SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
| ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(197,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i] :
( ( ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) )
| ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(198,plain,
! [SV7: $i,SV2: $i,SV21: $i,SV12: $i] :
( ( ( ~ ( member @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV7 ) )
= $false )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(199,plain,
! [SV7: $i,SV21: $i,SV12: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV21 ) )
= $false )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(200,plain,
! [SV12: $i,SV2: $i,SV7: $i,SV24: $i] :
( ( ( member @ SV24 @ SV7 )
= $false )
| ( ( ~ ( apply @ SV2 @ SV24 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) ) )
= $true )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(203,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(204,plain,
! [SV14: $i,SV17: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) )
| ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV15: $i,SV5: $i,SV26: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) @ SV15 )
| ~ ( apply @ SV5 @ SV26 @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) ) ) )
= $false )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[192]) ).
thf(206,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) )
| ~ ( member @ SV29 @ SV15 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ! [SY181: $i,SY182: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ SY181 @ SV15 ) )
| ~ ( member @ SY182 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SY181 )
| ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SY182 ) )
| ( SY181 = SY182 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[194]) ).
thf(208,plain,
! [SV10: $i,SV5: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( ~ ( member @ SV30 @ SV15 )
| ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 ) ) )
= $false )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(209,plain,
! [SV20: $i,SV19: $i,SV18: $i,SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 ) )
= $true )
| ( ( ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(210,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i] :
( ( ( ~ ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(211,plain,
! [SV7: $i,SV2: $i,SV21: $i,SV12: $i] :
( ( ( member @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV7 )
= $true )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(212,plain,
! [SV7: $i,SV21: $i,SV12: $i,SV2: $i] :
( ( ( apply @ SV2 @ ( sK12_SY168 @ SV12 @ SV21 @ SV2 @ SV7 ) @ SV21 )
= $true )
| ( ( member @ SV21 @ SV12 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(213,plain,
! [SV12: $i,SV7: $i,SV24: $i,SV2: $i] :
( ( ( apply @ SV2 @ SV24 @ ( sK7_SY129 @ SV2 @ SV7 @ SV12 ) )
= $false )
| ( ( member @ SV24 @ SV7 )
= $false )
| ( ( surjective @ SV2 @ SV7 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(214,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) ) )
= $false )
| ( ( ~ ( member @ SV25 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(215,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(216,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ( member @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(217,plain,
! [SV14: $i,SV17: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(218,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[204]) ).
thf(219,plain,
! [SV15: $i,SV5: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) @ SV15 )
| ~ ( apply @ SV5 @ SV26 @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) ) ) )
= $true )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(220,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) )
| ~ ( member @ SV29 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(221,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ! [SY183: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
| ~ ( member @ SY183 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SY183 ) )
| ( ( sK15_SY181 @ SV10 @ SV15 @ SV5 )
= SY183 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[207]) ).
thf(222,plain,
! [SV10: $i,SV5: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ SV15 )
| ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 ) )
= $true )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(223,plain,
! [SV20: $i,SV19: $i,SV18: $i,SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( ~ ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(224,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i] :
( ( ( ~ ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(225,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV14 )
| ~ ( member @ SV23 @ SV17 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(226,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(227,plain,
! [SV14: $i,SV17: $i,SV9: $i,SV4: $i] :
( ( ( apply @ SV4 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(228,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( apply @ SV9 @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ ( sK10_SY175 @ SV14 @ SV17 @ SV4 @ SV9 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(229,plain,
! [SV15: $i,SV5: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) @ SV15 )
| ~ ( apply @ SV5 @ SV26 @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) ) )
= $false )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(230,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) ) )
= $true )
| ( ( ~ ( member @ SV29 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(231,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
| ~ ( member @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) )
| ( ( sK15_SY181 @ SV10 @ SV15 @ SV5 )
= ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[221]) ).
thf(232,plain,
! [SV10: $i,SV5: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ SV15 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 ) )
= $true )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(233,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i] :
( ( ( ! [SY166: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY166 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY166 ) )
| ~ ( apply @ SV1 @ SY166 @ SV20 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(234,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i] :
( ( ( ! [SY167: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY167 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SY167 ) )
| ~ ( apply @ SV1 @ SY167 @ SV20 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(235,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV23 @ SV17 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(236,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(237,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 ) )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(238,plain,
! [SV15: $i,SV5: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(239,plain,
! [SV15: $i,SV10: $i,SV26: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV26 @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) ) )
= $false )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(240,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) ) )
= $false )
| ( ( ~ ( member @ SV29 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
| ~ ( member @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) @ SV15 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(242,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) )
| ( ( sK15_SY181 @ SV10 @ SV15 @ SV5 )
= ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(243,plain,
! [SV10: $i,SV5: $i,SV15: $i,SV30: $i] :
( ( ( member @ SV30 @ SV15 )
= $false )
| ( ( ~ ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 ) )
= $true )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) ) )
| ~ ( apply @ SV1 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV20 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[233]) ).
thf(245,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV31 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SV31 ) )
| ~ ( apply @ SV1 @ SV31 @ SV20 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(246,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV17: $i,SV23: $i,SV14: $i,SV22: $i] :
( ( ( member @ SV22 @ SV14 )
= $false )
| ( ( ~ ( member @ SV23 @ SV17 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(247,plain,
! [SV14: $i,SV17: $i,SV4: $i,SV9: $i] :
( ( ( member @ ( sK8_SY156 @ SV9 @ SV4 @ SV17 @ SV14 ) @ SV14 )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(248,plain,
! [SV9: $i,SV4: $i,SV17: $i,SV14: $i] :
( ( ( member @ ( sK9_SY172 @ SV14 @ SV17 @ SV4 @ SV9 ) @ SV17 )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(249,plain,
! [SV15: $i,SV5: $i,SV26: $i,SV10: $i] :
( ( ( member @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(250,plain,
! [SV15: $i,SV10: $i,SV26: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV26 @ ( sK13_SY176 @ SV10 @ SV26 @ SV5 @ SV15 ) )
= $true )
| ( ( member @ SV26 @ SV10 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(251,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV10 )
| ~ ( member @ SV28 @ SV15 ) )
= $true )
| ( ( ~ ( member @ SV29 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(252,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
| ~ ( member @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) @ SV15 ) ) )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(253,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(254,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ( sK15_SY181 @ SV10 @ SV15 @ SV5 )
= ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(255,plain,
! [SV30: $i,SV10: $i,SV15: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( ~ ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(256,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) ) )
| ~ ( apply @ SV1 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV20 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(257,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV31 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SV31 ) )
| ~ ( apply @ SV1 @ SV31 @ SV20 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(258,plain,
! [SV9: $i,SV4: $i,SV25: $i,SV14: $i,SV22: $i,SV17: $i,SV23: $i] :
( ( ( member @ SV23 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( ~ ( member @ SV25 @ SV17 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(259,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV10 ) )
= $true )
| ( ( ~ ( member @ SV28 @ SV15 ) )
= $true )
| ( ( ~ ( member @ SV29 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(260,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
| ~ ( member @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(261,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) ) )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(262,plain,
! [SV30: $i,SV5: $i,SV15: $i,SV10: $i] :
( ( ( ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY145 @ SV10 )
| ~ ( member @ SY146 @ SV15 ) )
| ~ ( member @ SY147 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY145 @ SY146 )
| ~ ( apply @ SV5 @ SY145 @ SY147 ) )
| ( SY146 = SY147 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(263,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) ) )
| ~ ( apply @ SV1 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV20 ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(264,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SV31 ) )
| ~ ( apply @ SV1 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(265,plain,
! [SV9: $i,SV4: $i,SV23: $i,SV14: $i,SV22: $i,SV17: $i,SV25: $i] :
( ( ( member @ SV25 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV23 @ SV17 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
| ( SV23 = SV25 ) )
= $true )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(266,plain,
! [SV5: $i,SV29: $i,SV15: $i,SV28: $i,SV10: $i,SV27: $i] :
( ( ( member @ SV27 @ SV10 )
= $false )
| ( ( ~ ( member @ SV28 @ SV15 ) )
= $true )
| ( ( ~ ( member @ SV29 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(267,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(268,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(269,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(270,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ! [SY184: $i,SY185: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ SY184 @ SV15 ) )
| ~ ( member @ SY185 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SY184 )
| ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SY185 ) )
| ( SY184 = SY185 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[262]) ).
thf(271,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(272,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV20: $i,SV11: $i,SV18: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV20 ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(273,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ SV31 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SV31 ) ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(274,plain,
! [SV14: $i,SV17: $i,SV25: $i,SV9: $i,SV23: $i,SV22: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) ) )
= $true )
| ( ( SV23 = SV25 )
= $true )
| ( ( member @ SV23 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV25 @ SV17 )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(275,plain,
! [SV5: $i,SV29: $i,SV10: $i,SV27: $i,SV15: $i,SV28: $i] :
( ( ( member @ SV28 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( ~ ( member @ SV29 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(276,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) ) )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(277,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( member @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) @ SV15 )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(278,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(279,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(280,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ! [SY186: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
| ~ ( member @ SY186 @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) )
| ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SY186 ) )
| ( ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 )
= SY186 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(281,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( ~ ( ~ ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(282,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV20: $i,SV11: $i,SV18: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV20 )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(283,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( ~ ( ~ ( member @ SV31 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SV31 ) ) )
= $false )
| ( ( ~ ( apply @ SV1 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(284,plain,
! [SV14: $i,SV17: $i,SV25: $i,SV9: $i,SV23: $i,SV22: $i,SV4: $i] :
( ( ( ~ ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) ) )
= $false )
| ( ( SV23 = SV25 )
= $true )
| ( ( member @ SV23 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV25 @ SV17 )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(285,plain,
! [SV5: $i,SV28: $i,SV10: $i,SV27: $i,SV15: $i,SV29: $i] :
( ( ( member @ SV29 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( member @ SV28 @ SV15 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
| ( SV28 = SV29 ) )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(286,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(288,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ ( sK16_SY183 @ SV10 @ SV15 @ SV5 ) )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(289,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
| ~ ( member @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) )
| ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) )
| ( ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 )
= ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[280]) ).
thf(290,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(291,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV16 )
| ~ ( apply @ SV6 @ SV19 @ SV31 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(292,plain,
! [SV14: $i,SV17: $i,SV25: $i,SV9: $i,SV23: $i,SV22: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ SV22 @ SV23 )
| ~ ( apply @ SV9 @ SV22 @ SV25 ) )
= $true )
| ( ( SV23 = SV25 )
= $true )
| ( ( member @ SV23 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV25 @ SV17 )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(293,plain,
! [SV10: $i,SV15: $i,SV29: $i,SV28: $i,SV27: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) ) )
= $true )
| ( ( SV28 = SV29 )
= $true )
| ( ( member @ SV28 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( member @ SV29 @ SV15 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(294,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(295,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 ) )
= $false )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(296,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
| ~ ( member @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(297,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) )
| ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) )
| ( ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 )
= ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(298,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( ~ ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(299,plain,
! [SV16: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i,SV19: $i,SV6: $i] :
( ( ( ~ ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(300,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ SV16 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV19 @ SV31 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(301,plain,
! [SV14: $i,SV17: $i,SV25: $i,SV9: $i,SV23: $i,SV22: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ SV22 @ SV23 ) )
= $true )
| ( ( ~ ( apply @ SV9 @ SV22 @ SV25 ) )
= $true )
| ( ( SV23 = SV25 )
= $true )
| ( ( member @ SV23 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV25 @ SV17 )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(302,plain,
! [SV10: $i,SV15: $i,SV29: $i,SV28: $i,SV27: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) ) )
= $false )
| ( ( SV28 = SV29 )
= $true )
| ( ( member @ SV28 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( member @ SV29 @ SV15 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(303,plain,
! [SV10: $i,SV15: $i,SV5: $i] :
( ( ( member @ ( sK14_SY145 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(304,plain,
! [SV5: $i,SV15: $i,SV10: $i] :
( ( ( member @ ( sK15_SY181 @ SV10 @ SV15 @ SV5 ) @ SV15 )
= $true )
| ( ( member @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(305,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
| ~ ( member @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) ) )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(306,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) )
| ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(307,plain,
! [SV30: $i,SV5: $i,SV15: $i,SV10: $i] :
( ( ( ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 )
= ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(308,plain,
! [SV16: $i,SV6: $i,SV19: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i] :
( ( ( member @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) @ SV16 )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(309,plain,
! [SV16: $i,SV1: $i,SV20: $i,SV11: $i,SV18: $i,SV19: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV19 @ ( sK17_SY166 @ SV18 @ SV11 @ SV20 @ SV1 @ SV19 @ SV6 @ SV16 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(310,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV19: $i,SV6: $i,SV16: $i,SV31: $i] :
( ( ( member @ SV31 @ SV16 )
= $false )
| ( ( ~ ( apply @ SV6 @ SV19 @ SV31 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(311,plain,
! [SV14: $i,SV17: $i,SV25: $i,SV9: $i,SV23: $i,SV22: $i,SV4: $i] :
( ( ( apply @ SV4 @ SV22 @ SV23 )
= $false )
| ( ( ~ ( apply @ SV9 @ SV22 @ SV25 ) )
= $true )
| ( ( SV23 = SV25 )
= $true )
| ( ( member @ SV23 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV25 @ SV17 )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(312,plain,
! [SV10: $i,SV15: $i,SV29: $i,SV28: $i,SV27: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV27 @ SV28 )
| ~ ( apply @ SV5 @ SV27 @ SV29 ) )
= $true )
| ( ( SV28 = SV29 )
= $true )
| ( ( member @ SV28 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( member @ SV29 @ SV15 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(313,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
| ~ ( member @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(314,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) )
| ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) ) )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(315,plain,
! [SV18: $i,SV11: $i,SV20: $i,SV1: $i,SV16: $i,SV31: $i,SV19: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV19 @ SV31 )
= $false )
| ( ( member @ SV31 @ SV16 )
= $false )
| ( ( ~ ( apply @ SV1 @ SV31 @ SV20 ) )
= $true )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(316,plain,
! [SV14: $i,SV17: $i,SV23: $i,SV4: $i,SV25: $i,SV22: $i,SV9: $i] :
( ( ( apply @ SV9 @ SV22 @ SV25 )
= $false )
| ( ( apply @ SV4 @ SV22 @ SV23 )
= $false )
| ( ( SV23 = SV25 )
= $true )
| ( ( member @ SV23 @ SV17 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV25 @ SV17 )
= $false )
| ( ( equal_maps @ SV4 @ SV9 @ SV14 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(317,plain,
! [SV10: $i,SV15: $i,SV29: $i,SV28: $i,SV27: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV27 @ SV28 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV27 @ SV29 ) )
= $true )
| ( ( SV28 = SV29 )
= $true )
| ( ( member @ SV28 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( member @ SV29 @ SV15 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(318,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(319,plain,
! [SV30: $i,SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(320,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) )
| ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(321,plain,
! [SV18: $i,SV11: $i,SV19: $i,SV6: $i,SV16: $i,SV20: $i,SV31: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV31 @ SV20 )
= $false )
| ( ( member @ SV31 @ SV16 )
= $false )
| ( ( apply @ SV6 @ SV19 @ SV31 )
= $false )
| ( ( apply @ ( compose_function @ SV1 @ SV6 @ SV11 @ SV16 @ SV18 ) @ SV19 @ SV20 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV20 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(322,plain,
! [SV10: $i,SV15: $i,SV29: $i,SV28: $i,SV27: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV27 @ SV28 )
= $false )
| ( ( ~ ( apply @ SV5 @ SV27 @ SV29 ) )
= $true )
| ( ( SV28 = SV29 )
= $true )
| ( ( member @ SV28 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( member @ SV29 @ SV15 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(323,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) ) )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(324,plain,
! [SV30: $i,SV5: $i,SV15: $i,SV10: $i] :
( ( ( member @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(325,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(326,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(327,plain,
! [SV10: $i,SV15: $i,SV28: $i,SV29: $i,SV27: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV27 @ SV29 )
= $false )
| ( ( apply @ SV5 @ SV27 @ SV28 )
= $false )
| ( ( SV28 = SV29 )
= $true )
| ( ( member @ SV28 @ SV15 )
= $false )
| ( ( member @ SV27 @ SV10 )
= $false )
| ( ( member @ SV29 @ SV15 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(328,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(329,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(330,plain,
! [SV10: $i,SV15: $i,SV30: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ ( sK20_SY186 @ SV10 @ SV15 @ SV5 @ SV30 ) )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(331,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( ~ ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(332,plain,
! [SV30: $i,SV5: $i,SV15: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 ) )
= $false )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(333,plain,
! [SV10: $i,SV15: $i,SV5: $i,SV30: $i] :
( ( ( member @ ( sK18_SY145 @ SV30 @ SV5 @ SV15 @ SV10 ) @ SV10 )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(334,plain,
! [SV30: $i,SV5: $i,SV15: $i,SV10: $i] :
( ( ( member @ ( sK19_SY184 @ SV10 @ SV15 @ SV5 @ SV30 ) @ SV15 )
= $true )
| ( ( member @ SV30 @ SV15 )
= $false )
| ( ( apply @ SV5 @ ( sK11_SY143 @ SV5 @ SV15 @ SV10 ) @ SV30 )
= $false )
| ( ( maps @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(335,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,334,333,330,329,327,324,321,316,309,308,307,304,303,288,287,282,277,254,250,249,248,247,228,227,216,213,212,211,180,158,148,147,145,66,59,58,57,56]) ).
thf(336,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[335]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET724+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 14:50:01 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.03/6.84
% 40.03/6.84 No.of.Axioms: 5
% 40.03/6.84
% 40.03/6.84 Length.of.Defs: 0
% 40.03/6.84
% 40.03/6.84 Contains.Choice.Funs: false
% 40.03/6.84 ...............
% 40.03/6.84
% 40.03/6.84 ********************************
% 40.03/6.84 * All subproblems solved! *
% 40.03/6.84 ********************************
% 40.03/6.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:335,loop_count:0,foatp_calls:1,translation:fof_full)
% 40.03/6.84
% 40.03/6.84 %**** Beginning of derivation protocol ****
% 40.03/6.84 % SZS output start CNFRefutation
% See solution above
% 40.03/6.84
% 40.03/6.84 %**** End of derivation protocol ****
% 40.03/6.84 %**** no. of clauses in derivation: 313 ****
% 40.03/6.84 %**** clause counter: 335 ****
% 40.03/6.84
% 40.03/6.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:335,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------