%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET708+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:40:54 AM UTC 2026
% Result : Theorem 22.01s 3.93s
% Output : CNFRefutation 22.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 4
% Syntax : Number of formulae : 320 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 4123 (1093 equ; 0 cnn)
% Maximal formula atoms : 10 ( 12 avg)
% Number of connectives : 13562 (2918 ~;1746 |; 63 &;8795 @)
% ( 12 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 53 usr; 10 con; 0-8 aty)
% Number of variables : 2057 ( 0 ^;2051 !; 6 ?;2057 :)
% 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_SY122,type,
sK10_SY122: $i > $i > $i > $i ).
thf(tp_sK11_SY174,type,
sK11_SY174: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK12_SY183,type,
sK12_SY183: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY191,type,
sK13_SY191: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_SY184,type,
sK14_SY184: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY124,type,
sK15_SY124: $i > $i > $i > $i ).
thf(tp_sK16_SY199,type,
sK16_SY199: $i > $i > $i > $i ).
thf(tp_sK17_SY201,type,
sK17_SY201: $i > $i > $i > $i ).
thf(tp_sK18_SY124,type,
sK18_SY124: $i > $i > $i > $i > $i ).
thf(tp_sK19_SY202,type,
sK19_SY202: $i > $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK20_SY204,type,
sK20_SY204: $i > $i > $i > $i > $i ).
thf(tp_sK21_SY198,type,
sK21_SY198: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK22_SY195,type,
sK22_SY195: $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK23_SY198,type,
sK23_SY198: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK2_SY31,type,
sK2_SY31: $i ).
thf(tp_sK3_SY37,type,
sK3_SY37: $i ).
thf(tp_sK4_SY42,type,
sK4_SY42: $i ).
thf(tp_sK5_SY46,type,
sK5_SY46: $i ).
thf(tp_sK6_SY49,type,
sK6_SY49: $i ).
thf(tp_sK7_SY51,type,
sK7_SY51: $i ).
thf(tp_sK8_SY158,type,
sK8_SY158: $i > $i > $i > $i > $i ).
thf(tp_sK9_SY180,type,
sK9_SY180: $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(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/sandbox/benchmark/theBenchmark.p',equal_maps) ).
thf(16,axiom,
! [H: $i,G: $i,F: $i,A: $i,B: $i,C: $i] :
( ( compose_predicate @ H @ G @ F @ A @ B @ C )
<=> ! [X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ H @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_predicate) ).
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/sandbox/benchmark/theBenchmark.p',maps) ).
thf(29,conjecture,
! [F: $i,G: $i,H1: $i,H2: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( maps @ G @ B @ C )
& ( compose_predicate @ H1 @ G @ F @ A @ B @ C )
& ( compose_predicate @ H2 @ G @ F @ A @ B @ C ) )
=> ( equal_maps @ H1 @ H2 @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII01a) ).
thf(30,negated_conjecture,
( ( ! [F: $i,G: $i,H1: $i,H2: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( maps @ G @ B @ C )
& ( compose_predicate @ H1 @ G @ F @ A @ B @ C )
& ( compose_predicate @ H2 @ G @ F @ A @ B @ C ) )
=> ( equal_maps @ H1 @ H2 @ A @ C ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [F: $i,G: $i,H1: $i,H2: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( maps @ G @ B @ C )
& ( compose_predicate @ H1 @ G @ F @ A @ B @ C )
& ( compose_predicate @ H2 @ G @ F @ A @ B @ C ) )
=> ( equal_maps @ H1 @ H2 @ A @ C ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,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(33,plain,
( ( ! [H: $i,G: $i,F: $i,A: $i,B: $i,C: $i] :
( ( compose_predicate @ H @ G @ F @ A @ B @ C )
<=> ! [X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ H @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(34,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(35,plain,
( ( ! [SY31: $i,SY32: $i,SY33: $i,SY34: $i,SY35: $i,SY36: $i] :
( ( ( maps @ sK1_F @ SY34 @ SY35 )
& ( maps @ SY31 @ SY35 @ SY36 )
& ( compose_predicate @ SY32 @ SY31 @ sK1_F @ SY34 @ SY35 @ SY36 )
& ( compose_predicate @ SY33 @ SY31 @ sK1_F @ SY34 @ SY35 @ SY36 ) )
=> ( equal_maps @ SY32 @ SY33 @ SY34 @ SY36 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(36,plain,
( ( ! [SY37: $i,SY38: $i,SY39: $i,SY40: $i,SY41: $i] :
( ( ( maps @ sK1_F @ SY39 @ SY40 )
& ( maps @ sK2_SY31 @ SY40 @ SY41 )
& ( compose_predicate @ SY37 @ sK2_SY31 @ sK1_F @ SY39 @ SY40 @ SY41 )
& ( compose_predicate @ SY38 @ sK2_SY31 @ sK1_F @ SY39 @ SY40 @ SY41 ) )
=> ( equal_maps @ SY37 @ SY38 @ SY39 @ SY41 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(37,plain,
( ( ! [SY42: $i,SY43: $i,SY44: $i,SY45: $i] :
( ( ( maps @ sK1_F @ SY43 @ SY44 )
& ( maps @ sK2_SY31 @ SY44 @ SY45 )
& ( compose_predicate @ sK3_SY37 @ sK2_SY31 @ sK1_F @ SY43 @ SY44 @ SY45 )
& ( compose_predicate @ SY42 @ sK2_SY31 @ sK1_F @ SY43 @ SY44 @ SY45 ) )
=> ( equal_maps @ sK3_SY37 @ SY42 @ SY43 @ SY45 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(38,plain,
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ( ( maps @ sK1_F @ SY46 @ SY47 )
& ( maps @ sK2_SY31 @ SY47 @ SY48 )
& ( compose_predicate @ sK3_SY37 @ sK2_SY31 @ sK1_F @ SY46 @ SY47 @ SY48 )
& ( compose_predicate @ sK4_SY42 @ sK2_SY31 @ sK1_F @ SY46 @ SY47 @ SY48 ) )
=> ( equal_maps @ sK3_SY37 @ sK4_SY42 @ SY46 @ SY48 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(39,plain,
( ( ! [SY49: $i,SY50: $i] :
( ( ( maps @ sK1_F @ sK5_SY46 @ SY49 )
& ( maps @ sK2_SY31 @ SY49 @ SY50 )
& ( compose_predicate @ sK3_SY37 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ SY49 @ SY50 )
& ( compose_predicate @ sK4_SY42 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ SY49 @ SY50 ) )
=> ( equal_maps @ sK3_SY37 @ sK4_SY42 @ sK5_SY46 @ SY50 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ! [SY51: $i] :
( ( ( maps @ sK1_F @ sK5_SY46 @ sK6_SY49 )
& ( maps @ sK2_SY31 @ sK6_SY49 @ SY51 )
& ( compose_predicate @ sK3_SY37 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ SY51 )
& ( compose_predicate @ sK4_SY42 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ SY51 ) )
=> ( equal_maps @ sK3_SY37 @ sK4_SY42 @ sK5_SY46 @ SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ( ( maps @ sK1_F @ sK5_SY46 @ sK6_SY49 )
& ( maps @ sK2_SY31 @ sK6_SY49 @ sK7_SY51 )
& ( compose_predicate @ sK3_SY37 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ sK7_SY51 )
& ( compose_predicate @ sK4_SY42 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ sK7_SY51 ) )
=> ( equal_maps @ sK3_SY37 @ sK4_SY42 @ sK5_SY46 @ sK7_SY51 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( maps @ sK1_F @ sK5_SY46 @ sK6_SY49 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(43,plain,
( ( maps @ sK2_SY31 @ sK6_SY49 @ sK7_SY51 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(44,plain,
( ( compose_predicate @ sK3_SY37 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ sK7_SY51 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(45,plain,
( ( compose_predicate @ sK4_SY42 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ sK7_SY51 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(46,plain,
( ( equal_maps @ sK3_SY37 @ sK4_SY42 @ sK5_SY46 @ sK7_SY51 )
= $false ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(47,plain,
( ( ~ ( equal_maps @ sK3_SY37 @ sK4_SY42 @ sK5_SY46 @ sK7_SY51 ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(48,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)],[34]) ).
thf(49,plain,
( ( ! [H: $i,G: $i,F: $i,A: $i,B: $i,C: $i] :
( ( compose_predicate @ H @ G @ F @ A @ B @ C )
<=> ! [X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ H @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(50,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)],[32]) ).
thf(51,plain,
( ( compose_predicate @ sK4_SY42 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ sK7_SY51 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(52,plain,
( ( compose_predicate @ sK3_SY37 @ sK2_SY31 @ sK1_F @ sK5_SY46 @ sK6_SY49 @ sK7_SY51 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( maps @ sK2_SY31 @ sK6_SY49 @ sK7_SY51 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( maps @ sK1_F @ sK5_SY46 @ sK6_SY49 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ~ ( equal_maps @ sK3_SY37 @ sK4_SY42 @ sK5_SY46 @ sK7_SY51 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( maps @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ~ ( apply @ SX0 @ SX3 @ SX5 ) )
| ( SX4 = SX5 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX1 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX2 )
| ~ ( apply @ SX0 @ SX3 @ SX4 ) ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( member @ SX4 @ SX2 ) )
| ~ ( member @ SX5 @ SX2 ) )
| ~ ~ ( ~ ( apply @ SX0 @ SX3 @ SX4 )
| ~ ( apply @ SX0 @ SX3 @ SX5 ) )
| ( SX4 = SX5 ) ) )
| ( maps @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
~ ( ~ ( ~ ( compose_predicate @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 )
| ! [SX6: $i,SX7: $i] :
( ~ ~ ( ~ ( member @ SX6 @ SX3 )
| ~ ( member @ SX7 @ SX5 ) )
| ~ ( ~ ( ~ ( apply @ SX0 @ SX6 @ SX7 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) )
| ( apply @ SX0 @ SX6 @ SX7 ) ) ) ) )
| ~ ( ~ ! [SX6: $i,SX7: $i] :
( ~ ~ ( ~ ( member @ SX6 @ SX3 )
| ~ ( member @ SX7 @ SX5 ) )
| ~ ( ~ ( ~ ( apply @ SX0 @ SX6 @ SX7 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SX4 )
| ~ ( apply @ SX2 @ SX6 @ SX8 ) )
| ~ ( apply @ SX1 @ SX8 @ SX7 ) )
| ( apply @ SX0 @ SX6 @ SX7 ) ) ) )
| ( compose_predicate @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(58,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)],[50]) ).
thf(59,plain,
( ( equal_maps @ sK3_SY37 @ sK4_SY42 @ sK5_SY46 @ sK7_SY51 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV1: $i] :
( ( ! [SY52: $i,SY53: $i] :
~ ( ~ ( ~ ( maps @ SV1 @ SY52 @ SY53 )
| ~ ( ~ ! [SY54: $i] :
( ~ ( member @ SY54 @ SY52 )
| ~ ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SY53 )
| ~ ( apply @ SV1 @ SY54 @ SY55 ) ) )
| ~ ! [SY56: $i,SY57: $i,SY58: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY56 @ SY52 )
| ~ ( member @ SY57 @ SY53 ) )
| ~ ( member @ SY58 @ SY53 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY56 @ SY57 )
| ~ ( apply @ SV1 @ SY56 @ SY58 ) )
| ( SY57 = SY58 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY59: $i] :
( ~ ( member @ SY59 @ SY52 )
| ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ SY53 )
| ~ ( apply @ SV1 @ SY59 @ SY60 ) ) )
| ~ ! [SY61: $i,SY62: $i,SY63: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY61 @ SY52 )
| ~ ( member @ SY62 @ SY53 ) )
| ~ ( member @ SY63 @ SY53 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY61 @ SY62 )
| ~ ( apply @ SV1 @ SY61 @ SY63 ) )
| ( SY62 = SY63 ) ) )
| ( maps @ SV1 @ SY52 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV2: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i,SY67: $i,SY68: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV2 @ SY64 @ SY65 @ SY66 @ SY67 @ SY68 )
| ! [SY69: $i,SY70: $i] :
( ~ ~ ( ~ ( member @ SY69 @ SY66 )
| ~ ( member @ SY70 @ SY68 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY69 @ SY70 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY67 )
| ~ ( apply @ SY65 @ SY69 @ SX8 ) )
| ~ ( apply @ SY64 @ SX8 @ SY70 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY67 )
| ~ ( apply @ SY65 @ SY69 @ SX8 ) )
| ~ ( apply @ SY64 @ SX8 @ SY70 ) )
| ( apply @ SV2 @ SY69 @ SY70 ) ) ) ) )
| ~ ( ~ ! [SY73: $i,SY74: $i] :
( ~ ~ ( ~ ( member @ SY73 @ SY66 )
| ~ ( member @ SY74 @ SY68 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY73 @ SY74 )
| ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY67 )
| ~ ( apply @ SY65 @ SY73 @ SX8 ) )
| ~ ( apply @ SY64 @ SX8 @ SY74 ) ) )
| ~ ( ~ ~ ! [SX8: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX8 @ SY67 )
| ~ ( apply @ SY65 @ SY73 @ SX8 ) )
| ~ ( apply @ SY64 @ SX8 @ SY74 ) )
| ( apply @ SV2 @ SY73 @ SY74 ) ) ) )
| ( compose_predicate @ SV2 @ SY64 @ SY65 @ SY66 @ SY67 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV3: $i] :
( ( ! [SY77: $i,SY78: $i,SY79: $i] :
~ ( ~ ( ~ ( equal_maps @ SV3 @ SY77 @ SY78 @ SY79 )
| ! [SY80: $i,SY81: $i,SY82: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY80 @ SY78 )
| ~ ( member @ SY81 @ SY79 ) )
| ~ ( member @ SY82 @ SY79 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY80 @ SY81 )
| ~ ( apply @ SY77 @ SY80 @ SY82 ) )
| ( SY81 = SY82 ) ) )
| ~ ( ~ ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY83 @ SY78 )
| ~ ( member @ SY84 @ SY79 ) )
| ~ ( member @ SY85 @ SY79 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY83 @ SY84 )
| ~ ( apply @ SY77 @ SY83 @ SY85 ) )
| ( SY84 = SY85 ) )
| ( equal_maps @ SV3 @ SY77 @ SY78 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY86: $i] :
~ ( ~ ( ~ ( maps @ SV1 @ SV4 @ SY86 )
| ~ ( ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV4 )
| ~ ! [SY55: $i] :
~ ~ ( ~ ( member @ SY55 @ SY86 )
| ~ ( apply @ SV1 @ SY87 @ SY55 ) ) )
| ~ ! [SY89: $i,SY90: $i,SY91: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY89 @ SV4 )
| ~ ( member @ SY90 @ SY86 ) )
| ~ ( member @ SY91 @ SY86 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY89 @ SY90 )
| ~ ( apply @ SV1 @ SY89 @ SY91 ) )
| ( SY90 = SY91 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY92: $i] :
( ~ ( member @ SY92 @ SV4 )
| ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ SY86 )
| ~ ( apply @ SV1 @ SY92 @ SY60 ) ) )
| ~ ! [SY94: $i,SY95: $i,SY96: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY94 @ SV4 )
| ~ ( member @ SY95 @ SY86 ) )
| ~ ( member @ SY96 @ SY86 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY94 @ SY95 )
| ~ ( apply @ SV1 @ SY94 @ SY96 ) )
| ( SY95 = SY96 ) ) )
| ( maps @ SV1 @ SV4 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i,SY100: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV2 @ SV5 @ SY97 @ SY98 @ SY99 @ SY100 )
| ! [SY101: $i,SY102: $i] :
( ~ ~ ( ~ ( member @ SY101 @ SY98 )
| ~ ( member @ SY102 @ SY100 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY101 @ SY102 )
| ~ ! [SY103: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY103 @ SY99 )
| ~ ( apply @ SY97 @ SY101 @ SY103 ) )
| ~ ( apply @ SV5 @ SY103 @ SY102 ) ) )
| ~ ( ~ ~ ! [SY104: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY104 @ SY99 )
| ~ ( apply @ SY97 @ SY101 @ SY104 ) )
| ~ ( apply @ SV5 @ SY104 @ SY102 ) )
| ( apply @ SV2 @ SY101 @ SY102 ) ) ) ) )
| ~ ( ~ ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( member @ SY105 @ SY98 )
| ~ ( member @ SY106 @ SY100 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY105 @ SY106 )
| ~ ! [SY107: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY107 @ SY99 )
| ~ ( apply @ SY97 @ SY105 @ SY107 ) )
| ~ ( apply @ SV5 @ SY107 @ SY106 ) ) )
| ~ ( ~ ~ ! [SY108: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY108 @ SY99 )
| ~ ( apply @ SY97 @ SY105 @ SY108 ) )
| ~ ( apply @ SV5 @ SY108 @ SY106 ) )
| ( apply @ SV2 @ SY105 @ SY106 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SY97 @ SY98 @ SY99 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY109: $i,SY110: $i] :
~ ( ~ ( ~ ( equal_maps @ SV3 @ SV6 @ SY109 @ SY110 )
| ! [SY111: $i,SY112: $i,SY113: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY111 @ SY109 )
| ~ ( member @ SY112 @ SY110 ) )
| ~ ( member @ SY113 @ SY110 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY111 @ SY112 )
| ~ ( apply @ SV6 @ SY111 @ SY113 ) )
| ( SY112 = SY113 ) ) )
| ~ ( ~ ! [SY114: $i,SY115: $i,SY116: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY114 @ SY109 )
| ~ ( member @ SY115 @ SY110 ) )
| ~ ( member @ SY116 @ SY110 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY114 @ SY115 )
| ~ ( apply @ SV6 @ SY114 @ SY116 ) )
| ( SY115 = SY116 ) )
| ( equal_maps @ SV3 @ SV6 @ SY109 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( maps @ SV1 @ SV4 @ SV7 )
| ~ ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) )
| ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
| ( maps @ SV1 @ SV4 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV8: $i,SV5: $i,SV2: $i] :
( ( ! [SY127: $i,SY128: $i,SY129: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SY127 @ SY128 @ SY129 )
| ! [SY130: $i,SY131: $i] :
( ~ ~ ( ~ ( member @ SY130 @ SY127 )
| ~ ( member @ SY131 @ SY129 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY130 @ SY131 )
| ~ ! [SY132: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY132 @ SY128 )
| ~ ( apply @ SV8 @ SY130 @ SY132 ) )
| ~ ( apply @ SV5 @ SY132 @ SY131 ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY133 @ SY128 )
| ~ ( apply @ SV8 @ SY130 @ SY133 ) )
| ~ ( apply @ SV5 @ SY133 @ SY131 ) )
| ( apply @ SV2 @ SY130 @ SY131 ) ) ) ) )
| ~ ( ~ ! [SY134: $i,SY135: $i] :
( ~ ~ ( ~ ( member @ SY134 @ SY127 )
| ~ ( member @ SY135 @ SY129 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY134 @ SY135 )
| ~ ! [SY136: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY136 @ SY128 )
| ~ ( apply @ SV8 @ SY134 @ SY136 ) )
| ~ ( apply @ SV5 @ SY136 @ SY135 ) ) )
| ~ ( ~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY137 @ SY128 )
| ~ ( apply @ SV8 @ SY134 @ SY137 ) )
| ~ ( apply @ SV5 @ SY137 @ SY135 ) )
| ( apply @ SV2 @ SY134 @ SY135 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SV8 @ SY127 @ SY128 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ! [SY138: $i] :
~ ( ~ ( ~ ( equal_maps @ SV3 @ SV6 @ SV9 @ SY138 )
| ! [SY139: $i,SY140: $i,SY141: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY139 @ SV9 )
| ~ ( member @ SY140 @ SY138 ) )
| ~ ( member @ SY141 @ SY138 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY139 @ SY140 )
| ~ ( apply @ SV6 @ SY139 @ SY141 ) )
| ( SY140 = SY141 ) ) )
| ~ ( ~ ! [SY142: $i,SY143: $i,SY144: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY142 @ SV9 )
| ~ ( member @ SY143 @ SY138 ) )
| ~ ( member @ SY144 @ SY138 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY142 @ SY143 )
| ~ ( apply @ SV6 @ SY142 @ SY144 ) )
| ( SY143 = SY144 ) )
| ( equal_maps @ SV3 @ SV6 @ SV9 @ SY138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( ~ ( maps @ SV1 @ SV4 @ SV7 )
| ~ ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) )
| ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
| ( maps @ SV1 @ SV4 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ! [SY145: $i,SY146: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SY145 @ SY146 )
| ! [SY147: $i,SY148: $i] :
( ~ ~ ( ~ ( member @ SY147 @ SV10 )
| ~ ( member @ SY148 @ SY146 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY147 @ SY148 )
| ~ ! [SY132: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY132 @ SY145 )
| ~ ( apply @ SV8 @ SY147 @ SY132 ) )
| ~ ( apply @ SV5 @ SY132 @ SY148 ) ) )
| ~ ( ~ ~ ! [SY133: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY133 @ SY145 )
| ~ ( apply @ SV8 @ SY147 @ SY133 ) )
| ~ ( apply @ SV5 @ SY133 @ SY148 ) )
| ( apply @ SV2 @ SY147 @ SY148 ) ) ) ) )
| ~ ( ~ ! [SY151: $i,SY152: $i] :
( ~ ~ ( ~ ( member @ SY151 @ SV10 )
| ~ ( member @ SY152 @ SY146 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY151 @ SY152 )
| ~ ! [SY136: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY136 @ SY145 )
| ~ ( apply @ SV8 @ SY151 @ SY136 ) )
| ~ ( apply @ SV5 @ SY136 @ SY152 ) ) )
| ~ ( ~ ~ ! [SY137: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY137 @ SY145 )
| ~ ( apply @ SV8 @ SY151 @ SY137 ) )
| ~ ( apply @ SV5 @ SY137 @ SY152 ) )
| ( apply @ SV2 @ SY151 @ SY152 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SY145 @ SY146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
| ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY155 @ SV9 )
| ~ ( member @ SY156 @ SV11 ) )
| ~ ( member @ SY157 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY155 @ SY156 )
| ~ ( apply @ SV6 @ SY155 @ SY157 ) )
| ( SY156 = SY157 ) ) )
| ~ ( ~ ! [SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY158 @ SV9 )
| ~ ( member @ SY159 @ SV11 ) )
| ~ ( member @ SY160 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY158 @ SY159 )
| ~ ( apply @ SV6 @ SY158 @ SY160 ) )
| ( SY159 = SY160 ) )
| ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( ~ ( maps @ SV1 @ SV4 @ SV7 )
| ~ ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) )
| ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
| ( maps @ SV1 @ SV4 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV12: $i,SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ! [SY161: $i] :
~ ( ~ ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SY161 )
| ! [SY162: $i,SY163: $i] :
( ~ ~ ( ~ ( member @ SY162 @ SV10 )
| ~ ( member @ SY163 @ SY161 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY162 @ SY163 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV12 )
| ~ ( apply @ SV8 @ SY162 @ SY164 ) )
| ~ ( apply @ SV5 @ SY164 @ SY163 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( apply @ SV8 @ SY162 @ SY165 ) )
| ~ ( apply @ SV5 @ SY165 @ SY163 ) )
| ( apply @ SV2 @ SY162 @ SY163 ) ) ) ) )
| ~ ( ~ ! [SY166: $i,SY167: $i] :
( ~ ~ ( ~ ( member @ SY166 @ SV10 )
| ~ ( member @ SY167 @ SY161 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY166 @ SY167 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY168 @ SV12 )
| ~ ( apply @ SV8 @ SY166 @ SY168 ) )
| ~ ( apply @ SV5 @ SY168 @ SY167 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( apply @ SV8 @ SY166 @ SY169 ) )
| ~ ( apply @ SV5 @ SY169 @ SY167 ) )
| ( apply @ SV2 @ SY166 @ SY167 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ~ ( ~ ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
| ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY155 @ SV9 )
| ~ ( member @ SY156 @ SV11 ) )
| ~ ( member @ SY157 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY155 @ SY156 )
| ~ ( apply @ SV6 @ SY155 @ SY157 ) )
| ( SY156 = SY157 ) ) )
| ~ ( ~ ! [SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY158 @ SV9 )
| ~ ( member @ SY159 @ SV11 ) )
| ~ ( member @ SY160 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY158 @ SY159 )
| ~ ( apply @ SV6 @ SY158 @ SY160 ) )
| ( SY159 = SY160 ) )
| ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ( maps @ SV1 @ SV4 @ SV7 )
| ~ ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ~ ~ ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) )
| ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
| ( maps @ SV1 @ SV4 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
| ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ( member @ SY170 @ SV10 )
| ~ ( member @ SY171 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY170 @ SY171 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY164 ) )
| ~ ( apply @ SV5 @ SY164 @ SY171 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY165 ) )
| ~ ( apply @ SV5 @ SY165 @ SY171 ) )
| ( apply @ SV2 @ SY170 @ SY171 ) ) ) ) )
| ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ~ ( ~ ( member @ SY174 @ SV10 )
| ~ ( member @ SY175 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY174 @ SY175 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY168 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY168 ) )
| ~ ( apply @ SV5 @ SY168 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY169 ) )
| ~ ( apply @ SV5 @ SY169 @ SY175 ) )
| ( apply @ SV2 @ SY174 @ SY175 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ~ ( ~ ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
| ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY155 @ SV9 )
| ~ ( member @ SY156 @ SV11 ) )
| ~ ( member @ SY157 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY155 @ SY156 )
| ~ ( apply @ SV6 @ SY155 @ SY157 ) )
| ( SY156 = SY157 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(80,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ~ ( ~ ! [SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY158 @ SV9 )
| ~ ( member @ SY159 @ SV11 ) )
| ~ ( member @ SY160 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY158 @ SY159 )
| ~ ( apply @ SV6 @ SY158 @ SY160 ) )
| ( SY159 = SY160 ) )
| ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(81,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( maps @ SV1 @ SV4 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) )
| ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
| ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ( member @ SY170 @ SV10 )
| ~ ( member @ SY171 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY170 @ SY171 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY164 ) )
| ~ ( apply @ SV5 @ SY164 @ SY171 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY165 ) )
| ~ ( apply @ SV5 @ SY165 @ SY171 ) )
| ( apply @ SV2 @ SY170 @ SY171 ) ) ) ) )
| ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ~ ( ~ ( member @ SY174 @ SV10 )
| ~ ( member @ SY175 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY174 @ SY175 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY168 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY168 ) )
| ~ ( apply @ SV5 @ SY168 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY169 ) )
| ~ ( apply @ SV5 @ SY169 @ SY175 ) )
| ( apply @ SV2 @ SY174 @ SY175 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ~ ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
| ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY155 @ SV9 )
| ~ ( member @ SY156 @ SV11 ) )
| ~ ( member @ SY157 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY155 @ SY156 )
| ~ ( apply @ SV6 @ SY155 @ SY157 ) )
| ( SY156 = SY157 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(85,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ~ ! [SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY158 @ SV9 )
| ~ ( member @ SY159 @ SV11 ) )
| ~ ( member @ SY160 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY158 @ SY159 )
| ~ ( apply @ SV6 @ SY158 @ SY160 ) )
| ( SY159 = SY160 ) )
| ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(86,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( maps @ SV1 @ SV4 @ SV7 )
= $false )
| ( ( ~ ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) )
| ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) ) )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
| ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ( member @ SY170 @ SV10 )
| ~ ( member @ SY171 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY170 @ SY171 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY164 ) )
| ~ ( apply @ SV5 @ SY164 @ SY171 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY165 ) )
| ~ ( apply @ SV5 @ SY165 @ SY171 ) )
| ( apply @ SV2 @ SY170 @ SY171 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ~ ( ~ ! [SY174: $i,SY175: $i] :
( ~ ~ ( ~ ( member @ SY174 @ SV10 )
| ~ ( member @ SY175 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY174 @ SY175 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY168 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY168 ) )
| ~ ( apply @ SV5 @ SY168 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY169 ) )
| ~ ( apply @ SV5 @ SY169 @ SY175 ) )
| ( apply @ SV2 @ SY174 @ SY175 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(90,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 ) )
= $true )
| ( ( ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY155 @ SV9 )
| ~ ( member @ SY156 @ SV11 ) )
| ~ ( member @ SY157 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY155 @ SY156 )
| ~ ( apply @ SV6 @ SY155 @ SY157 ) )
| ( SY156 = SY157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ( ~ ! [SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY158 @ SV9 )
| ~ ( member @ SY159 @ SV11 ) )
| ~ ( member @ SY160 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY158 @ SY159 )
| ~ ( apply @ SV6 @ SY158 @ SY160 ) )
| ( SY159 = SY160 ) ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) )
| ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) )
| ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
| ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ( member @ SY170 @ SV10 )
| ~ ( member @ SY171 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY170 @ SY171 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY164 ) )
| ~ ( apply @ SV5 @ SY164 @ SY171 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY165 ) )
| ~ ( apply @ SV5 @ SY165 @ SY171 ) )
| ( apply @ SV2 @ SY170 @ SY171 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(95,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ~ ( ~ ( member @ SY174 @ SV10 )
| ~ ( member @ SY175 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY174 @ SY175 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY168 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY168 ) )
| ~ ( apply @ SV5 @ SY168 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY169 ) )
| ~ ( apply @ SV5 @ SY169 @ SY175 ) )
| ( apply @ SV2 @ SY174 @ SY175 ) ) ) )
| ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(96,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false )
| ( ( ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY155 @ SV9 )
| ~ ( member @ SY156 @ SV11 ) )
| ~ ( member @ SY157 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY155 @ SY156 )
| ~ ( apply @ SV6 @ SY155 @ SY157 ) )
| ( SY156 = SY157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ( ! [SY158: $i,SY159: $i,SY160: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY158 @ SV9 )
| ~ ( member @ SY159 @ SV11 ) )
| ~ ( member @ SY160 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SY158 @ SY159 )
| ~ ( apply @ SV6 @ SY158 @ SY160 ) )
| ( SY159 = SY160 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) ) )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(100,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) ) )
= $true )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 ) )
= $true )
| ( ( ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ( member @ SY170 @ SV10 )
| ~ ( member @ SY171 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY170 @ SY171 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY164 ) )
| ~ ( apply @ SV5 @ SY164 @ SY171 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY165 ) )
| ~ ( apply @ SV5 @ SY165 @ SY171 ) )
| ( apply @ SV2 @ SY170 @ SY171 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ! [SY174: $i,SY175: $i] :
( ~ ~ ( ~ ( member @ SY174 @ SV10 )
| ~ ( member @ SY175 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY174 @ SY175 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY168 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY168 ) )
| ~ ( apply @ SV5 @ SY168 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY169 ) )
| ~ ( apply @ SV5 @ SY169 @ SY175 ) )
| ( apply @ SV2 @ SY174 @ SY175 ) ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i,SV14: $i] :
( ( ( ! [SY178: $i,SY179: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SY178 @ SV11 ) )
| ~ ( member @ SY179 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SY178 )
| ~ ( apply @ SV6 @ SV14 @ SY179 ) )
| ( SY178 = SY179 ) ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ! [SY180: $i,SY181: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ SY180 @ SV11 ) )
| ~ ( member @ SY181 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SY180 )
| ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SY181 ) )
| ( SY180 = SY181 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(105,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY117: $i] :
( ~ ( member @ SY117 @ SV4 )
| ~ ! [SY118: $i] :
~ ~ ( ~ ( member @ SY118 @ SV7 )
| ~ ( apply @ SV1 @ SY117 @ SY118 ) ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY119 @ SV4 )
| ~ ( member @ SY120 @ SV7 ) )
| ~ ( member @ SY121 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY119 @ SY120 )
| ~ ( apply @ SV1 @ SY119 @ SY121 ) )
| ( SY120 = SY121 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY122: $i] :
( ~ ( member @ SY122 @ SV4 )
| ~ ! [SY123: $i] :
~ ~ ( ~ ( member @ SY123 @ SV7 )
| ~ ( apply @ SV1 @ SY122 @ SY123 ) ) ) )
= $false )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV13: $i,SV12: $i,SV10: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false )
| ( ( ! [SY170: $i,SY171: $i] :
( ~ ~ ( ~ ( member @ SY170 @ SV10 )
| ~ ( member @ SY171 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY170 @ SY171 )
| ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY164 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY164 ) )
| ~ ( apply @ SV5 @ SY164 @ SY171 ) ) )
| ~ ( ~ ~ ! [SY165: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY165 @ SV12 )
| ~ ( apply @ SV8 @ SY170 @ SY165 ) )
| ~ ( apply @ SV5 @ SY165 @ SY171 ) )
| ( apply @ SV2 @ SY170 @ SY171 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ! [SY174: $i,SY175: $i] :
( ~ ~ ( ~ ( member @ SY174 @ SV10 )
| ~ ( member @ SY175 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SY174 @ SY175 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY168 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY168 ) )
| ~ ( apply @ SV5 @ SY168 @ SY175 ) ) )
| ~ ( ~ ~ ! [SY169: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY169 @ SV12 )
| ~ ( apply @ SV8 @ SY174 @ SY169 ) )
| ~ ( apply @ SV5 @ SY169 @ SY175 ) )
| ( apply @ SV2 @ SY174 @ SY175 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ! [SY182: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) )
| ~ ( member @ SY182 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SY182 ) )
| ( SV15 = SY182 ) ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ! [SY183: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
| ~ ( member @ SY183 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) )
| ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SY183 ) )
| ( ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 )
= SY183 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(112,plain,
! [SV1: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV4 )
| ~ ! [SY184: $i] :
~ ~ ( ~ ( member @ SY184 @ SV7 )
| ~ ( apply @ SV1 @ SV16 @ SY184 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV1: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( ! [SY185: $i,SY186: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SY185 @ SV7 ) )
| ~ ( member @ SY186 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SY185 )
| ~ ( apply @ SV1 @ SV17 @ SY186 ) )
| ( SY185 = SY186 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ! [SY187: $i] :
~ ~ ( ~ ( member @ SY187 @ SV7 )
| ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SY187 ) ) )
= $false )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[107]) ).
thf(115,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i,SV18: $i] :
( ( ( ! [SY188: $i] :
( ~ ~ ( ~ ( member @ SV18 @ SV10 )
| ~ ( member @ SY188 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SY188 )
| ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY189 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY189 ) )
| ~ ( apply @ SV5 @ SY189 @ SY188 ) ) )
| ~ ( ~ ~ ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY190 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY190 ) )
| ~ ( apply @ SV5 @ SY190 @ SY188 ) )
| ( apply @ SV2 @ SV18 @ SY188 ) ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV8: $i,SV5: $i] :
( ( ( ! [SY191: $i] :
( ~ ~ ( ~ ( member @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV10 )
| ~ ( member @ SY191 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY191 )
| ~ ! [SY192: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY192 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY192 ) )
| ~ ( apply @ SV5 @ SY192 @ SY191 ) ) )
| ~ ( ~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY193 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY193 ) )
| ~ ( apply @ SV5 @ SY193 @ SY191 ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY191 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(117,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) )
| ~ ( member @ SV19 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) )
| ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) )
| ( ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 )
= ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(119,plain,
! [SV1: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ! [SY184: $i] :
~ ~ ( ~ ( member @ SY184 @ SV7 )
| ~ ( apply @ SV1 @ SV16 @ SY184 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV1: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ! [SY194: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) )
| ~ ( member @ SY194 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SY194 ) )
| ( SV20 = SY194 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 ) )
= $false )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ! [SY187: $i] :
~ ~ ( ~ ( member @ SY187 @ SV7 )
| ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SY187 ) ) )
= $false )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV21: $i,SV10: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( member @ SV18 @ SV10 )
| ~ ( member @ SV21 @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(124,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV8: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) @ SV13 ) )
| ~ ( ~ ( ~ ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
| ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY197 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY197 ) )
| ~ ( apply @ SV5 @ SY197 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
| ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(125,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) )
| ~ ( member @ SV19 @ SV11 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(127,plain,
! [SV9: $i,SV11: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) )
| ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) )
| ( ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 )
= ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(128,plain,
! [SV1: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( member @ SV16 @ SV4 )
= $false )
| ( ( ~ ! [SY184: $i] :
~ ~ ( ~ ( member @ SY184 @ SV7 )
| ~ ( apply @ SV1 @ SV16 @ SY184 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) )
| ~ ( member @ SV22 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(131,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ! [SY187: $i] :
~ ~ ( ~ ( member @ SY187 @ SV7 )
| ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SY187 ) ) )
= $true )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(132,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV21: $i,SV10: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( member @ SV18 @ SV10 )
| ~ ( member @ SV21 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV8: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) @ SV13 ) ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(134,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( ~ ( ~ ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
| ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY197 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY197 ) )
| ~ ( apply @ SV5 @ SY197 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
| ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(135,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) )
| ~ ( member @ SV19 @ SV11 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(137,plain,
! [SV9: $i,SV11: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) )
| ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(138,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ( ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 )
= ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(139,plain,
! [SV4: $i,SV16: $i,SV1: $i,SV7: $i] :
( ( ( ! [SY184: $i] :
~ ~ ( ~ ( member @ SY184 @ SV7 )
| ~ ( apply @ SV1 @ SV16 @ SY184 ) ) )
= $false )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) )
| ~ ( member @ SV22 @ SV7 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ SV23 @ SV7 )
| ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 ) ) )
= $true )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV21: $i,SV10: $i,SV18: $i] :
( ( ( ~ ( ~ ( member @ SV18 @ SV10 )
| ~ ( member @ SV21 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( ~ ( member @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) @ SV13 ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(145,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
| ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY197 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY197 ) )
| ~ ( apply @ SV5 @ SY197 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
| ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(146,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) )
| ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(147,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV9: $i,SV11: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) )
| ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV7: $i,SV1: $i,SV16: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) @ SV7 )
| ~ ( apply @ SV1 @ SV16 @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) ) ) )
= $false )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[139]) ).
thf(150,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) )
| ~ ( member @ SV22 @ SV7 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ! [SY199: $i,SY200: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ SY199 @ SV7 ) )
| ~ ( member @ SY200 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SY199 )
| ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SY200 ) )
| ( SY199 = SY200 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[141]) ).
thf(152,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ SV23 @ SV7 )
| ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 ) ) )
= $false )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV21: $i,SV10: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ SV10 )
| ~ ( member @ SV21 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(154,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV10 )
| ~ ( member @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) @ SV13 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
| ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY197 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY197 ) )
| ~ ( apply @ SV5 @ SY197 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) ) )
= $true )
| ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(158,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(159,plain,
! [SV9: $i,SV11: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) )
| ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV7: $i,SV1: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( ~ ( member @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) @ SV7 )
| ~ ( apply @ SV1 @ SV16 @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) ) ) )
= $true )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(161,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) )
| ~ ( member @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(162,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ! [SY201: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
| ~ ( member @ SY201 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SY201 ) )
| ( ( sK16_SY199 @ SV4 @ SV7 @ SV1 )
= SY201 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[151]) ).
thf(163,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV7 )
| ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 ) )
= $true )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(164,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV21: $i,SV10: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ SV10 ) )
= $true )
| ( ( ~ ( member @ SV21 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV10 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(166,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) @ SV13 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(167,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
| ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY197 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY197 ) )
| ~ ( apply @ SV5 @ SY197 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) ) )
= $false )
| ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(170,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ( member @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(171,plain,
! [SV9: $i,SV11: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(172,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(173,plain,
! [SV7: $i,SV1: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) @ SV7 )
| ~ ( apply @ SV1 @ SV16 @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) ) )
= $false )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
| ~ ( member @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) )
| ( ( sK16_SY199 @ SV4 @ SV7 @ SV1 )
= ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[162]) ).
thf(176,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV7 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 ) )
= $true )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV21: $i,SV10: $i,SV18: $i] :
( ( ( member @ SV18 @ SV10 )
= $false )
| ( ( ~ ( member @ SV21 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(178,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV8: $i,SV5: $i] :
( ( ( member @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV10 )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(179,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( member @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) @ SV13 )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(180,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(181,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY197 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY197 ) )
| ~ ( apply @ SV5 @ SY197 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(182,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV9 )
| ~ ( member @ SV15 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(183,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
| ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(184,plain,
! [SV9: $i,SV11: $i,SV6: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(185,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( apply @ SV6 @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ ( sK12_SY183 @ SV9 @ SV11 @ SV3 @ SV6 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(186,plain,
! [SV7: $i,SV1: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) @ SV7 ) )
= $false )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(187,plain,
! [SV7: $i,SV4: $i,SV16: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV16 @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) ) )
= $false )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(188,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) ) )
= $false )
| ( ( ~ ( member @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(189,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
| ~ ( member @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) @ SV7 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(190,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) )
| ( ( sK16_SY199 @ SV4 @ SV7 @ SV1 )
= ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(191,plain,
! [SV4: $i,SV1: $i,SV7: $i,SV23: $i] :
( ( ( member @ SV23 @ SV7 )
= $false )
| ( ( ~ ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 ) )
= $true )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(192,plain,
! [SV5: $i,SV8: $i,SV12: $i,SV2: $i,SV10: $i,SV18: $i,SV13: $i,SV21: $i] :
( ( ( member @ SV21 @ SV13 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(193,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(194,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY197 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY197 ) )
| ~ ( apply @ SV5 @ SY197 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(195,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV9 ) )
= $true )
| ( ( ~ ( member @ SV15 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(196,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(197,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 ) )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(198,plain,
! [SV7: $i,SV1: $i,SV16: $i,SV4: $i] :
( ( ( member @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) @ SV7 )
= $true )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(199,plain,
! [SV7: $i,SV4: $i,SV16: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV16 @ ( sK14_SY184 @ SV4 @ SV16 @ SV1 @ SV7 ) )
= $true )
| ( ( member @ SV16 @ SV4 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(200,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV4 )
| ~ ( member @ SV20 @ SV7 ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(201,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
| ~ ( member @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) @ SV7 ) ) )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(202,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(203,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ( sK16_SY199 @ SV4 @ SV7 @ SV1 )
= ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(204,plain,
! [SV23: $i,SV4: $i,SV7: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( ~ ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV13: $i,SV10: $i,SV5: $i,SV8: $i,SV12: $i,SV21: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
| ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(206,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV24 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) )
| ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(208,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV11: $i,SV15: $i,SV9: $i,SV14: $i] :
( ( ( member @ SV14 @ SV9 )
= $false )
| ( ( ~ ( member @ SV15 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(209,plain,
! [SV9: $i,SV11: $i,SV3: $i,SV6: $i] :
( ( ( member @ ( sK8_SY158 @ SV6 @ SV3 @ SV11 @ SV9 ) @ SV9 )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(210,plain,
! [SV6: $i,SV3: $i,SV11: $i,SV9: $i] :
( ( ( member @ ( sK9_SY180 @ SV9 @ SV11 @ SV3 @ SV6 ) @ SV11 )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(211,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV4 ) )
= $true )
| ( ( ~ ( member @ SV20 @ SV7 ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
| ~ ( member @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) ) )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(214,plain,
! [SV23: $i,SV1: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV4 )
| ~ ( member @ SY125 @ SV7 ) )
| ~ ( member @ SY126 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY124 @ SY125 )
| ~ ( apply @ SV1 @ SY124 @ SY126 ) )
| ( SY125 = SY126 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV13: $i,SV10: $i,SV5: $i,SV8: $i,SV12: $i,SV21: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) ) )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(216,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) ) )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(217,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(218,plain,
! [SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(219,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV24 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) )
| ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(220,plain,
! [SV6: $i,SV3: $i,SV19: $i,SV9: $i,SV14: $i,SV11: $i,SV15: $i] :
( ( ( member @ SV15 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(221,plain,
! [SV1: $i,SV22: $i,SV7: $i,SV20: $i,SV4: $i,SV17: $i] :
( ( ( member @ SV17 @ SV4 )
= $false )
| ( ( ~ ( member @ SV20 @ SV7 ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(222,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(223,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(224,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(225,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ! [SY202: $i,SY203: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ SY202 @ SV7 ) )
| ~ ( member @ SY203 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SY202 )
| ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SY203 ) )
| ( SY202 = SY203 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[214]) ).
thf(226,plain,
! [SV13: $i,SV10: $i,SV5: $i,SV8: $i,SV12: $i,SV21: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ SV18 @ SV21 )
| ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(227,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) )
| ( apply @ SV2 @ SV18 @ SV21 ) )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(228,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(229,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ SV24 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) )
| ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(230,plain,
! [SV6: $i,SV3: $i,SV15: $i,SV9: $i,SV14: $i,SV11: $i,SV19: $i] :
( ( ( member @ SV19 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( member @ SV15 @ SV11 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
| ( SV15 = SV19 ) )
= $true )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(231,plain,
! [SV1: $i,SV22: $i,SV4: $i,SV17: $i,SV7: $i,SV20: $i] :
( ( ( member @ SV20 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( ~ ( member @ SV22 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(232,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) ) )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(233,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( member @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) @ SV7 )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(234,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(235,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(236,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ! [SY204: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
| ~ ( member @ SY204 @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) )
| ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SY204 ) )
| ( ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 )
= SY204 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[225]) ).
thf(237,plain,
! [SV13: $i,SV10: $i,SV5: $i,SV8: $i,SV12: $i,SV21: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ SV18 @ SV21 ) )
= $true )
| ( ( ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(239,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(240,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ SV24 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV9: $i,SV11: $i,SV19: $i,SV6: $i,SV15: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) ) )
= $true )
| ( ( SV15 = SV19 )
= $true )
| ( ( member @ SV15 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV1: $i,SV20: $i,SV4: $i,SV17: $i,SV7: $i,SV22: $i] :
( ( ( member @ SV22 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( member @ SV20 @ SV7 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
| ( SV20 = SV22 ) )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(245,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ ( sK17_SY201 @ SV4 @ SV7 @ SV1 ) )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(246,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
| ~ ( member @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) )
| ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) )
| ( ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 )
= ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[236]) ).
thf(247,plain,
! [SV13: $i,SV10: $i,SV5: $i,SV8: $i,SV12: $i,SV21: $i,SV18: $i,SV2: $i] :
( ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i] :
( ( ( ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[239]) ).
thf(250,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( ~ ( ~ ( member @ SV24 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) ) )
= $false )
| ( ( ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(251,plain,
! [SV9: $i,SV11: $i,SV19: $i,SV6: $i,SV15: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) ) )
= $false )
| ( ( SV15 = SV19 )
= $true )
| ( ( member @ SV15 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(252,plain,
! [SV4: $i,SV7: $i,SV22: $i,SV20: $i,SV17: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) ) )
= $true )
| ( ( SV20 = SV22 )
= $true )
| ( ( member @ SV20 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( member @ SV22 @ SV7 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(253,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(254,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 ) )
= $false )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(255,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
| ~ ( member @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(256,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) )
| ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) )
| ( ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 )
= ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(257,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i] :
( ( ( ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY195 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY195 ) )
| ~ ( apply @ SV5 @ SY195 @ SV21 ) ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(258,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i] :
( ( ( ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY196 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SY196 ) )
| ~ ( apply @ SV5 @ SY196 @ SV21 ) ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(259,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(260,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(261,plain,
! [SV9: $i,SV11: $i,SV19: $i,SV6: $i,SV15: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ SV14 @ SV15 )
| ~ ( apply @ SV6 @ SV14 @ SV19 ) )
= $true )
| ( ( SV15 = SV19 )
= $true )
| ( ( member @ SV15 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(262,plain,
! [SV4: $i,SV7: $i,SV22: $i,SV20: $i,SV17: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) ) )
= $false )
| ( ( SV20 = SV22 )
= $true )
| ( ( member @ SV20 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( member @ SV22 @ SV7 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(263,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( member @ ( sK15_SY124 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(264,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( member @ ( sK16_SY199 @ SV4 @ SV7 @ SV1 ) @ SV7 )
= $true )
| ( ( member @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(265,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
| ~ ( member @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) ) )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(266,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) )
| ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(267,plain,
! [SV23: $i,SV1: $i,SV7: $i,SV4: $i] :
( ( ( ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 )
= ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(268,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV21 ) ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[257]) ).
thf(269,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SV25 ) )
| ~ ( apply @ SV5 @ SV25 @ SV21 ) ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV12 ) )
= $true )
| ( ( ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV9: $i,SV11: $i,SV19: $i,SV6: $i,SV15: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ SV14 @ SV15 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV14 @ SV19 ) )
= $true )
| ( ( SV15 = SV19 )
= $true )
| ( ( member @ SV15 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(273,plain,
! [SV4: $i,SV7: $i,SV22: $i,SV20: $i,SV17: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV17 @ SV20 )
| ~ ( apply @ SV1 @ SV17 @ SV22 ) )
= $true )
| ( ( SV20 = SV22 )
= $true )
| ( ( member @ SV20 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( member @ SV22 @ SV7 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(274,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
| ~ ( member @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(275,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) )
| ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) ) )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(276,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV21 ) ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(277,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SV25 ) )
| ~ ( apply @ SV5 @ SV25 @ SV21 ) ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(278,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(279,plain,
! [SV12: $i,SV8: $i,SV2: $i,SV13: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(280,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i,SV24: $i] :
( ( ( member @ SV24 @ SV12 )
= $false )
| ( ( ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(281,plain,
! [SV9: $i,SV11: $i,SV19: $i,SV6: $i,SV15: $i,SV14: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV14 @ SV15 )
= $false )
| ( ( ~ ( apply @ SV6 @ SV14 @ SV19 ) )
= $true )
| ( ( SV15 = SV19 )
= $true )
| ( ( member @ SV15 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(282,plain,
! [SV4: $i,SV7: $i,SV22: $i,SV20: $i,SV17: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV17 @ SV20 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV17 @ SV22 ) )
= $true )
| ( ( SV20 = SV22 )
= $true )
| ( ( member @ SV20 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( member @ SV22 @ SV7 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(283,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(284,plain,
! [SV23: $i,SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(285,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) )
| ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(286,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV21 ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SV25 ) )
| ~ ( apply @ SV5 @ SV25 @ SV21 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(288,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( ~ ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) ) )
= $true )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(289,plain,
! [SV12: $i,SV8: $i,SV2: $i,SV13: $i,SV10: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(290,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV5: $i,SV8: $i] :
( ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( ~ ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(291,plain,
! [SV9: $i,SV11: $i,SV15: $i,SV3: $i,SV19: $i,SV14: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV14 @ SV19 )
= $false )
| ( ( apply @ SV3 @ SV14 @ SV15 )
= $false )
| ( ( SV15 = SV19 )
= $true )
| ( ( member @ SV15 @ SV11 )
= $false )
| ( ( member @ SV14 @ SV9 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( equal_maps @ SV3 @ SV6 @ SV9 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(292,plain,
! [SV4: $i,SV7: $i,SV22: $i,SV20: $i,SV17: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV17 @ SV20 )
= $false )
| ( ( ~ ( apply @ SV1 @ SV17 @ SV22 ) )
= $true )
| ( ( SV20 = SV22 )
= $true )
| ( ( member @ SV20 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( member @ SV22 @ SV7 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(293,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) ) )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(294,plain,
! [SV23: $i,SV1: $i,SV7: $i,SV4: $i] :
( ( ( member @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(295,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(296,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(297,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) ) ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(298,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV21 ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(299,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SV25 ) ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV25 @ SV21 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(301,plain,
! [SV8: $i,SV12: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( ~ ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(302,plain,
! [SV4: $i,SV7: $i,SV20: $i,SV22: $i,SV17: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV17 @ SV22 )
= $false )
| ( ( apply @ SV1 @ SV17 @ SV20 )
= $false )
| ( ( SV20 = SV22 )
= $true )
| ( ( member @ SV20 @ SV7 )
= $false )
| ( ( member @ SV17 @ SV4 )
= $false )
| ( ( member @ SV22 @ SV7 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(303,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(304,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(305,plain,
! [SV4: $i,SV7: $i,SV23: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ ( sK20_SY204 @ SV4 @ SV7 @ SV1 @ SV23 ) )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(306,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) ) ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(307,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV21 )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(308,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( ~ ( member @ SV25 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SV25 ) ) )
= $false )
| ( ( ~ ( apply @ SV5 @ SV25 @ SV21 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(309,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( ~ ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(310,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
= $false )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(311,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
| ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(312,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(313,plain,
! [SV23: $i,SV1: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 ) )
= $false )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(314,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(315,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV12 )
| ~ ( apply @ SV8 @ SV18 @ SV25 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV25 @ SV21 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(316,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i] :
( ( ( member @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
= $true )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(317,plain,
! [SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV5: $i,SV8: $i] :
( ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK21_SY198 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) )
= $true )
| ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(318,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(319,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV12: $i,SV8: $i,SV5: $i,SV2: $i] :
( ( ( apply @ SV2 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(320,plain,
! [SV4: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( member @ ( sK18_SY124 @ SV23 @ SV1 @ SV7 @ SV4 ) @ SV4 )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(321,plain,
! [SV23: $i,SV1: $i,SV7: $i,SV4: $i] :
( ( ( member @ ( sK19_SY202 @ SV4 @ SV7 @ SV1 @ SV23 ) @ SV7 )
= $true )
| ( ( member @ SV23 @ SV7 )
= $false )
| ( ( apply @ SV1 @ ( sK10_SY122 @ SV1 @ SV7 @ SV4 ) @ SV23 )
= $false )
| ( ( maps @ SV1 @ SV4 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(322,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(323,plain,
! [SV12: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) ) )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(324,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( ~ ( member @ SV25 @ SV12 ) )
= $true )
| ( ( ~ ( apply @ SV8 @ SV18 @ SV25 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV25 @ SV21 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(325,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(326,plain,
! [SV12: $i,SV8: $i,SV18: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i] :
( ( ( member @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) @ SV12 )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(327,plain,
! [SV12: $i,SV5: $i,SV21: $i,SV2: $i,SV10: $i,SV13: $i,SV18: $i,SV8: $i] :
( ( ( apply @ SV8 @ SV18 @ ( sK22_SY195 @ SV13 @ SV10 @ SV2 @ SV21 @ SV5 @ SV18 @ SV8 @ SV12 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $false )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(328,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV18: $i,SV8: $i,SV12: $i,SV25: $i] :
( ( ( member @ SV25 @ SV12 )
= $false )
| ( ( ~ ( apply @ SV8 @ SV18 @ SV25 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV25 @ SV21 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(329,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV2: $i,SV5: $i,SV8: $i,SV12: $i] :
( ( ( ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY198 @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SY198 ) )
| ~ ( apply @ SV5 @ SY198 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(330,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV21: $i,SV5: $i,SV12: $i,SV25: $i,SV18: $i,SV8: $i] :
( ( ( apply @ SV8 @ SV18 @ SV25 )
= $false )
| ( ( member @ SV25 @ SV12 )
= $false )
| ( ( ~ ( apply @ SV5 @ SV25 @ SV21 ) )
= $true )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(331,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[329]) ).
thf(332,plain,
! [SV13: $i,SV10: $i,SV2: $i,SV18: $i,SV8: $i,SV12: $i,SV21: $i,SV25: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV25 @ SV21 )
= $false )
| ( ( member @ SV25 @ SV12 )
= $false )
| ( ( apply @ SV8 @ SV18 @ SV25 )
= $false )
| ( ( apply @ SV2 @ SV18 @ SV21 )
= $true )
| ( ( member @ SV18 @ SV10 )
= $false )
| ( ( member @ SV21 @ SV13 )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(333,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(334,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
| ~ ( apply @ SV5 @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(335,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(336,plain,
! [SV12: $i,SV8: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(337,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( ~ ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) ) )
= $true )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(338,plain,
! [SV12: $i,SV8: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $true )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(339,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
| ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(340,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( ~ ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(341,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) ) )
= $false )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(342,plain,
! [SV12: $i,SV8: $i,SV5: $i,SV2: $i,SV13: $i,SV10: $i,SV24: $i] :
( ( ( member @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) @ SV12 )
= $true )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(343,plain,
! [SV24: $i,SV10: $i,SV13: $i,SV2: $i,SV12: $i,SV5: $i,SV8: $i] :
( ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ ( sK23_SY198 @ SV24 @ SV10 @ SV13 @ SV2 @ SV5 @ SV8 @ SV12 ) )
= $true )
| ( ( apply @ SV8 @ ( sK11_SY174 @ SV5 @ SV8 @ SV12 @ SV2 @ SV13 @ SV10 ) @ SV24 )
= $false )
| ( ( member @ SV24 @ SV12 )
= $false )
| ( ( apply @ SV5 @ SV24 @ ( sK13_SY191 @ SV10 @ SV13 @ SV2 @ SV12 @ SV8 @ SV5 ) )
= $false )
| ( ( compose_predicate @ SV2 @ SV5 @ SV8 @ SV10 @ SV12 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(344,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,343,342,338,332,327,326,321,320,319,317,316,307,305,304,302,294,291,289,267,264,263,245,244,233,218,210,209,203,199,198,185,184,179,178,170,138,59,54,53,52]) ).
thf(345,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET708+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n003.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 14:51:10 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.01/3.93
% 22.01/3.93 No.of.Axioms: 3
% 22.01/3.93
% 22.01/3.93 Length.of.Defs: 0
% 22.01/3.93
% 22.01/3.93 Contains.Choice.Funs: false
% 22.01/3.93 ................
% 22.01/3.93
% 22.01/3.93 ********************************
% 22.01/3.93 * All subproblems solved! *
% 22.01/3.93 ********************************
% 22.01/3.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:344,loop_count:0,foatp_calls:1,translation:fof_full)
% 22.01/3.93
% 22.01/3.93 %**** Beginning of derivation protocol ****
% 22.01/3.93 % SZS output start CNFRefutation
% See solution above
% 22.01/3.94
% 22.01/3.94 %**** End of derivation protocol ****
% 22.01/3.94 %**** no. of clauses in derivation: 320 ****
% 22.01/3.94 %**** clause counter: 344 ****
% 22.01/3.94
% 22.01/3.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:344,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------