%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET751+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 : n001.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 10:40:58 AM UTC 2026
% Result : Theorem 1.04s 0.42s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 6
% Syntax : Number of formulae : 229 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 2195 ( 598 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 5609 (1307 ~; 828 |; 45 &;3394 @)
% ( 15 <=>; 20 =>; 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; 8 con; 0-6 aty)
% Number of variables : 922 ( 0 ^; 916 !; 6 ?; 922 :)
% 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_SY78,type,
sK10_SY78: $i > $i > $i > $i ).
thf(tp_sK11_SY88,type,
sK11_SY88: $i > $i > $i > $i ).
thf(tp_sK12_SY90,type,
sK12_SY90: $i > $i > $i > $i ).
thf(tp_sK13_SY78,type,
sK13_SY78: $i > $i > $i > $i > $i ).
thf(tp_sK14_SY91,type,
sK14_SY91: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY93,type,
sK15_SY93: $i > $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SY28,type,
sK3_SY28: $i ).
thf(tp_sK4_SY31,type,
sK4_SY31: $i ).
thf(tp_sK5_SY33,type,
sK5_SY33: $i ).
thf(tp_sK6_SY67,type,
sK6_SY67: $i > $i > $i ).
thf(tp_sK7_SY81,type,
sK7_SY81: $i > $i > $i > $i ).
thf(tp_sK8_SY76,type,
sK8_SY76: $i > $i > $i > $i ).
thf(tp_sK9_SY83,type,
sK9_SY83: $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(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,X: $i,Y: $i] :
( ( ( maps @ F @ A @ B )
& ( subset @ X @ A )
& ( subset @ Y @ A )
& ( subset @ X @ Y ) )
=> ( subset @ ( image2 @ F @ X ) @ ( image2 @ F @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa01) ).
thf(30,negated_conjecture,
( ( ! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( maps @ F @ A @ B )
& ( subset @ X @ A )
& ( subset @ Y @ A )
& ( subset @ X @ Y ) )
=> ( subset @ ( image2 @ F @ X ) @ ( image2 @ F @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [F: $i,A: $i,B: $i,X: $i,Y: $i] :
( ( ( maps @ F @ A @ B )
& ( subset @ X @ A )
& ( subset @ Y @ A )
& ( subset @ X @ Y ) )
=> ( subset @ ( image2 @ F @ X ) @ ( image2 @ F @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,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(33,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(34,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(37,plain,
( ( ! [SY24: $i,SY25: $i,SY26: $i,SY27: $i] :
( ( ( maps @ sK1_F @ SY24 @ SY25 )
& ( subset @ SY26 @ SY24 )
& ( subset @ SY27 @ SY24 )
& ( subset @ SY26 @ SY27 ) )
=> ( subset @ ( image2 @ sK1_F @ SY26 ) @ ( image2 @ sK1_F @ SY27 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(38,plain,
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
( ( ( maps @ sK1_F @ sK2_SY24 @ SY28 )
& ( subset @ SY29 @ sK2_SY24 )
& ( subset @ SY30 @ sK2_SY24 )
& ( subset @ SY29 @ SY30 ) )
=> ( subset @ ( image2 @ sK1_F @ SY29 ) @ ( image2 @ sK1_F @ SY30 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(39,plain,
( ( ! [SY31: $i,SY32: $i] :
( ( ( maps @ sK1_F @ sK2_SY24 @ sK3_SY28 )
& ( subset @ SY31 @ sK2_SY24 )
& ( subset @ SY32 @ sK2_SY24 )
& ( subset @ SY31 @ SY32 ) )
=> ( subset @ ( image2 @ sK1_F @ SY31 ) @ ( image2 @ sK1_F @ SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ! [SY33: $i] :
( ( ( maps @ sK1_F @ sK2_SY24 @ sK3_SY28 )
& ( subset @ sK4_SY31 @ sK2_SY24 )
& ( subset @ SY33 @ sK2_SY24 )
& ( subset @ sK4_SY31 @ SY33 ) )
=> ( subset @ ( image2 @ sK1_F @ sK4_SY31 ) @ ( image2 @ sK1_F @ SY33 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( ( ( maps @ sK1_F @ sK2_SY24 @ sK3_SY28 )
& ( subset @ sK4_SY31 @ sK2_SY24 )
& ( subset @ sK5_SY33 @ sK2_SY24 )
& ( subset @ sK4_SY31 @ sK5_SY33 ) )
=> ( subset @ ( image2 @ sK1_F @ sK4_SY31 ) @ ( image2 @ sK1_F @ sK5_SY33 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( maps @ sK1_F @ sK2_SY24 @ sK3_SY28 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(43,plain,
( ( subset @ sK4_SY31 @ sK2_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(44,plain,
( ( subset @ sK5_SY33 @ sK2_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(45,plain,
( ( subset @ sK4_SY31 @ sK5_SY33 )
= $true ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(46,plain,
( ( subset @ ( image2 @ sK1_F @ sK4_SY31 ) @ ( image2 @ sK1_F @ sK5_SY33 ) )
= $false ),
inference(standard_cnf,[status(thm)],[41]) ).
thf(47,plain,
( ( ~ ( subset @ ( image2 @ sK1_F @ sK4_SY31 ) @ ( image2 @ sK1_F @ sK5_SY33 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(50,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(51,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)],[33]) ).
thf(52,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)],[32]) ).
thf(53,plain,
( ( subset @ sK4_SY31 @ sK5_SY33 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(54,plain,
( ( subset @ sK5_SY33 @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(55,plain,
( ( subset @ sK4_SY31 @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(56,plain,
( ( maps @ sK1_F @ sK2_SY24 @ sK3_SY28 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(57,plain,
( ( ~ ( subset @ ( image2 @ sK1_F @ sK4_SY31 ) @ ( image2 @ sK1_F @ sK5_SY33 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(58,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)],[51]) ).
thf(59,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)],[48]) ).
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)],[52]) ).
thf(61,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)],[49]) ).
thf(62,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)],[50]) ).
thf(63,plain,
( ( subset @ ( image2 @ sK1_F @ sK4_SY31 ) @ ( image2 @ sK1_F @ sK5_SY33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV1: $i] :
( ( ! [SY34: $i,SY35: $i] :
~ ( ~ ( ~ ( maps @ SV1 @ SY34 @ SY35 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( member @ SY36 @ SY34 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( member @ SY37 @ SY35 )
| ~ ( apply @ SV1 @ SY36 @ SY37 ) ) )
| ~ ! [SY38: $i,SY39: $i,SY40: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY38 @ SY34 )
| ~ ( member @ SY39 @ SY35 ) )
| ~ ( member @ SY40 @ SY35 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY38 @ SY39 )
| ~ ( apply @ SV1 @ SY38 @ SY40 ) )
| ( SY39 = SY40 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY41: $i] :
( ~ ( member @ SY41 @ SY34 )
| ~ ! [SY42: $i] :
~ ~ ( ~ ( member @ SY42 @ SY35 )
| ~ ( apply @ SV1 @ SY41 @ SY42 ) ) )
| ~ ! [SY43: $i,SY44: $i,SY45: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY43 @ SY34 )
| ~ ( member @ SY44 @ SY35 ) )
| ~ ( member @ SY45 @ SY35 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY43 @ SY44 )
| ~ ( apply @ SV1 @ SY43 @ SY45 ) )
| ( SY44 = SY45 ) ) )
| ( maps @ SV1 @ SY34 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV2: $i] :
( ( ! [SY46: $i] :
~ ( ~ ( ~ ( subset @ SV2 @ SY46 )
| ! [SY47: $i] :
( ~ ( member @ SY47 @ SV2 )
| ( member @ SY47 @ SY46 ) ) )
| ~ ( ~ ! [SY48: $i] :
( ~ ( member @ SY48 @ SV2 )
| ( member @ SY48 @ SY46 ) )
| ( subset @ SV2 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV3: $i] :
( ( ! [SY49: $i,SY50: $i] :
~ ( ~ ( ~ ( member @ SY50 @ ( image2 @ SV3 @ SY49 ) )
| ~ ! [SY51: $i] :
~ ~ ( ~ ( member @ SY51 @ SY49 )
| ~ ( apply @ SV3 @ SY51 @ SY50 ) ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( member @ SY52 @ SY49 )
| ~ ( apply @ SV3 @ SY52 @ SY50 ) )
| ( member @ SY50 @ ( image2 @ SV3 @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV4: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( equal_set @ SV4 @ SY53 )
| ~ ( ~ ( subset @ SV4 @ SY53 )
| ~ ( subset @ SY53 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV4 @ SY53 )
| ~ ( subset @ SY53 @ SV4 ) )
| ( equal_set @ SV4 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV5: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( member @ SV5 @ ( power_set @ SY54 ) )
| ( subset @ SV5 @ SY54 ) )
| ~ ( ~ ( subset @ SV5 @ SY54 )
| ( member @ SV5 @ ( power_set @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY55: $i] :
~ ( ~ ( ~ ( maps @ SV1 @ SV6 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( member @ SY56 @ SV6 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( member @ SY37 @ SY55 )
| ~ ( apply @ SV1 @ SY56 @ SY37 ) ) )
| ~ ! [SY58: $i,SY59: $i,SY60: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY58 @ SV6 )
| ~ ( member @ SY59 @ SY55 ) )
| ~ ( member @ SY60 @ SY55 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY58 @ SY59 )
| ~ ( apply @ SV1 @ SY58 @ SY60 ) )
| ( SY59 = SY60 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY61: $i] :
( ~ ( member @ SY61 @ SV6 )
| ~ ! [SY42: $i] :
~ ~ ( ~ ( member @ SY42 @ SY55 )
| ~ ( apply @ SV1 @ SY61 @ SY42 ) ) )
| ~ ! [SY63: $i,SY64: $i,SY65: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY63 @ SV6 )
| ~ ( member @ SY64 @ SY55 ) )
| ~ ( member @ SY65 @ SY55 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY63 @ SY64 )
| ~ ( apply @ SV1 @ SY63 @ SY65 ) )
| ( SY64 = SY65 ) ) )
| ( maps @ SV1 @ SV6 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV2 @ SV7 )
| ! [SY66: $i] :
( ~ ( member @ SY66 @ SV2 )
| ( member @ SY66 @ SV7 ) ) )
| ~ ( ~ ! [SY67: $i] :
( ~ ( member @ SY67 @ SV2 )
| ( member @ SY67 @ SV7 ) )
| ( subset @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY68: $i] :
~ ( ~ ( ~ ( member @ SY68 @ ( image2 @ SV3 @ SV8 ) )
| ~ ! [SY69: $i] :
~ ~ ( ~ ( member @ SY69 @ SV8 )
| ~ ( apply @ SV3 @ SY69 @ SY68 ) ) )
| ~ ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ( member @ SY70 @ SV8 )
| ~ ( apply @ SV3 @ SY70 @ SY68 ) )
| ( member @ SY68 @ ( image2 @ SV3 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV4 @ SV9 )
| ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) )
| ( equal_set @ SV4 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( member @ SV5 @ ( power_set @ SV10 ) )
| ( subset @ SV5 @ SV10 ) )
| ~ ( ~ ( subset @ SV5 @ SV10 )
| ( member @ SV5 @ ( power_set @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) )
| ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV7 )
| ! [SY66: $i] :
( ~ ( member @ SY66 @ SV2 )
| ( member @ SY66 @ SV7 ) ) )
| ~ ( ~ ! [SY67: $i] :
( ~ ( member @ SY67 @ SV2 )
| ( member @ SY67 @ SV7 ) )
| ( subset @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( member @ SY81 @ SV8 )
| ~ ( apply @ SV3 @ SY81 @ SV12 ) ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( member @ SY82 @ SV8 )
| ~ ( apply @ SV3 @ SY82 @ SV12 ) )
| ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( equal_set @ SV4 @ SV9 )
| ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) )
| ( equal_set @ SV4 @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ( member @ SV5 @ ( power_set @ SV10 ) )
| ( subset @ SV5 @ SV10 ) )
| ~ ( ~ ( subset @ SV5 @ SV10 )
| ( member @ SV5 @ ( power_set @ SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) )
| ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ( subset @ SV2 @ SV7 )
| ! [SY66: $i] :
( ~ ( member @ SY66 @ SV2 )
| ( member @ SY66 @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(81,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ! [SY67: $i] :
( ~ ( member @ SY67 @ SV2 )
| ( member @ SY67 @ SV7 ) )
| ( subset @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( member @ SY81 @ SV8 )
| ~ ( apply @ SV3 @ SY81 @ SV12 ) ) )
| ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( member @ SY82 @ SV8 )
| ~ ( apply @ SV3 @ SY82 @ SV12 ) )
| ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( equal_set @ SV4 @ SV9 )
| ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(84,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) )
| ( equal_set @ SV4 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(85,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ( member @ SV5 @ ( power_set @ SV10 ) )
| ( subset @ SV5 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(86,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( ~ ( subset @ SV5 @ SV10 )
| ( member @ SV5 @ ( power_set @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(87,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(88,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) )
| ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(89,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV7 )
| ! [SY66: $i] :
( ~ ( member @ SY66 @ SV2 )
| ( member @ SY66 @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(90,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ! [SY67: $i] :
( ~ ( member @ SY67 @ SV2 )
| ( member @ SY67 @ SV7 ) )
| ( subset @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( member @ SY81 @ SV8 )
| ~ ( apply @ SV3 @ SY81 @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(92,plain,
! [SV12: $i,SV3: $i,SV8: $i] :
( ( ~ ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( member @ SY82 @ SV8 )
| ~ ( apply @ SV3 @ SY82 @ SV12 ) )
| ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(93,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( equal_set @ SV4 @ SV9 )
| ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) )
| ( equal_set @ SV4 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(95,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( power_set @ SV10 ) )
| ( subset @ SV5 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(96,plain,
! [SV10: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV10 )
| ( member @ SV5 @ ( power_set @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(97,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(98,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) )
| ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(99,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV7 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( member @ SY66 @ SV2 )
| ( member @ SY66 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ! [SY67: $i] :
( ~ ( member @ SY67 @ SV2 )
| ( member @ SY67 @ SV7 ) ) )
= $true )
| ( ( subset @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ~ ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
| ~ ! [SY81: $i] :
~ ~ ( ~ ( member @ SY81 @ SV8 )
| ~ ( apply @ SV3 @ SY81 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(102,plain,
! [SV12: $i,SV3: $i,SV8: $i] :
( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( member @ SY82 @ SV8 )
| ~ ( apply @ SV3 @ SY82 @ SV12 ) )
| ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(103,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( equal_set @ SV4 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) )
= $true )
| ( ( equal_set @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( power_set @ SV10 ) ) )
= $true )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(106,plain,
! [SV10: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV10 ) )
= $true )
| ( ( member @ SV5 @ ( power_set @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(107,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( maps @ SV1 @ SV6 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) )
| ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV7: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV7 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( member @ SY66 @ SV2 )
| ( member @ SY66 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV7: $i,SV2: $i] :
( ( ( ! [SY67: $i] :
( ~ ( member @ SY67 @ SV2 )
| ( member @ SY67 @ SV7 ) ) )
= $false )
| ( ( subset @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ! [SY81: $i] :
~ ~ ( ~ ( member @ SY81 @ SV8 )
| ~ ( apply @ SV3 @ SY81 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV12: $i,SV3: $i,SV8: $i] :
( ( ( ~ ~ ! [SY82: $i] :
~ ~ ( ~ ( member @ SY82 @ SV8 )
| ~ ( apply @ SV3 @ SY82 @ SV12 ) ) )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV9: $i,SV4: $i] :
( ( ( equal_set @ SV4 @ SV9 )
= $false )
| ( ( ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) ) )
= $false )
| ( ( equal_set @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV10: $i,SV5: $i] :
( ( ( member @ SV5 @ ( power_set @ SV10 ) )
= $false )
| ( ( subset @ SV5 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV10: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV10 )
= $false )
| ( ( member @ SV5 @ ( power_set @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( maps @ SV1 @ SV6 @ SV11 )
= $false )
| ( ( ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) )
| ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV7: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( member @ SV13 @ SV2 )
| ( member @ SV13 @ SV7 ) )
= $true )
| ( ( subset @ SV2 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK6_SY67 @ SV7 @ SV2 ) @ SV2 )
| ( member @ ( sK6_SY67 @ SV7 @ SV2 ) @ SV7 ) )
= $false )
| ( ( subset @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(121,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false )
| ( ( ~ ! [SY81: $i] :
~ ~ ( ~ ( member @ SY81 @ SV8 )
| ~ ( apply @ SV3 @ SY81 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV12: $i,SV3: $i,SV8: $i] :
( ( ( ~ ! [SY82: $i] :
~ ~ ( ~ ( member @ SY82 @ SV8 )
| ~ ( apply @ SV3 @ SY82 @ SV12 ) ) )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) )
= $false )
| ( ( equal_set @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV9 )
| ~ ( subset @ SV9 @ SV4 ) )
= $true )
| ( ( equal_set @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(125,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(126,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) )
| ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(127,plain,
! [SV7: $i,SV2: $i,SV13: $i] :
( ( ( ~ ( member @ SV13 @ SV2 ) )
= $true )
| ( ( member @ SV13 @ SV7 )
= $true )
| ( ( subset @ SV2 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV2: $i,SV7: $i] :
( ( ( ~ ( member @ ( sK6_SY67 @ SV7 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(129,plain,
! [SV2: $i,SV7: $i] :
( ( ( member @ ( sK6_SY67 @ SV7 @ SV2 ) @ SV7 )
= $false )
| ( ( subset @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(130,plain,
! [SV12: $i,SV3: $i,SV8: $i] :
( ( ( ! [SY81: $i] :
~ ~ ( ~ ( member @ SY81 @ SV8 )
| ~ ( apply @ SV3 @ SY81 @ SV12 ) ) )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(131,plain,
! [SV12: $i,SV3: $i,SV8: $i] :
( ( ( ! [SY82: $i] :
~ ~ ( ~ ( member @ SY82 @ SV8 )
| ~ ( apply @ SV3 @ SY82 @ SV12 ) ) )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(132,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV9 ) )
= $false )
| ( ( equal_set @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(133,plain,
! [SV4: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV4 ) )
= $false )
| ( ( equal_set @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(134,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV9 ) )
= $true )
| ( ( ~ ( subset @ SV9 @ SV4 ) )
= $true )
| ( ( equal_set @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(136,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(137,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) ) )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV7: $i,SV2: $i,SV13: $i] :
( ( ( member @ SV13 @ SV2 )
= $false )
| ( ( member @ SV13 @ SV7 )
= $true )
| ( ( subset @ SV2 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV2: $i,SV7: $i] :
( ( ( member @ ( sK6_SY67 @ SV7 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(140,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV8 )
| ~ ( apply @ SV3 @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV12 ) ) )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(141,plain,
! [SV12: $i,SV3: $i,SV8: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( member @ SV14 @ SV8 )
| ~ ( apply @ SV3 @ SV14 @ SV12 ) ) )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV9: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV9 )
= $true )
| ( ( equal_set @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(143,plain,
! [SV4: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV4 )
= $true )
| ( ( equal_set @ SV4 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(144,plain,
! [SV9: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV9 )
= $false )
| ( ( ~ ( subset @ SV9 @ SV4 ) )
= $true )
| ( ( equal_set @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY71: $i] :
( ~ ( member @ SY71 @ SV6 )
| ~ ! [SY72: $i] :
~ ~ ( ~ ( member @ SY72 @ SV11 )
| ~ ( apply @ SV1 @ SY71 @ SY72 ) ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(146,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY73 @ SV6 )
| ~ ( member @ SY74 @ SV11 ) )
| ~ ( member @ SY75 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY73 @ SY74 )
| ~ ( apply @ SV1 @ SY73 @ SY75 ) )
| ( SY74 = SY75 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(147,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY76: $i] :
( ~ ( member @ SY76 @ SV6 )
| ~ ! [SY77: $i] :
~ ~ ( ~ ( member @ SY77 @ SV11 )
| ~ ( apply @ SV1 @ SY76 @ SY77 ) ) ) )
= $false )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( ~ ( member @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV8 )
| ~ ( apply @ SV3 @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV12 ) ) )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(149,plain,
! [SV12: $i,SV3: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( ~ ( member @ SV14 @ SV8 )
| ~ ( apply @ SV3 @ SV14 @ SV12 ) ) )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(150,plain,
! [SV4: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV4 )
= $false )
| ( ( subset @ SV4 @ SV9 )
= $false )
| ( ( equal_set @ SV4 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV6 )
| ~ ! [SY83: $i] :
~ ~ ( ~ ( member @ SY83 @ SV11 )
| ~ ( apply @ SV1 @ SV15 @ SY83 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(152,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV16: $i] :
( ( ( ! [SY84: $i,SY85: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SY84 @ SV11 ) )
| ~ ( member @ SY85 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SY84 )
| ~ ( apply @ SV1 @ SV16 @ SY85 ) )
| ( SY84 = SY85 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SY86 ) ) )
= $false )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(154,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( member @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV8 )
| ~ ( apply @ SV3 @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV12 ) )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV12: $i,SV3: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV8 )
| ~ ( apply @ SV3 @ SV14 @ SV12 ) )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(156,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV6 ) )
= $true )
| ( ( ~ ! [SY83: $i] :
~ ~ ( ~ ( member @ SY83 @ SV11 )
| ~ ( apply @ SV1 @ SV15 @ SY83 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV1: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ! [SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) )
| ~ ( member @ SY87 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SY87 ) )
| ( SV17 = SY87 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(158,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(159,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ( ~ ! [SY86: $i] :
~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SY86 ) ) )
= $false )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(160,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( ~ ( member @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV8 ) )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(161,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( apply @ SV3 @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV12 ) )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(162,plain,
! [SV12: $i,SV3: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ SV8 ) )
= $true )
| ( ( ~ ( apply @ SV3 @ SV14 @ SV12 ) )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(163,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV15: $i] :
( ( ( member @ SV15 @ SV6 )
= $false )
| ( ( ~ ! [SY83: $i] :
~ ~ ( ~ ( member @ SY83 @ SV11 )
| ~ ( apply @ SV1 @ SV15 @ SY83 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(164,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) )
| ~ ( member @ SV18 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(165,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(166,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ( ! [SY86: $i] :
~ ~ ( ~ ( member @ SY86 @ SV11 )
| ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SY86 ) ) )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(167,plain,
! [SV8: $i,SV3: $i,SV12: $i] :
( ( ( member @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV8 )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(168,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK7_SY81 @ SV12 @ SV3 @ SV8 ) @ SV12 )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(169,plain,
! [SV12: $i,SV3: $i,SV8: $i,SV14: $i] :
( ( ( member @ SV14 @ SV8 )
= $false )
| ( ( ~ ( apply @ SV3 @ SV14 @ SV12 ) )
= $true )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(170,plain,
! [SV6: $i,SV15: $i,SV1: $i,SV11: $i] :
( ( ( ! [SY83: $i] :
~ ~ ( ~ ( member @ SY83 @ SV11 )
| ~ ( apply @ SV1 @ SV15 @ SY83 ) ) )
= $false )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(171,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) )
| ~ ( member @ SV18 @ SV11 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(172,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(173,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 ) ) )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(174,plain,
! [SV8: $i,SV12: $i,SV14: $i,SV3: $i] :
( ( ( apply @ SV3 @ SV14 @ SV12 )
= $false )
| ( ( member @ SV14 @ SV8 )
= $false )
| ( ( member @ SV12 @ ( image2 @ SV3 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(175,plain,
! [SV11: $i,SV1: $i,SV15: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) @ SV11 )
| ~ ( apply @ SV1 @ SV15 @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) ) ) )
= $false )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[170]) ).
thf(176,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) )
| ~ ( member @ SV18 @ SV11 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(177,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ! [SY88: $i,SY89: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ SY88 @ SV11 ) )
| ~ ( member @ SY89 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SY88 )
| ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SY89 ) )
| ( SY88 = SY89 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[172]) ).
thf(178,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( ~ ( member @ SV19 @ SV11 )
| ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 ) ) )
= $false )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(179,plain,
! [SV11: $i,SV1: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( ~ ( member @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) @ SV11 )
| ~ ( apply @ SV1 @ SV15 @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) ) ) )
= $true )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(180,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) )
| ~ ( member @ SV18 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(181,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ! [SY90: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ SY90 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SY90 ) )
| ( ( sK11_SY88 @ SV6 @ SV11 @ SV1 )
= SY90 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[177]) ).
thf(182,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 )
| ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 ) )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(183,plain,
! [SV11: $i,SV1: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) @ SV11 )
| ~ ( apply @ SV1 @ SV15 @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) ) )
= $false )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(184,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) ) )
= $true )
| ( ( ~ ( member @ SV18 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) )
| ( ( sK11_SY88 @ SV6 @ SV11 @ SV1 )
= ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[181]) ).
thf(186,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 ) )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(187,plain,
! [SV11: $i,SV1: $i,SV15: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) @ SV11 ) )
= $false )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(188,plain,
! [SV11: $i,SV6: $i,SV15: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV15 @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) ) )
= $false )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(189,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) ) )
= $false )
| ( ( ~ ( member @ SV18 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(190,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(191,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) )
| ( ( sK11_SY88 @ SV6 @ SV11 @ SV1 )
= ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(192,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV19: $i] :
( ( ( member @ SV19 @ SV11 )
= $false )
| ( ( ~ ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 ) )
= $true )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(193,plain,
! [SV11: $i,SV1: $i,SV15: $i,SV6: $i] :
( ( ( member @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) @ SV11 )
= $true )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(194,plain,
! [SV11: $i,SV6: $i,SV15: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV15 @ ( sK9_SY83 @ SV6 @ SV15 @ SV1 @ SV11 ) )
= $true )
| ( ( member @ SV15 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(195,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV6 )
| ~ ( member @ SV17 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV18 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(196,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(197,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(198,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ( sK11_SY88 @ SV6 @ SV11 @ SV1 )
= ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(199,plain,
! [SV19: $i,SV6: $i,SV11: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( ~ ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(200,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV6 ) )
= $true )
| ( ( ~ ( member @ SV17 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV18 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(201,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) ) )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(203,plain,
! [SV19: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY78 @ SV6 )
| ~ ( member @ SY79 @ SV11 ) )
| ~ ( member @ SY80 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY78 @ SY79 )
| ~ ( apply @ SV1 @ SY78 @ SY80 ) )
| ( SY79 = SY80 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(204,plain,
! [SV1: $i,SV18: $i,SV11: $i,SV17: $i,SV6: $i,SV16: $i] :
( ( ( member @ SV16 @ SV6 )
= $false )
| ( ( ~ ( member @ SV17 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV18 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(206,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(207,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ! [SY91: $i,SY92: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ SY91 @ SV11 ) )
| ~ ( member @ SY92 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SY91 )
| ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SY92 ) )
| ( SY91 = SY92 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[203]) ).
thf(209,plain,
! [SV1: $i,SV18: $i,SV6: $i,SV16: $i,SV11: $i,SV17: $i] :
( ( ( member @ SV17 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( ~ ( member @ SV18 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(210,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) @ SV11 )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(212,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(213,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(214,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ! [SY93: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
| ~ ( member @ SY93 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) )
| ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SY93 ) )
| ( ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 )
= SY93 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[208]) ).
thf(215,plain,
! [SV1: $i,SV17: $i,SV6: $i,SV16: $i,SV11: $i,SV18: $i] :
( ( ( member @ SV18 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( member @ SV17 @ SV11 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
| ( SV17 = SV18 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(217,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(218,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY90 @ SV6 @ SV11 @ SV1 ) )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(219,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
| ~ ( member @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) )
| ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) )
| ( ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 )
= ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[214]) ).
thf(220,plain,
! [SV6: $i,SV11: $i,SV18: $i,SV17: $i,SV16: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) ) )
= $true )
| ( ( SV17 = SV18 )
= $true )
| ( ( member @ SV17 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( member @ SV18 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(221,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(222,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(223,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
| ~ ( member @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(224,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) )
| ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) )
| ( ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 )
= ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(225,plain,
! [SV6: $i,SV11: $i,SV18: $i,SV17: $i,SV16: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) ) )
= $false )
| ( ( SV17 = SV18 )
= $true )
| ( ( member @ SV17 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( member @ SV18 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( member @ ( sK10_SY78 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(227,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK11_SY88 @ SV6 @ SV11 @ SV1 ) @ SV11 )
= $true )
| ( ( member @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(228,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
| ~ ( member @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(229,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) )
| ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(230,plain,
! [SV19: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 )
= ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(231,plain,
! [SV6: $i,SV11: $i,SV18: $i,SV17: $i,SV16: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV16 @ SV17 )
| ~ ( apply @ SV1 @ SV16 @ SV18 ) )
= $true )
| ( ( SV17 = SV18 )
= $true )
| ( ( member @ SV17 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( member @ SV18 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(232,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
| ~ ( member @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(233,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) )
| ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(234,plain,
! [SV6: $i,SV11: $i,SV18: $i,SV17: $i,SV16: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV16 @ SV17 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV16 @ SV18 ) )
= $true )
| ( ( SV17 = SV18 )
= $true )
| ( ( member @ SV17 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( member @ SV18 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(235,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(236,plain,
! [SV19: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(237,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) )
| ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(238,plain,
! [SV6: $i,SV11: $i,SV18: $i,SV17: $i,SV16: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV16 @ SV17 )
= $false )
| ( ( ~ ( apply @ SV1 @ SV16 @ SV18 ) )
= $true )
| ( ( SV17 = SV18 )
= $true )
| ( ( member @ SV17 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( member @ SV18 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(240,plain,
! [SV19: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(241,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(242,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(243,plain,
! [SV6: $i,SV11: $i,SV17: $i,SV18: $i,SV16: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV16 @ SV18 )
= $false )
| ( ( apply @ SV1 @ SV16 @ SV17 )
= $false )
| ( ( SV17 = SV18 )
= $true )
| ( ( member @ SV17 @ SV11 )
= $false )
| ( ( member @ SV16 @ SV6 )
= $false )
| ( ( member @ SV18 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(244,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(246,plain,
! [SV6: $i,SV11: $i,SV19: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY93 @ SV6 @ SV11 @ SV1 @ SV19 ) )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(247,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( ~ ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(248,plain,
! [SV19: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 ) )
= $false )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(249,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV19: $i] :
( ( ( member @ ( sK13_SY78 @ SV19 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(250,plain,
! [SV19: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK14_SY91 @ SV6 @ SV11 @ SV1 @ SV19 ) @ SV11 )
= $true )
| ( ( member @ SV19 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK8_SY76 @ SV1 @ SV11 @ SV6 ) @ SV19 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(251,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[53,250,249,246,245,243,240,230,227,226,218,217,211,198,194,193,174,168,167,150,143,142,139,138,129,116,115,63,56,55,54]) ).
thf(252,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET751+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
% 0.10/0.18 % Computer : n001.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 14:56:54 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.04/0.42
% 1.04/0.42 No.of.Axioms: 5
% 1.04/0.42
% 1.04/0.42 Length.of.Defs: 0
% 1.04/0.42
% 1.04/0.42 Contains.Choice.Funs: false
% 1.04/0.42 ........
% 1.04/0.42
% 1.04/0.42 ********************************
% 1.04/0.42 * All subproblems solved! *
% 1.04/0.42 ********************************
% 1.04/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:251,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.04/0.42
% 1.04/0.42 %**** Beginning of derivation protocol ****
% 1.04/0.42 % SZS output start CNFRefutation
% See solution above
% 1.04/0.43
% 1.04/0.43 %**** End of derivation protocol ****
% 1.04/0.43 %**** no. of clauses in derivation: 229 ****
% 1.04/0.43 %**** clause counter: 251 ****
% 1.04/0.43
% 1.04/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:251,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------