%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET754+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 : n013.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 10:40:59 AM UTC 2026
% Result : Theorem 56.76s 11.84s
% Output : CNFRefutation 56.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 7
% Syntax : Number of formulae : 255 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 2370 ( 645 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 6110 (1460 ~; 895 |; 31 &;3687 @)
% ( 18 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 7 con; 0-6 aty)
% Number of variables : 1037 ( 0 ^;1028 !; 9 ?;1037 :)
% 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_SY86,type,
sK10_SY86: $i > $i > $i > $i ).
thf(tp_sK11_SY96,type,
sK11_SY96: $i > $i > $i > $i ).
thf(tp_sK12_SY98,type,
sK12_SY98: $i > $i > $i > $i ).
thf(tp_sK13_SY86,type,
sK13_SY86: $i > $i > $i > $i > $i ).
thf(tp_sK14_SY99,type,
sK14_SY99: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY101,type,
sK15_SY101: $i > $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK2_SY27,type,
sK2_SY27: $i ).
thf(tp_sK3_SY30,type,
sK3_SY30: $i ).
thf(tp_sK4_SY32,type,
sK4_SY32: $i ).
thf(tp_sK5_SY62,type,
sK5_SY62: $i > $i > $i ).
thf(tp_sK6_SY77,type,
sK6_SY77: $i > $i > $i > $i ).
thf(tp_sK7_SY89,type,
sK7_SY89: $i > $i > $i > $i ).
thf(tp_sK8_SY84,type,
sK8_SY84: $i > $i > $i > $i ).
thf(tp_sK9_SY91,type,
sK9_SY91: $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(5,axiom,
! [F: $i,B: $i,X: $i] :
( ( member @ X @ ( inverse_image2 @ F @ B ) )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).
thf(7,axiom,
! [F: $i,A: $i,Y: $i] :
( ( member @ Y @ ( image2 @ F @ A ) )
<=> ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
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(26,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(29,conjecture,
! [F: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( subset @ C @ A ) )
=> ( subset @ C @ ( inverse_image2 @ F @ ( image2 @ F @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa04) ).
thf(30,negated_conjecture,
( ( ! [F: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( subset @ C @ A ) )
=> ( subset @ C @ ( inverse_image2 @ F @ ( image2 @ F @ C ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [F: $i,A: $i,B: $i,C: $i] :
( ( ( maps @ F @ A @ B )
& ( subset @ C @ A ) )
=> ( subset @ C @ ( inverse_image2 @ F @ ( image2 @ F @ C ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [F: $i,B: $i,X: $i] :
( ( member @ X @ ( inverse_image2 @ F @ B ) )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(33,plain,
( ( ! [F: $i,A: $i,Y: $i] :
( ( member @ Y @ ( image2 @ F @ A ) )
<=> ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
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,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [SY27: $i,SY28: $i,SY29: $i] :
( ( ( maps @ sK1_F @ SY27 @ SY28 )
& ( subset @ SY29 @ SY27 ) )
=> ( subset @ SY29 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ SY29 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(39,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( ( maps @ sK1_F @ sK2_SY27 @ SY30 )
& ( subset @ SY31 @ sK2_SY27 ) )
=> ( subset @ SY31 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ SY31 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ! [SY32: $i] :
( ( ( maps @ sK1_F @ sK2_SY27 @ sK3_SY30 )
& ( subset @ SY32 @ sK2_SY27 ) )
=> ( subset @ SY32 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ SY32 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ( ( maps @ sK1_F @ sK2_SY27 @ sK3_SY30 )
& ( subset @ sK4_SY32 @ sK2_SY27 ) )
=> ( subset @ sK4_SY32 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ sK4_SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( maps @ sK1_F @ sK2_SY27 @ sK3_SY30 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(43,plain,
( ( subset @ sK4_SY32 @ sK2_SY27 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(44,plain,
( ( subset @ sK4_SY32 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ sK4_SY32 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(45,plain,
( ( ~ ( subset @ sK4_SY32 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ sK4_SY32 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(48,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(49,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(50,plain,
( ( ! [F: $i,A: $i,Y: $i] :
( ( member @ Y @ ( image2 @ F @ A ) )
<=> ? [X: $i] :
( ( member @ X @ A )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(51,plain,
( ( ! [F: $i,B: $i,X: $i] :
( ( member @ X @ ( inverse_image2 @ F @ B ) )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(52,plain,
( ( subset @ sK4_SY32 @ sK2_SY27 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(53,plain,
( ( maps @ sK1_F @ sK2_SY27 @ sK3_SY30 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(54,plain,
( ( ~ ( subset @ sK4_SY32 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ sK4_SY32 ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( inverse_image2 @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX2 @ SX3 ) )
| ( member @ SX2 @ ( inverse_image2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_set @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( equal_set @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(59,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)],[49]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX2 @ ( image2 @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( member @ SX3 @ SX1 )
| ~ ( apply @ SX0 @ SX3 @ SX2 ) )
| ( member @ SX2 @ ( image2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(61,plain,
( ( subset @ sK4_SY32 @ ( inverse_image2 @ sK1_F @ ( image2 @ sK1_F @ sK4_SY32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV1: $i] :
( ( ! [SY33: $i,SY34: $i] :
~ ( ~ ( ~ ( member @ SY34 @ ( inverse_image2 @ SV1 @ SY33 ) )
| ~ ! [SY35: $i] :
~ ~ ( ~ ( member @ SY35 @ SY33 )
| ~ ( apply @ SV1 @ SY34 @ SY35 ) ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ~ ( ~ ( member @ SY36 @ SY33 )
| ~ ( apply @ SV1 @ SY34 @ SY36 ) )
| ( member @ SY34 @ ( inverse_image2 @ SV1 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV2: $i] :
( ( ! [SY37: $i] :
~ ( ~ ( ~ ( subset @ SV2 @ SY37 )
| ! [SY38: $i] :
( ~ ( member @ SY38 @ SV2 )
| ( member @ SY38 @ SY37 ) ) )
| ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SV2 )
| ( member @ SY39 @ SY37 ) )
| ( subset @ SV2 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV3: $i] :
( ( ! [SY40: $i] :
~ ( ~ ( ~ ( equal_set @ SV3 @ SY40 )
| ~ ( ~ ( subset @ SV3 @ SY40 )
| ~ ( subset @ SY40 @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV3 @ SY40 )
| ~ ( subset @ SY40 @ SV3 ) )
| ( equal_set @ SV3 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV4: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( member @ SV4 @ ( power_set @ SY41 ) )
| ( subset @ SV4 @ SY41 ) )
| ~ ( ~ ( subset @ SV4 @ SY41 )
| ( member @ SV4 @ ( power_set @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV5: $i] :
( ( ! [SY42: $i,SY43: $i] :
~ ( ~ ( ~ ( maps @ SV5 @ SY42 @ SY43 )
| ~ ( ~ ! [SY44: $i] :
( ~ ( member @ SY44 @ SY42 )
| ~ ! [SY45: $i] :
~ ~ ( ~ ( member @ SY45 @ SY43 )
| ~ ( apply @ SV5 @ SY44 @ SY45 ) ) )
| ~ ! [SY46: $i,SY47: $i,SY48: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY46 @ SY42 )
| ~ ( member @ SY47 @ SY43 ) )
| ~ ( member @ SY48 @ SY43 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY46 @ SY47 )
| ~ ( apply @ SV5 @ SY46 @ SY48 ) )
| ( SY47 = SY48 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY49: $i] :
( ~ ( member @ SY49 @ SY42 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( member @ SY50 @ SY43 )
| ~ ( apply @ SV5 @ SY49 @ SY50 ) ) )
| ~ ! [SY51: $i,SY52: $i,SY53: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY51 @ SY42 )
| ~ ( member @ SY52 @ SY43 ) )
| ~ ( member @ SY53 @ SY43 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY51 @ SY52 )
| ~ ( apply @ SV5 @ SY51 @ SY53 ) )
| ( SY52 = SY53 ) ) )
| ( maps @ SV5 @ SY42 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV6: $i] :
( ( ! [SY54: $i,SY55: $i] :
~ ( ~ ( ~ ( member @ SY55 @ ( image2 @ SV6 @ SY54 ) )
| ~ ! [SY56: $i] :
~ ~ ( ~ ( member @ SY56 @ SY54 )
| ~ ( apply @ SV6 @ SY56 @ SY55 ) ) )
| ~ ( ~ ~ ! [SY57: $i] :
~ ~ ( ~ ( member @ SY57 @ SY54 )
| ~ ( apply @ SV6 @ SY57 @ SY55 ) )
| ( member @ SY55 @ ( image2 @ SV6 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV7: $i,SV1: $i] :
( ( ! [SY58: $i] :
~ ( ~ ( ~ ( member @ SY58 @ ( inverse_image2 @ SV1 @ SV7 ) )
| ~ ! [SY59: $i] :
~ ~ ( ~ ( member @ SY59 @ SV7 )
| ~ ( apply @ SV1 @ SY58 @ SY59 ) ) )
| ~ ( ~ ~ ! [SY60: $i] :
~ ~ ( ~ ( member @ SY60 @ SV7 )
| ~ ( apply @ SV1 @ SY58 @ SY60 ) )
| ( member @ SY58 @ ( inverse_image2 @ SV1 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV2 @ SV8 )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV2 )
| ( member @ SY61 @ SV8 ) ) )
| ~ ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV2 )
| ( member @ SY62 @ SV8 ) )
| ( subset @ SV2 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV3 @ SV9 )
| ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) )
| ( equal_set @ SV3 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( member @ SV4 @ ( power_set @ SV10 ) )
| ( subset @ SV4 @ SV10 ) )
| ~ ( ~ ( subset @ SV4 @ SV10 )
| ( member @ SV4 @ ( power_set @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY63: $i] :
~ ( ~ ( ~ ( maps @ SV5 @ SV11 @ SY63 )
| ~ ( ~ ! [SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ~ ! [SY45: $i] :
~ ~ ( ~ ( member @ SY45 @ SY63 )
| ~ ( apply @ SV5 @ SY64 @ SY45 ) ) )
| ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY66 @ SV11 )
| ~ ( member @ SY67 @ SY63 ) )
| ~ ( member @ SY68 @ SY63 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY66 @ SY67 )
| ~ ( apply @ SV5 @ SY66 @ SY68 ) )
| ( SY67 = SY68 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY69: $i] :
( ~ ( member @ SY69 @ SV11 )
| ~ ! [SY50: $i] :
~ ~ ( ~ ( member @ SY50 @ SY63 )
| ~ ( apply @ SV5 @ SY69 @ SY50 ) ) )
| ~ ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY71 @ SV11 )
| ~ ( member @ SY72 @ SY63 ) )
| ~ ( member @ SY73 @ SY63 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY71 @ SY72 )
| ~ ( apply @ SV5 @ SY71 @ SY73 ) )
| ( SY72 = SY73 ) ) )
| ( maps @ SV5 @ SV11 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY74: $i] :
~ ( ~ ( ~ ( member @ SY74 @ ( image2 @ SV6 @ SV12 ) )
| ~ ! [SY75: $i] :
~ ~ ( ~ ( member @ SY75 @ SV12 )
| ~ ( apply @ SV6 @ SY75 @ SY74 ) ) )
| ~ ( ~ ~ ! [SY76: $i] :
~ ~ ( ~ ( member @ SY76 @ SV12 )
| ~ ( apply @ SV6 @ SY76 @ SY74 ) )
| ( member @ SY74 @ ( image2 @ SV6 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY77 ) ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SY78 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY78 ) )
| ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV8 )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV2 )
| ( member @ SY61 @ SV8 ) ) )
| ~ ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV2 )
| ( member @ SY62 @ SV8 ) )
| ( subset @ SV2 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( ~ ( equal_set @ SV3 @ SV9 )
| ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) )
| ( equal_set @ SV3 @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( member @ SV4 @ ( power_set @ SV10 ) )
| ( subset @ SV4 @ SV10 ) )
| ~ ( ~ ( subset @ SV4 @ SV10 )
| ( member @ SV4 @ ( power_set @ SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( maps @ SV5 @ SV11 @ SV14 )
| ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
| ( maps @ SV5 @ SV11 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ( member @ SY89 @ SV12 )
| ~ ( apply @ SV6 @ SY89 @ SV15 ) ) )
| ~ ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV12 )
| ~ ( apply @ SV6 @ SY90 @ SV15 ) )
| ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ~ ( ~ ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY77 ) ) )
| ~ ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SY78 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY78 ) )
| ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV8 )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV2 )
| ( member @ SY61 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV2 )
| ( member @ SY62 @ SV8 ) )
| ( subset @ SV2 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(83,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( ~ ( equal_set @ SV3 @ SV9 )
| ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(84,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) )
| ( equal_set @ SV3 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(85,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( member @ SV4 @ ( power_set @ SV10 ) )
| ( subset @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(86,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( subset @ SV4 @ SV10 )
| ( member @ SV4 @ ( power_set @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(87,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ~ ( ~ ( maps @ SV5 @ SV11 @ SV14 )
| ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
| ( maps @ SV5 @ SV11 @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ( member @ SY89 @ SV12 )
| ~ ( apply @ SV6 @ SY89 @ SV15 ) ) )
| ~ ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV12 )
| ~ ( apply @ SV6 @ SY90 @ SV15 ) )
| ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ~ ( ~ ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(90,plain,
! [SV13: $i,SV1: $i,SV7: $i] :
( ( ~ ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SY78 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY78 ) )
| ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(91,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV8 )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV2 )
| ( member @ SY61 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(92,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV2 )
| ( member @ SY62 @ SV8 ) )
| ( subset @ SV2 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(93,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ( equal_set @ SV3 @ SV9 )
| ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
! [SV9: $i,SV3: $i] :
( ( ~ ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) )
| ( equal_set @ SV3 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(95,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ ( power_set @ SV10 ) )
| ( subset @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ SV10 )
| ( member @ SV4 @ ( power_set @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(97,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ~ ( ~ ( maps @ SV5 @ SV11 @ SV14 )
| ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(98,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
| ( maps @ SV5 @ SV11 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(99,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( ~ ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ( member @ SY89 @ SV12 )
| ~ ( apply @ SV6 @ SY89 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(100,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ~ ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV12 )
| ~ ( apply @ SV6 @ SY90 @ SV15 ) )
| ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(101,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ~ ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(102,plain,
! [SV13: $i,SV1: $i,SV7: $i] :
( ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SY78 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY78 ) )
| ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(103,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV8 ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( member @ SY61 @ SV2 )
| ( member @ SY61 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV2 )
| ( member @ SY62 @ SV8 ) ) )
= $true )
| ( ( subset @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(105,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( equal_set @ SV3 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) )
= $true )
| ( ( equal_set @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( power_set @ SV10 ) ) )
= $true )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV10 ) )
= $true )
| ( ( member @ SV4 @ ( power_set @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ~ ( maps @ SV5 @ SV11 @ SV14 )
| ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(110,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
| ( maps @ SV5 @ SV11 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(111,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ( member @ SY89 @ SV12 )
| ~ ( apply @ SV6 @ SY89 @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(112,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV12 )
| ~ ( apply @ SV6 @ SY90 @ SV15 ) )
| ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(113,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV13: $i,SV1: $i,SV7: $i] :
( ( ( ~ ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SY78 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY78 ) ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV8: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV8 )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( member @ SY61 @ SV2 )
| ( member @ SY61 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV8: $i,SV2: $i] :
( ( ( ! [SY62: $i] :
( ~ ( member @ SY62 @ SV2 )
| ( member @ SY62 @ SV8 ) ) )
= $false )
| ( ( subset @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV9: $i,SV3: $i] :
( ( ( equal_set @ SV3 @ SV9 )
= $false )
| ( ( ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) ) )
= $false )
| ( ( equal_set @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV10: $i,SV4: $i] :
( ( ( member @ SV4 @ ( power_set @ SV10 ) )
= $false )
| ( ( subset @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV10: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV10 )
= $false )
| ( ( member @ SV4 @ ( power_set @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( maps @ SV5 @ SV11 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) ) )
= $true )
| ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ( member @ SY89 @ SV12 )
| ~ ( apply @ SV6 @ SY89 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV12 )
| ~ ( apply @ SV6 @ SY90 @ SV15 ) ) )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false )
| ( ( ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV13: $i,SV1: $i,SV7: $i] :
( ( ( ~ ! [SY78: $i] :
~ ~ ( ~ ( member @ SY78 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY78 ) ) )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV8: $i,SV2: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV2 )
| ( member @ SV16 @ SV8 ) )
= $true )
| ( ( subset @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( member @ ( sK5_SY62 @ SV8 @ SV2 ) @ SV2 )
| ( member @ ( sK5_SY62 @ SV8 @ SV2 ) @ SV8 ) )
= $false )
| ( ( subset @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(129,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) )
= $false )
| ( ( equal_set @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV9 )
| ~ ( subset @ SV9 @ SV3 ) )
= $true )
| ( ( equal_set @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(131,plain,
! [SV14: $i,SV11: $i,SV5: $i] :
( ( ( maps @ SV5 @ SV11 @ SV14 )
= $false )
| ( ( ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) ) )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false )
| ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ( member @ SY89 @ SV12 )
| ~ ( apply @ SV6 @ SY89 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV12 )
| ~ ( apply @ SV6 @ SY90 @ SV15 ) ) )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV13: $i,SV1: $i,SV7: $i] :
( ( ( ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY77 ) ) )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV13: $i,SV1: $i,SV7: $i] :
( ( ( ! [SY78: $i] :
~ ~ ( ~ ( member @ SY78 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SY78 ) ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(137,plain,
! [SV8: $i,SV2: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV2 ) )
= $true )
| ( ( member @ SV16 @ SV8 )
= $true )
| ( ( subset @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV2: $i,SV8: $i] :
( ( ( ~ ( member @ ( sK5_SY62 @ SV8 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(139,plain,
! [SV2: $i,SV8: $i] :
( ( ( member @ ( sK5_SY62 @ SV8 @ SV2 ) @ SV8 )
= $false )
| ( ( subset @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(140,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV9 ) )
= $false )
| ( ( equal_set @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(141,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV3 ) )
= $false )
| ( ( equal_set @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(142,plain,
! [SV9: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV9 ) )
= $true )
| ( ( ~ ( subset @ SV9 @ SV3 ) )
= $true )
| ( ( equal_set @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) )
| ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(145,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ! [SY89: $i] :
~ ~ ( ~ ( member @ SY89 @ SV12 )
| ~ ( apply @ SV6 @ SY89 @ SV15 ) ) )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV15: $i,SV6: $i,SV12: $i] :
( ( ( ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV12 )
| ~ ( apply @ SV6 @ SY90 @ SV15 ) ) )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(147,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) ) ) )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[135]) ).
thf(148,plain,
! [SV13: $i,SV1: $i,SV7: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SV17 ) ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV8: $i,SV2: $i,SV16: $i] :
( ( ( member @ SV16 @ SV2 )
= $false )
| ( ( member @ SV16 @ SV8 )
= $true )
| ( ( subset @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV2: $i,SV8: $i] :
( ( ( member @ ( sK5_SY62 @ SV8 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(151,plain,
! [SV9: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV9 )
= $true )
| ( ( equal_set @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(152,plain,
! [SV3: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV3 )
= $true )
| ( ( equal_set @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(153,plain,
! [SV9: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV9 )
= $false )
| ( ( ~ ( subset @ SV9 @ SV3 ) )
= $true )
| ( ( equal_set @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) ) )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(155,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(156,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) ) )
= $true )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV12 )
| ~ ( apply @ SV6 @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV15 ) ) )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[145]) ).
thf(158,plain,
! [SV15: $i,SV6: $i,SV12: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( member @ SV18 @ SV12 )
| ~ ( apply @ SV6 @ SV18 @ SV15 ) ) )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) ) ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(160,plain,
! [SV13: $i,SV1: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ SV17 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SV17 ) ) )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV3: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV3 )
= $false )
| ( ( subset @ SV3 @ SV9 )
= $false )
| ( ( equal_set @ SV3 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ! [SY79: $i] :
( ~ ( member @ SY79 @ SV11 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( member @ SY80 @ SV14 )
| ~ ( apply @ SV5 @ SY79 @ SY80 ) ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY81 @ SV11 )
| ~ ( member @ SY82 @ SV14 ) )
| ~ ( member @ SY83 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY81 @ SY82 )
| ~ ( apply @ SV5 @ SY81 @ SY83 ) )
| ( SY82 = SY83 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(164,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ! [SY84: $i] :
( ~ ( member @ SY84 @ SV11 )
| ~ ! [SY85: $i] :
~ ~ ( ~ ( member @ SY85 @ SV14 )
| ~ ( apply @ SV5 @ SY84 @ SY85 ) ) ) )
= $false )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV12 )
| ~ ( apply @ SV6 @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV15 ) ) )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(166,plain,
! [SV15: $i,SV6: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( ~ ( member @ SV18 @ SV12 )
| ~ ( apply @ SV6 @ SV18 @ SV15 ) ) )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) ) )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV13: $i,SV1: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV7 )
| ~ ( apply @ SV1 @ SV13 @ SV17 ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(169,plain,
! [SV5: $i,SV14: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 )
| ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV14 )
| ~ ( apply @ SV5 @ SV19 @ SY91 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(170,plain,
! [SV5: $i,SV14: $i,SV11: $i,SV20: $i] :
( ( ( ! [SY92: $i,SY93: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SY92 @ SV14 ) )
| ~ ( member @ SY93 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SY92 )
| ~ ( apply @ SV5 @ SV20 @ SY93 ) )
| ( SY92 = SY93 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(171,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ( member @ SY94 @ SV14 )
| ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SY94 ) ) )
= $false )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[164]) ).
thf(172,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( member @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV12 )
| ~ ( apply @ SV6 @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV15 ) )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(173,plain,
! [SV15: $i,SV6: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ SV12 )
| ~ ( apply @ SV6 @ SV18 @ SV15 ) )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(174,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) @ SV7 ) )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(175,plain,
! [SV7: $i,SV13: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV13 @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) ) )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(176,plain,
! [SV13: $i,SV1: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV7 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV13 @ SV17 ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV5: $i,SV14: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV14 )
| ~ ( apply @ SV5 @ SV19 @ SY91 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV5: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ! [SY95: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) )
| ~ ( member @ SY95 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SY95 ) )
| ( SV21 = SY95 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 ) )
= $false )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(180,plain,
! [SV11: $i,SV5: $i,SV14: $i] :
( ( ( ~ ! [SY94: $i] :
~ ~ ( ~ ( member @ SY94 @ SV14 )
| ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SY94 ) ) )
= $false )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(181,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( member @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV12 ) )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(182,plain,
! [SV12: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( apply @ SV6 @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV15 ) )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV15: $i,SV6: $i,SV12: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ SV12 ) )
= $true )
| ( ( ~ ( apply @ SV6 @ SV18 @ SV15 ) )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV7: $i,SV1: $i,SV13: $i] :
( ( ( member @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) @ SV7 )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(185,plain,
! [SV7: $i,SV13: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV13 @ ( sK6_SY77 @ SV13 @ SV1 @ SV7 ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(186,plain,
! [SV13: $i,SV1: $i,SV7: $i,SV17: $i] :
( ( ( member @ SV17 @ SV7 )
= $false )
| ( ( ~ ( apply @ SV1 @ SV13 @ SV17 ) )
= $true )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV5: $i,SV14: $i,SV11: $i,SV19: $i] :
( ( ( member @ SV19 @ SV11 )
= $false )
| ( ( ~ ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV14 )
| ~ ( apply @ SV5 @ SV19 @ SY91 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) )
| ~ ( member @ SV22 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(190,plain,
! [SV11: $i,SV5: $i,SV14: $i] :
( ( ( ! [SY94: $i] :
~ ~ ( ~ ( member @ SY94 @ SV14 )
| ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SY94 ) ) )
= $true )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(191,plain,
! [SV12: $i,SV6: $i,SV15: $i] :
( ( ( member @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV12 )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(192,plain,
! [SV12: $i,SV15: $i,SV6: $i] :
( ( ( apply @ SV6 @ ( sK7_SY89 @ SV15 @ SV6 @ SV12 ) @ SV15 )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(193,plain,
! [SV15: $i,SV6: $i,SV12: $i,SV18: $i] :
( ( ( member @ SV18 @ SV12 )
= $false )
| ( ( ~ ( apply @ SV6 @ SV18 @ SV15 ) )
= $true )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(194,plain,
! [SV7: $i,SV17: $i,SV13: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV13 @ SV17 )
= $false )
| ( ( member @ SV17 @ SV7 )
= $false )
| ( ( member @ SV13 @ ( inverse_image2 @ SV1 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV11: $i,SV19: $i,SV5: $i,SV14: $i] :
( ( ( ! [SY91: $i] :
~ ~ ( ~ ( member @ SY91 @ SV14 )
| ~ ( apply @ SV5 @ SV19 @ SY91 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) )
| ~ ( member @ SV22 @ SV14 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV11: $i,SV5: $i,SV14: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ SV23 @ SV14 )
| ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 ) ) )
= $true )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV12: $i,SV15: $i,SV18: $i,SV6: $i] :
( ( ( apply @ SV6 @ SV18 @ SV15 )
= $false )
| ( ( member @ SV18 @ SV12 )
= $false )
| ( ( member @ SV15 @ ( image2 @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV14: $i,SV5: $i,SV19: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) @ SV14 )
| ~ ( apply @ SV5 @ SV19 @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[195]) ).
thf(201,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) )
| ~ ( member @ SV22 @ SV14 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ! [SY96: $i,SY97: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ SY96 @ SV14 ) )
| ~ ( member @ SY97 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SY96 )
| ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SY97 ) )
| ( SY96 = SY97 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[197]) ).
thf(203,plain,
! [SV11: $i,SV5: $i,SV14: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ SV23 @ SV14 )
| ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 ) ) )
= $false )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(204,plain,
! [SV14: $i,SV5: $i,SV19: $i,SV11: $i] :
( ( ( ~ ( ~ ( member @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) @ SV14 )
| ~ ( apply @ SV5 @ SV19 @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) ) ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(205,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) )
| ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(206,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ! [SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
| ~ ( member @ SY98 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SY98 ) )
| ( ( sK11_SY96 @ SV11 @ SV14 @ SV5 )
= SY98 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[202]) ).
thf(207,plain,
! [SV11: $i,SV5: $i,SV14: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV14 )
| ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 ) )
= $true )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(208,plain,
! [SV14: $i,SV5: $i,SV19: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) @ SV14 )
| ~ ( apply @ SV5 @ SV19 @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(209,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
| ~ ( member @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) )
| ( ( sK11_SY96 @ SV11 @ SV14 @ SV5 )
= ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(211,plain,
! [SV11: $i,SV5: $i,SV14: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV14 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 ) )
= $true )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(212,plain,
! [SV14: $i,SV5: $i,SV19: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) @ SV14 ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(213,plain,
! [SV14: $i,SV11: $i,SV19: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV19 @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(214,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) ) )
= $false )
| ( ( ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(215,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
| ~ ( member @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) @ SV14 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(216,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) )
| ( ( sK11_SY96 @ SV11 @ SV14 @ SV5 )
= ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(217,plain,
! [SV11: $i,SV5: $i,SV14: $i,SV23: $i] :
( ( ( member @ SV23 @ SV14 )
= $false )
| ( ( ~ ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 ) )
= $true )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV14: $i,SV5: $i,SV19: $i,SV11: $i] :
( ( ( member @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) @ SV14 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(219,plain,
! [SV14: $i,SV11: $i,SV19: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV19 @ ( sK9_SY91 @ SV11 @ SV19 @ SV5 @ SV14 ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV11 )
| ~ ( member @ SV21 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(221,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
| ~ ( member @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) @ SV14 ) ) )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(222,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(223,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ( sK11_SY96 @ SV11 @ SV14 @ SV5 )
= ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(224,plain,
! [SV23: $i,SV11: $i,SV14: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( ~ ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV21 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
| ~ ( member @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) ) )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(228,plain,
! [SV23: $i,SV5: $i,SV14: $i,SV11: $i] :
( ( ( ! [SY86: $i,SY87: $i,SY88: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( member @ SY87 @ SV14 ) )
| ~ ( member @ SY88 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ SY86 @ SY87 )
| ~ ( apply @ SV5 @ SY86 @ SY88 ) )
| ( SY87 = SY88 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV5: $i,SV22: $i,SV14: $i,SV21: $i,SV11: $i,SV20: $i] :
( ( ( member @ SV20 @ SV11 )
= $false )
| ( ( ~ ( member @ SV21 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(230,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(231,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(232,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) )
| ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(233,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ! [SY99: $i,SY100: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ SY99 @ SV14 ) )
| ~ ( member @ SY100 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SY99 )
| ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SY100 ) )
| ( SY99 = SY100 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[228]) ).
thf(234,plain,
! [SV5: $i,SV22: $i,SV11: $i,SV20: $i,SV14: $i,SV21: $i] :
( ( ( member @ SV21 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( ~ ( member @ SV22 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(235,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) ) )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(236,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( member @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) @ SV14 )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(237,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(238,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(239,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ! [SY101: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
| ~ ( member @ SY101 @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) )
| ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SY101 ) )
| ( ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 )
= SY101 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[233]) ).
thf(240,plain,
! [SV5: $i,SV21: $i,SV11: $i,SV20: $i,SV14: $i,SV22: $i] :
( ( ( member @ SV22 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV21 @ SV14 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
| ( SV21 = SV22 ) )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(241,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(242,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(243,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ ( sK12_SY98 @ SV11 @ SV14 @ SV5 ) )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(244,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
| ~ ( member @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
| ~ ~ ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) )
| ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) )
| ( ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 )
= ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[239]) ).
thf(245,plain,
! [SV11: $i,SV14: $i,SV22: $i,SV21: $i,SV20: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) ) )
= $true )
| ( ( SV21 = SV22 )
= $true )
| ( ( member @ SV21 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(246,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(247,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 ) )
= $false )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(248,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
| ~ ( member @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(249,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) )
| ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) )
| ( ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 )
= ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(250,plain,
! [SV11: $i,SV14: $i,SV22: $i,SV21: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) ) )
= $false )
| ( ( SV21 = SV22 )
= $true )
| ( ( member @ SV21 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(251,plain,
! [SV11: $i,SV14: $i,SV5: $i] :
( ( ( member @ ( sK10_SY86 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(252,plain,
! [SV5: $i,SV14: $i,SV11: $i] :
( ( ( member @ ( sK11_SY96 @ SV11 @ SV14 @ SV5 ) @ SV14 )
= $true )
| ( ( member @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(253,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
| ~ ( member @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) ) )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(254,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) )
| ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(255,plain,
! [SV23: $i,SV5: $i,SV14: $i,SV11: $i] :
( ( ( ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 )
= ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(256,plain,
! [SV11: $i,SV14: $i,SV22: $i,SV21: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV20 @ SV21 )
| ~ ( apply @ SV5 @ SV20 @ SV22 ) )
= $true )
| ( ( SV21 = SV22 )
= $true )
| ( ( member @ SV21 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(257,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
| ~ ( member @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(258,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( ~ ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) )
| ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) ) )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(259,plain,
! [SV11: $i,SV14: $i,SV22: $i,SV21: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ SV20 @ SV21 ) )
= $true )
| ( ( ~ ( apply @ SV5 @ SV20 @ SV22 ) )
= $true )
| ( ( SV21 = SV22 )
= $true )
| ( ( member @ SV21 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(260,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(261,plain,
! [SV23: $i,SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(262,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) )
| ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(263,plain,
! [SV11: $i,SV14: $i,SV22: $i,SV21: $i,SV20: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV20 @ SV21 )
= $false )
| ( ( ~ ( apply @ SV5 @ SV20 @ SV22 ) )
= $true )
| ( ( SV21 = SV22 )
= $true )
| ( ( member @ SV21 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(264,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) ) )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(265,plain,
! [SV23: $i,SV5: $i,SV14: $i,SV11: $i] :
( ( ( member @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(266,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(267,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( ~ ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(268,plain,
! [SV11: $i,SV14: $i,SV21: $i,SV22: $i,SV20: $i,SV5: $i] :
( ( ( apply @ SV5 @ SV20 @ SV22 )
= $false )
| ( ( apply @ SV5 @ SV20 @ SV21 )
= $false )
| ( ( SV21 = SV22 )
= $true )
| ( ( member @ SV21 @ SV14 )
= $false )
| ( ( member @ SV20 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV14 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(269,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
| ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(270,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(271,plain,
! [SV11: $i,SV14: $i,SV23: $i,SV5: $i] :
( ( ( apply @ SV5 @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ ( sK15_SY101 @ SV11 @ SV14 @ SV5 @ SV23 ) )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(272,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(273,plain,
! [SV23: $i,SV5: $i,SV14: $i,SV11: $i] :
( ( ( ~ ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 ) )
= $false )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(274,plain,
! [SV11: $i,SV14: $i,SV5: $i,SV23: $i] :
( ( ( member @ ( sK13_SY86 @ SV23 @ SV5 @ SV14 @ SV11 ) @ SV11 )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(275,plain,
! [SV23: $i,SV5: $i,SV14: $i,SV11: $i] :
( ( ( member @ ( sK14_SY99 @ SV11 @ SV14 @ SV5 @ SV23 ) @ SV14 )
= $true )
| ( ( member @ SV23 @ SV14 )
= $false )
| ( ( apply @ SV5 @ ( sK8_SY84 @ SV5 @ SV14 @ SV11 ) @ SV23 )
= $false )
| ( ( maps @ SV5 @ SV11 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(276,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,275,274,271,270,268,265,255,252,251,243,242,236,223,219,218,199,194,192,191,185,184,161,152,151,150,149,139,120,119,61,53]) ).
thf(277,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET754+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
% 0.12/0.18 % Computer : n013.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 14:50:21 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.76/11.84
% 56.76/11.84 No.of.Axioms: 6
% 56.76/11.84
% 56.76/11.84 Length.of.Defs: 0
% 56.76/11.84
% 56.76/11.84 Contains.Choice.Funs: false
% 56.76/11.84 .........
% 56.76/11.84
% 56.76/11.84 ********************************
% 56.76/11.84 * All subproblems solved! *
% 56.76/11.84 ********************************
% 56.76/11.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:276,loop_count:0,foatp_calls:1,translation:fof_full)
% 56.76/11.84
% 56.76/11.84 %**** Beginning of derivation protocol ****
% 56.76/11.84 % SZS output start CNFRefutation
% See solution above
% 56.76/11.84
% 56.76/11.84 %**** End of derivation protocol ****
% 56.76/11.84 %**** no. of clauses in derivation: 255 ****
% 56.76/11.84 %**** clause counter: 276 ****
% 56.76/11.84
% 56.76/11.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:276,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------