%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 10:40:57 AM UTC 2026
% Result : Theorem 1.78s 0.59s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 6
% Syntax : Number of formulae : 269 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 2880 ( 765 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 7952 (1848 ~;1135 |; 44 &;4885 @)
% ( 15 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 7 con; 0-7 aty)
% Number of variables : 1373 ( 0 ^;1364 !; 9 ?;1373 :)
% 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_SY101,type,
sK10_SY101: $i > $i > $i > $i ).
thf(tp_sK11_SY135,type,
sK11_SY135: $i > $i > $i > $i ).
thf(tp_sK12_SY137,type,
sK12_SY137: $i > $i > $i > $i ).
thf(tp_sK13_SY126,type,
sK13_SY126: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_SY101,type,
sK14_SY101: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY138,type,
sK15_SY138: $i > $i > $i > $i > $i ).
thf(tp_sK16_SY140,type,
sK16_SY140: $i > $i > $i > $i > $i ).
thf(tp_sK1_F,type,
sK1_F: $i ).
thf(tp_sK2_SY31,type,
sK2_SY31: $i ).
thf(tp_sK3_SY34,type,
sK3_SY34: $i ).
thf(tp_sK4_SY36,type,
sK4_SY36: $i ).
thf(tp_sK5_SY87,type,
sK5_SY87: $i > $i > $i ).
thf(tp_sK6_SY112,type,
sK6_SY112: $i > $i > $i > $i ).
thf(tp_sK7_SY99,type,
sK7_SY99: $i > $i > $i > $i ).
thf(tp_sK8_SY128,type,
sK8_SY128: $i > $i > $i > $i > $i ).
thf(tp_sK9_SY130,type,
sK9_SY130: $i > $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_surjective,type,
surjective: $i > $i > $i > $o ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(10,axiom,
! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one) ).
thf(11,axiom,
! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
thf(13,axiom,
! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
thf(15,axiom,
! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
thf(17,axiom,
! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
thf(29,conjecture,
! [F: $i,G: $i,A: $i,B: $i] :
( ( ( maps @ G @ A @ B )
& ( maps @ F @ B @ A )
& ( identity @ ( compose_function @ G @ F @ B @ A @ B ) @ B ) )
=> ( surjective @ G @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII25) ).
thf(30,negated_conjecture,
( ( ! [F: $i,G: $i,A: $i,B: $i] :
( ( ( maps @ G @ A @ B )
& ( maps @ F @ B @ A )
& ( identity @ ( compose_function @ G @ F @ B @ A @ B ) @ B ) )
=> ( surjective @ G @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ! [F: $i,G: $i,A: $i,B: $i] :
( ( ( maps @ G @ A @ B )
& ( maps @ F @ B @ A )
& ( identity @ ( compose_function @ G @ F @ B @ A @ B ) @ B ) )
=> ( surjective @ G @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(36,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(37,plain,
( ( ! [SY31: $i,SY32: $i,SY33: $i] :
( ( ( maps @ SY31 @ SY32 @ SY33 )
& ( maps @ sK1_F @ SY33 @ SY32 )
& ( identity @ ( compose_function @ SY31 @ sK1_F @ SY33 @ SY32 @ SY33 ) @ SY33 ) )
=> ( surjective @ SY31 @ SY32 @ SY33 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(38,plain,
( ( ! [SY34: $i,SY35: $i] :
( ( ( maps @ sK2_SY31 @ SY34 @ SY35 )
& ( maps @ sK1_F @ SY35 @ SY34 )
& ( identity @ ( compose_function @ sK2_SY31 @ sK1_F @ SY35 @ SY34 @ SY35 ) @ SY35 ) )
=> ( surjective @ sK2_SY31 @ SY34 @ SY35 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(39,plain,
( ( ! [SY36: $i] :
( ( ( maps @ sK2_SY31 @ sK3_SY34 @ SY36 )
& ( maps @ sK1_F @ SY36 @ sK3_SY34 )
& ( identity @ ( compose_function @ sK2_SY31 @ sK1_F @ SY36 @ sK3_SY34 @ SY36 ) @ SY36 ) )
=> ( surjective @ sK2_SY31 @ sK3_SY34 @ SY36 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(40,plain,
( ( ( ( maps @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 )
& ( maps @ sK1_F @ sK4_SY36 @ sK3_SY34 )
& ( identity @ ( compose_function @ sK2_SY31 @ sK1_F @ sK4_SY36 @ sK3_SY34 @ sK4_SY36 ) @ sK4_SY36 ) )
=> ( surjective @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(41,plain,
( ( maps @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(42,plain,
( ( maps @ sK1_F @ sK4_SY36 @ sK3_SY34 )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(43,plain,
( ( identity @ ( compose_function @ sK2_SY31 @ sK1_F @ sK4_SY36 @ sK3_SY34 @ sK4_SY36 ) @ sK4_SY36 )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(44,plain,
( ( surjective @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 )
= $false ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ( surjective @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 ) )
= $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( maps @ F @ A @ B )
<=> ( ! [X: $i] :
( ( member @ X @ A )
=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y ) ) )
& ! [X: $i,Y1: $i,Y2: $i] :
( ( ( member @ X @ A )
& ( member @ Y1 @ B )
& ( member @ Y2 @ B ) )
=> ( ( ( apply @ F @ X @ Y1 )
& ( apply @ F @ X @ Y2 ) )
=> ( Y1 = Y2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(47,plain,
( ( ! [G: $i,F: $i,A: $i,B: $i,C: $i,X: $i,Z: $i] :
( ( ( member @ X @ A )
& ( member @ Z @ C ) )
=> ( ( apply @ ( compose_function @ G @ F @ A @ B @ C ) @ X @ Z )
<=> ? [Y: $i] :
( ( member @ Y @ B )
& ( apply @ F @ X @ Y )
& ( apply @ G @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(48,plain,
( ( ! [F: $i,A: $i] :
( ( identity @ F @ A )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( apply @ F @ X @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(49,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( surjective @ F @ A @ B )
<=> ! [Y: $i] :
( ( member @ Y @ B )
=> ? [E: $i] :
( ( member @ E @ A )
& ( apply @ F @ E @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(50,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( one_to_one @ F @ A @ B )
<=> ( ( injective @ F @ A @ B )
& ( surjective @ F @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(51,plain,
( ( identity @ ( compose_function @ sK2_SY31 @ sK1_F @ sK4_SY36 @ sK3_SY34 @ sK4_SY36 ) @ sK4_SY36 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(52,plain,
( ( maps @ sK1_F @ sK4_SY36 @ sK3_SY34 )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(53,plain,
( ( maps @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(54,plain,
( ( ~ ( surjective @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,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)],[46]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ~ ~ ( ~ ( member @ SX5 @ SX2 )
| ~ ( member @ SX6 @ SX4 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 )
| ~ ! [SX7: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX7 @ SX3 )
| ~ ( apply @ SX1 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX7 @ SX6 ) ) )
| ~ ( ~ ~ ! [SX7: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SX7 @ SX3 )
| ~ ( apply @ SX1 @ SX5 @ SX7 ) )
| ~ ( apply @ SX0 @ SX7 @ SX6 ) )
| ( apply @ ( compose_function @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) @ SX5 @ SX6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( identity @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( apply @ SX0 @ SX2 @ SX2 ) )
| ( identity @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( surjective @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( member @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( member @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( member @ SX4 @ SX1 )
| ~ ( apply @ SX0 @ SX4 @ SX3 ) ) )
| ( surjective @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( one_to_one @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ~ ( surjective @ SX0 @ SX1 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SX0 @ SX1 @ SX2 )
| ~ ( surjective @ SX0 @ SX1 @ SX2 ) )
| ( one_to_one @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(60,plain,
( ( surjective @ sK2_SY31 @ sK3_SY34 @ sK4_SY36 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV1: $i] :
( ( ! [SY37: $i,SY38: $i] :
~ ( ~ ( ~ ( maps @ SV1 @ SY37 @ SY38 )
| ~ ( ~ ! [SY39: $i] :
( ~ ( member @ SY39 @ SY37 )
| ~ ! [SY40: $i] :
~ ~ ( ~ ( member @ SY40 @ SY38 )
| ~ ( apply @ SV1 @ SY39 @ SY40 ) ) )
| ~ ! [SY41: $i,SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY41 @ SY37 )
| ~ ( member @ SY42 @ SY38 ) )
| ~ ( member @ SY43 @ SY38 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY41 @ SY42 )
| ~ ( apply @ SV1 @ SY41 @ SY43 ) )
| ( SY42 = SY43 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY44: $i] :
( ~ ( member @ SY44 @ SY37 )
| ~ ! [SY45: $i] :
~ ~ ( ~ ( member @ SY45 @ SY38 )
| ~ ( apply @ SV1 @ SY44 @ SY45 ) ) )
| ~ ! [SY46: $i,SY47: $i,SY48: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY46 @ SY37 )
| ~ ( member @ SY47 @ SY38 ) )
| ~ ( member @ SY48 @ SY38 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY46 @ SY47 )
| ~ ( apply @ SV1 @ SY46 @ SY48 ) )
| ( SY47 = SY48 ) ) )
| ( maps @ SV1 @ SY37 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV2: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ~ ~ ( ~ ( member @ SY53 @ SY50 )
| ~ ( member @ SY54 @ SY52 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SY49 @ SY50 @ SY51 @ SY52 ) @ SY53 @ SY54 )
| ~ ! [SY55: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY55 @ SY51 )
| ~ ( apply @ SY49 @ SY53 @ SY55 ) )
| ~ ( apply @ SV2 @ SY55 @ SY54 ) ) )
| ~ ( ~ ~ ! [SY56: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY56 @ SY51 )
| ~ ( apply @ SY49 @ SY53 @ SY56 ) )
| ~ ( apply @ SV2 @ SY56 @ SY54 ) )
| ( apply @ ( compose_function @ SV2 @ SY49 @ SY50 @ SY51 @ SY52 ) @ SY53 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV3: $i] :
( ( ! [SY57: $i] :
~ ( ~ ( ~ ( identity @ SV3 @ SY57 )
| ! [SY58: $i] :
( ~ ( member @ SY58 @ SY57 )
| ( apply @ SV3 @ SY58 @ SY58 ) ) )
| ~ ( ~ ! [SY59: $i] :
( ~ ( member @ SY59 @ SY57 )
| ( apply @ SV3 @ SY59 @ SY59 ) )
| ( identity @ SV3 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV4: $i] :
( ( ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( surjective @ SV4 @ SY60 @ SY61 )
| ! [SY62: $i] :
( ~ ( member @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ( member @ SY63 @ SY60 )
| ~ ( apply @ SV4 @ SY63 @ SY62 ) ) ) )
| ~ ( ~ ! [SY64: $i] :
( ~ ( member @ SY64 @ SY61 )
| ~ ! [SY65: $i] :
~ ~ ( ~ ( member @ SY65 @ SY60 )
| ~ ( apply @ SV4 @ SY65 @ SY64 ) ) )
| ( surjective @ SV4 @ SY60 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV5: $i] :
( ( ! [SY66: $i,SY67: $i] :
~ ( ~ ( ~ ( one_to_one @ SV5 @ SY66 @ SY67 )
| ~ ( ~ ( injective @ SV5 @ SY66 @ SY67 )
| ~ ( surjective @ SV5 @ SY66 @ SY67 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV5 @ SY66 @ SY67 )
| ~ ( surjective @ SV5 @ SY66 @ SY67 ) )
| ( one_to_one @ SV5 @ SY66 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY68: $i] :
~ ( ~ ( ~ ( maps @ SV1 @ SV6 @ SY68 )
| ~ ( ~ ! [SY69: $i] :
( ~ ( member @ SY69 @ SV6 )
| ~ ! [SY40: $i] :
~ ~ ( ~ ( member @ SY40 @ SY68 )
| ~ ( apply @ SV1 @ SY69 @ SY40 ) ) )
| ~ ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY71 @ SV6 )
| ~ ( member @ SY72 @ SY68 ) )
| ~ ( member @ SY73 @ SY68 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY71 @ SY72 )
| ~ ( apply @ SV1 @ SY71 @ SY73 ) )
| ( SY72 = SY73 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY74: $i] :
( ~ ( member @ SY74 @ SV6 )
| ~ ! [SY45: $i] :
~ ~ ( ~ ( member @ SY45 @ SY68 )
| ~ ( apply @ SV1 @ SY74 @ SY45 ) ) )
| ~ ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY76 @ SV6 )
| ~ ( member @ SY77 @ SY68 ) )
| ~ ( member @ SY78 @ SY68 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY76 @ SY77 )
| ~ ( apply @ SV1 @ SY76 @ SY78 ) )
| ( SY77 = SY78 ) ) )
| ( maps @ SV1 @ SV6 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY79: $i,SY80: $i,SY81: $i,SY82: $i,SY83: $i] :
( ~ ~ ( ~ ( member @ SY82 @ SY79 )
| ~ ( member @ SY83 @ SY81 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SY79 @ SY80 @ SY81 ) @ SY82 @ SY83 )
| ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY84 @ SY80 )
| ~ ( apply @ SV7 @ SY82 @ SY84 ) )
| ~ ( apply @ SV2 @ SY84 @ SY83 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY85 @ SY80 )
| ~ ( apply @ SV7 @ SY82 @ SY85 ) )
| ~ ( apply @ SV2 @ SY85 @ SY83 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SY79 @ SY80 @ SY81 ) @ SY82 @ SY83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( identity @ SV3 @ SV8 )
| ! [SY86: $i] :
( ~ ( member @ SY86 @ SV8 )
| ( apply @ SV3 @ SY86 @ SY86 ) ) )
| ~ ( ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV8 )
| ( apply @ SV3 @ SY87 @ SY87 ) )
| ( identity @ SV3 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY88: $i] :
~ ( ~ ( ~ ( surjective @ SV4 @ SV9 @ SY88 )
| ! [SY89: $i] :
( ~ ( member @ SY89 @ SY88 )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV9 )
| ~ ( apply @ SV4 @ SY90 @ SY89 ) ) ) )
| ~ ( ~ ! [SY91: $i] :
( ~ ( member @ SY91 @ SY88 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( member @ SY92 @ SV9 )
| ~ ( apply @ SV4 @ SY92 @ SY91 ) ) )
| ( surjective @ SV4 @ SV9 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY93: $i] :
~ ( ~ ( ~ ( one_to_one @ SV5 @ SV10 @ SY93 )
| ~ ( ~ ( injective @ SV5 @ SV10 @ SY93 )
| ~ ( surjective @ SV5 @ SV10 @ SY93 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV5 @ SV10 @ SY93 )
| ~ ( surjective @ SV5 @ SV10 @ SY93 ) )
| ( one_to_one @ SV5 @ SV10 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) )
| ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV7: $i,SV2: $i,SV12: $i] :
( ( ! [SY104: $i,SY105: $i,SY106: $i,SY107: $i] :
( ~ ~ ( ~ ( member @ SY106 @ SV12 )
| ~ ( member @ SY107 @ SY105 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SY104 @ SY105 ) @ SY106 @ SY107 )
| ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY84 @ SY104 )
| ~ ( apply @ SV7 @ SY106 @ SY84 ) )
| ~ ( apply @ SV2 @ SY84 @ SY107 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY85 @ SY104 )
| ~ ( apply @ SV7 @ SY106 @ SY85 ) )
| ~ ( apply @ SV2 @ SY85 @ SY107 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SY104 @ SY105 ) @ SY106 @ SY107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( ~ ( identity @ SV3 @ SV8 )
| ! [SY86: $i] :
( ~ ( member @ SY86 @ SV8 )
| ( apply @ SV3 @ SY86 @ SY86 ) ) )
| ~ ( ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV8 )
| ( apply @ SV3 @ SY87 @ SY87 ) )
| ( identity @ SV3 @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( surjective @ SV4 @ SV9 @ SV13 )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV13 )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV9 )
| ~ ( apply @ SV4 @ SY90 @ SY110 ) ) ) )
| ~ ( ~ ! [SY112: $i] :
( ~ ( member @ SY112 @ SV13 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( member @ SY92 @ SV9 )
| ~ ( apply @ SV4 @ SY92 @ SY112 ) ) )
| ( surjective @ SV4 @ SV9 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( one_to_one @ SV5 @ SV10 @ SV14 )
| ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
| ( one_to_one @ SV5 @ SV10 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) ) )
| ~ ( ~ ~ ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) )
| ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV12: $i] :
( ( ! [SY114: $i,SY115: $i,SY116: $i] :
( ~ ~ ( ~ ( member @ SY115 @ SV12 )
| ~ ( member @ SY116 @ SY114 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SY114 ) @ SY115 @ SY116 )
| ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY117 @ SV15 )
| ~ ( apply @ SV7 @ SY115 @ SY117 ) )
| ~ ( apply @ SV2 @ SY117 @ SY116 ) ) )
| ~ ( ~ ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY118 @ SV15 )
| ~ ( apply @ SV7 @ SY115 @ SY118 ) )
| ~ ( apply @ SV2 @ SY118 @ SY116 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SY114 ) @ SY115 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( ~ ( identity @ SV3 @ SV8 )
| ! [SY86: $i] :
( ~ ( member @ SY86 @ SV8 )
| ( apply @ SV3 @ SY86 @ SY86 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(79,plain,
! [SV3: $i,SV8: $i] :
( ( ~ ( ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV8 )
| ( apply @ SV3 @ SY87 @ SY87 ) )
| ( identity @ SV3 @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(80,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( ~ ( surjective @ SV4 @ SV9 @ SV13 )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV13 )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV9 )
| ~ ( apply @ SV4 @ SY90 @ SY110 ) ) ) )
| ~ ( ~ ! [SY112: $i] :
( ~ ( member @ SY112 @ SV13 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( member @ SY92 @ SV9 )
| ~ ( apply @ SV4 @ SY92 @ SY112 ) ) )
| ( surjective @ SV4 @ SV9 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( one_to_one @ SV5 @ SV10 @ SV14 )
| ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
| ( one_to_one @ SV5 @ SV10 @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(83,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) )
| ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(84,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV12: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ~ ( ~ ( member @ SY119 @ SV12 )
| ~ ( member @ SY120 @ SV16 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SY119 @ SY120 )
| ~ ! [SY117: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY117 @ SV15 )
| ~ ( apply @ SV7 @ SY119 @ SY117 ) )
| ~ ( apply @ SV2 @ SY117 @ SY120 ) ) )
| ~ ( ~ ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY118 @ SV15 )
| ~ ( apply @ SV7 @ SY119 @ SY118 ) )
| ~ ( apply @ SV2 @ SY118 @ SY120 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SY119 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( identity @ SV3 @ SV8 )
| ! [SY86: $i] :
( ~ ( member @ SY86 @ SV8 )
| ( apply @ SV3 @ SY86 @ SY86 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(86,plain,
! [SV3: $i,SV8: $i] :
( ( ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV8 )
| ( apply @ SV3 @ SY87 @ SY87 ) )
| ( identity @ SV3 @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(87,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( ~ ( surjective @ SV4 @ SV9 @ SV13 )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV13 )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV9 )
| ~ ( apply @ SV4 @ SY90 @ SY110 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV4: $i,SV9: $i,SV13: $i] :
( ( ~ ( ~ ! [SY112: $i] :
( ~ ( member @ SY112 @ SV13 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( member @ SY92 @ SV9 )
| ~ ( apply @ SV4 @ SY92 @ SY112 ) ) )
| ( surjective @ SV4 @ SV9 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(89,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( one_to_one @ SV5 @ SV10 @ SV14 )
| ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(90,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
| ( one_to_one @ SV5 @ SV10 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(91,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( maps @ SV1 @ SV6 @ SV11 )
| ~ ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(92,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ~ ~ ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) )
| ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
| ( maps @ SV1 @ SV6 @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(93,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV12: $i,SV17: $i] :
( ( ! [SY123: $i] :
( ~ ~ ( ~ ( member @ SV17 @ SV12 )
| ~ ( member @ SY123 @ SV16 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SY123 )
| ~ ! [SY124: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY124 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY124 ) )
| ~ ( apply @ SV2 @ SY124 @ SY123 ) ) )
| ~ ( ~ ~ ! [SY125: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY125 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY125 ) )
| ~ ( apply @ SV2 @ SY125 @ SY123 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( identity @ SV3 @ SV8 ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ( member @ SY86 @ SV8 )
| ( apply @ SV3 @ SY86 @ SY86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV3: $i,SV8: $i] :
( ( ( ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV8 )
| ( apply @ SV3 @ SY87 @ SY87 ) ) )
= $true )
| ( ( identity @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( surjective @ SV4 @ SV9 @ SV13 )
| ! [SY110: $i] :
( ~ ( member @ SY110 @ SV13 )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV9 )
| ~ ( apply @ SV4 @ SY90 @ SY110 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV4: $i,SV9: $i,SV13: $i] :
( ( ~ ! [SY112: $i] :
( ~ ( member @ SY112 @ SV13 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( member @ SY92 @ SV9 )
| ~ ( apply @ SV4 @ SY92 @ SY112 ) ) )
| ( surjective @ SV4 @ SV9 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(98,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( one_to_one @ SV5 @ SV10 @ SV14 )
| ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(99,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
| ( one_to_one @ SV5 @ SV10 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(100,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( maps @ SV1 @ SV6 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) )
| ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV18: $i,SV12: $i,SV17: $i] :
( ( ~ ~ ( ~ ( member @ SV17 @ SV12 )
| ~ ( member @ SV18 @ SV16 ) )
| ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV8: $i,SV3: $i] :
( ( ( identity @ SV3 @ SV8 )
= $false )
| ( ( ! [SY86: $i] :
( ~ ( member @ SY86 @ SV8 )
| ( apply @ SV3 @ SY86 @ SY86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV3: $i,SV8: $i] :
( ( ( ! [SY87: $i] :
( ~ ( member @ SY87 @ SV8 )
| ( apply @ SV3 @ SY87 @ SY87 ) ) )
= $false )
| ( ( identity @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( surjective @ SV4 @ SV9 @ SV13 ) )
= $true )
| ( ( ! [SY110: $i] :
( ~ ( member @ SY110 @ SV13 )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV9 )
| ~ ( apply @ SV4 @ SY90 @ SY110 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV4: $i,SV9: $i,SV13: $i] :
( ( ( ~ ! [SY112: $i] :
( ~ ( member @ SY112 @ SV13 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( member @ SY92 @ SV9 )
| ~ ( apply @ SV4 @ SY92 @ SY112 ) ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( one_to_one @ SV5 @ SV10 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) )
= $true )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( maps @ SV1 @ SV6 @ SV11 )
= $false )
| ( ( ~ ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) )
| ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV18: $i,SV12: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( member @ SV17 @ SV12 )
| ~ ( member @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV3: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV8 )
| ( apply @ SV3 @ SV19 @ SV19 ) )
= $true )
| ( ( identity @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK5_SY87 @ SV3 @ SV8 ) @ SV8 )
| ( apply @ SV3 @ ( sK5_SY87 @ SV3 @ SV8 ) @ ( sK5_SY87 @ SV3 @ SV8 ) ) )
= $false )
| ( ( identity @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[104]) ).
thf(114,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false )
| ( ( ! [SY110: $i] :
( ~ ( member @ SY110 @ SV13 )
| ~ ! [SY90: $i] :
~ ~ ( ~ ( member @ SY90 @ SV9 )
| ~ ( apply @ SV4 @ SY90 @ SY110 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV4: $i,SV9: $i,SV13: $i] :
( ( ( ! [SY112: $i] :
( ~ ( member @ SY112 @ SV13 )
| ~ ! [SY92: $i] :
~ ~ ( ~ ( member @ SY92 @ SV9 )
| ~ ( apply @ SV4 @ SY92 @ SY112 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $false )
| ( ( ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) ) )
= $false )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(118,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(119,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) )
| ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(120,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV18: $i,SV12: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ SV17 @ SV12 )
| ~ ( member @ SV18 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV3: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( member @ SV19 @ SV8 ) )
= $true )
| ( ( apply @ SV3 @ SV19 @ SV19 )
= $true )
| ( ( identity @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(122,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( member @ ( sK5_SY87 @ SV3 @ SV8 ) @ SV8 ) )
= $false )
| ( ( identity @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(123,plain,
! [SV8: $i,SV3: $i] :
( ( ( apply @ SV3 @ ( sK5_SY87 @ SV3 @ SV8 ) @ ( sK5_SY87 @ SV3 @ SV8 ) )
= $false )
| ( ( identity @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(124,plain,
! [SV4: $i,SV9: $i,SV13: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV13 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( member @ SY128 @ SV9 )
| ~ ( apply @ SV4 @ SY128 @ SV20 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) @ SV13 )
| ~ ! [SY129: $i] :
~ ~ ( ~ ( member @ SY129 @ SV9 )
| ~ ( apply @ SV4 @ SY129 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(126,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
= $false )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( injective @ SV5 @ SV10 @ SV14 )
| ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
= $true )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(128,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(129,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(130,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) ) )
= $true )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV18: $i,SV12: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV12 )
| ~ ( member @ SV18 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(132,plain,
! [SV3: $i,SV8: $i,SV19: $i] :
( ( ( member @ SV19 @ SV8 )
= $false )
| ( ( apply @ SV3 @ SV19 @ SV19 )
= $true )
| ( ( identity @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV8: $i,SV3: $i] :
( ( ( member @ ( sK5_SY87 @ SV3 @ SV8 ) @ SV8 )
= $true )
| ( ( identity @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(134,plain,
! [SV4: $i,SV9: $i,SV13: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV13 ) )
= $true )
| ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( member @ SY128 @ SV9 )
| ~ ( apply @ SV4 @ SY128 @ SV20 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( member @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) @ SV13 ) )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(136,plain,
! [SV13: $i,SV4: $i,SV9: $i] :
( ( ( ~ ! [SY129: $i] :
~ ~ ( ~ ( member @ SY129 @ SV9 )
| ~ ( apply @ SV4 @ SY129 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(137,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( injective @ SV5 @ SV10 @ SV14 ) )
= $false )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(138,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
= $false )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(139,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( injective @ SV5 @ SV10 @ SV14 ) )
= $true )
| ( ( ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
= $true )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY94: $i] :
( ~ ( member @ SY94 @ SV6 )
| ~ ! [SY95: $i] :
~ ~ ( ~ ( member @ SY95 @ SV11 )
| ~ ( apply @ SV1 @ SY94 @ SY95 ) ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(141,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY96 @ SV6 )
| ~ ( member @ SY97 @ SV11 ) )
| ~ ( member @ SY98 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY96 @ SY97 )
| ~ ( apply @ SV1 @ SY96 @ SY98 ) )
| ( SY97 = SY98 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(142,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY99: $i] :
( ~ ( member @ SY99 @ SV6 )
| ~ ! [SY100: $i] :
~ ~ ( ~ ( member @ SY100 @ SV11 )
| ~ ( apply @ SV1 @ SY99 @ SY100 ) ) ) )
= $false )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV18: $i,SV12: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ SV12 ) )
= $true )
| ( ( ~ ( member @ SV18 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV4: $i,SV9: $i,SV13: $i,SV20: $i] :
( ( ( member @ SV20 @ SV13 )
= $false )
| ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( member @ SY128 @ SV9 )
| ~ ( apply @ SV4 @ SY128 @ SV20 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( member @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) @ SV13 )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(146,plain,
! [SV13: $i,SV4: $i,SV9: $i] :
( ( ( ! [SY129: $i] :
~ ~ ( ~ ( member @ SY129 @ SV9 )
| ~ ( apply @ SV4 @ SY129 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(147,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( injective @ SV5 @ SV10 @ SV14 )
= $true )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(148,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( surjective @ SV5 @ SV10 @ SV14 )
= $true )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(149,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( injective @ SV5 @ SV10 @ SV14 )
= $false )
| ( ( ~ ( surjective @ SV5 @ SV10 @ SV14 ) )
= $true )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(150,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV6 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV11 )
| ~ ( apply @ SV1 @ SV21 @ SY130 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV22: $i] :
( ( ( ! [SY131: $i,SY132: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SY131 @ SV11 ) )
| ~ ( member @ SY132 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SY131 )
| ~ ( apply @ SV1 @ SV22 @ SY132 ) )
| ( SY131 = SY132 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(152,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ! [SY133: $i] :
~ ~ ( ~ ( member @ SY133 @ SV11 )
| ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SY133 ) ) )
= $false )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[142]) ).
thf(153,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV16: $i,SV18: $i,SV12: $i,SV17: $i] :
( ( ( member @ SV17 @ SV12 )
= $false )
| ( ( ~ ( member @ SV18 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV13: $i,SV20: $i,SV4: $i,SV9: $i] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ( member @ SY128 @ SV9 )
| ~ ( apply @ SV4 @ SY128 @ SV20 ) ) )
= $false )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV13: $i,SV4: $i,SV9: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( member @ SV23 @ SV9 )
| ~ ( apply @ SV4 @ SV23 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(156,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( surjective @ SV5 @ SV10 @ SV14 )
= $false )
| ( ( injective @ SV5 @ SV10 @ SV14 )
= $false )
| ( ( one_to_one @ SV5 @ SV10 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(157,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV6 ) )
= $true )
| ( ( ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV11 )
| ~ ( apply @ SV1 @ SV21 @ SY130 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(158,plain,
! [SV1: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ! [SY134: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) )
| ~ ( member @ SY134 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SY134 ) )
| ( SV24 = SY134 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(160,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ( ~ ! [SY133: $i] :
~ ~ ( ~ ( member @ SY133 @ SV11 )
| ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SY133 ) ) )
= $false )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(161,plain,
! [SV15: $i,SV7: $i,SV2: $i,SV12: $i,SV17: $i,SV16: $i,SV18: $i] :
( ( ( member @ SV18 @ SV16 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( ~ ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV9: $i,SV4: $i,SV20: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV9 )
| ~ ( apply @ SV4 @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV20 ) ) )
= $false )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[154]) ).
thf(163,plain,
! [SV13: $i,SV4: $i,SV9: $i,SV23: $i] :
( ( ( ~ ( ~ ( member @ SV23 @ SV9 )
| ~ ( apply @ SV4 @ SV23 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) ) )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV1: $i,SV11: $i,SV6: $i,SV21: $i] :
( ( ( member @ SV21 @ SV6 )
= $false )
| ( ( ~ ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV11 )
| ~ ( apply @ SV1 @ SV21 @ SY130 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(165,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) )
| ~ ( member @ SV25 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(166,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(167,plain,
! [SV6: $i,SV1: $i,SV11: $i] :
( ( ( ! [SY133: $i] :
~ ~ ( ~ ( member @ SY133 @ SV11 )
| ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SY133 ) ) )
= $true )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(168,plain,
! [SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
| ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(169,plain,
! [SV9: $i,SV4: $i,SV20: $i,SV13: $i] :
( ( ( ~ ( ~ ( member @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV9 )
| ~ ( apply @ SV4 @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV20 ) ) )
= $true )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(170,plain,
! [SV13: $i,SV4: $i,SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV9 )
| ~ ( apply @ SV4 @ SV23 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(171,plain,
! [SV6: $i,SV21: $i,SV1: $i,SV11: $i] :
( ( ( ! [SY130: $i] :
~ ~ ( ~ ( member @ SY130 @ SV11 )
| ~ ( apply @ SV1 @ SV21 @ SY130 ) ) )
= $false )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(172,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) )
| ~ ( member @ SV25 @ SV11 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(173,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(174,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( member @ SV26 @ SV11 )
| ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 ) ) )
= $true )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(175,plain,
! [SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) ) )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(176,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) ) )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(177,plain,
! [SV9: $i,SV4: $i,SV20: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV9 )
| ~ ( apply @ SV4 @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV20 ) )
= $false )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV13: $i,SV4: $i,SV9: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV9 ) )
= $true )
| ( ( ~ ( apply @ SV4 @ SV23 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV11: $i,SV1: $i,SV21: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) @ SV11 )
| ~ ( apply @ SV1 @ SV21 @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) ) ) )
= $false )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(180,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) )
| ~ ( member @ SV25 @ SV11 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ! [SY135: $i,SY136: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ SY135 @ SV11 ) )
| ~ ( member @ SY136 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SY135 )
| ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SY136 ) )
| ( SY135 = SY136 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(182,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( member @ SV26 @ SV11 )
| ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
| ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(184,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i] :
( ( ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) )
| ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(185,plain,
! [SV9: $i,SV4: $i,SV20: $i,SV13: $i] :
( ( ( ~ ( member @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV9 ) )
= $false )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(186,plain,
! [SV9: $i,SV20: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( apply @ SV4 @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV20 ) )
= $false )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(187,plain,
! [SV13: $i,SV4: $i,SV9: $i,SV23: $i] :
( ( ( member @ SV23 @ SV9 )
= $false )
| ( ( ~ ( apply @ SV4 @ SV23 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) ) )
= $true )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV11: $i,SV1: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( ~ ( member @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) @ SV11 )
| ~ ( apply @ SV1 @ SV21 @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) ) ) )
= $true )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(189,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) )
| ~ ( member @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(190,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ! [SY137: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ SY137 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SY137 ) )
| ( ( sK11_SY135 @ SV6 @ SV11 @ SV1 )
= SY137 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[181]) ).
thf(191,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV11 )
| ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 ) )
= $true )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(192,plain,
! [SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(193,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i] :
( ( ( ~ ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(194,plain,
! [SV9: $i,SV4: $i,SV20: $i,SV13: $i] :
( ( ( member @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV9 )
= $true )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(195,plain,
! [SV9: $i,SV20: $i,SV13: $i,SV4: $i] :
( ( ( apply @ SV4 @ ( sK8_SY128 @ SV13 @ SV20 @ SV4 @ SV9 ) @ SV20 )
= $true )
| ( ( member @ SV20 @ SV13 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(196,plain,
! [SV13: $i,SV9: $i,SV23: $i,SV4: $i] :
( ( ( apply @ SV4 @ SV23 @ ( sK6_SY112 @ SV4 @ SV9 @ SV13 ) )
= $false )
| ( ( member @ SV23 @ SV9 )
= $false )
| ( ( surjective @ SV4 @ SV9 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(197,plain,
! [SV11: $i,SV1: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) @ SV11 )
| ~ ( apply @ SV1 @ SV21 @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) ) )
= $false )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(198,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(199,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) )
| ( ( sK11_SY135 @ SV6 @ SV11 @ SV1 )
= ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[190]) ).
thf(200,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ SV11 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 ) )
= $true )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(201,plain,
! [SV18: $i,SV17: $i,SV16: $i,SV15: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(202,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i] :
( ( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV11: $i,SV1: $i,SV21: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) @ SV11 ) )
= $false )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(204,plain,
! [SV11: $i,SV6: $i,SV21: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV21 @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) ) )
= $false )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(205,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) ) )
= $false )
| ( ( ~ ( member @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(206,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(207,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) )
| ( ( sK11_SY135 @ SV6 @ SV11 @ SV1 )
= ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(208,plain,
! [SV6: $i,SV1: $i,SV11: $i,SV26: $i] :
( ( ( member @ SV26 @ SV11 )
= $false )
| ( ( ~ ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 ) )
= $true )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY126 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY126 ) )
| ~ ( apply @ SV2 @ SY126 @ SV18 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i] :
( ( ( ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( member @ SY127 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SY127 ) )
| ~ ( apply @ SV2 @ SY127 @ SV18 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(211,plain,
! [SV11: $i,SV1: $i,SV21: $i,SV6: $i] :
( ( ( member @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) @ SV11 )
= $true )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(212,plain,
! [SV11: $i,SV6: $i,SV21: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV21 @ ( sK9_SY130 @ SV6 @ SV21 @ SV1 @ SV11 ) )
= $true )
| ( ( member @ SV21 @ SV6 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(213,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV6 )
| ~ ( member @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(214,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(215,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(216,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ( sK11_SY135 @ SV6 @ SV11 @ SV1 )
= ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(217,plain,
! [SV26: $i,SV6: $i,SV11: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( ~ ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) ) )
| ~ ( apply @ SV2 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV18 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(219,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ SV27 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SV27 ) )
| ~ ( apply @ SV2 @ SV27 @ SV18 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( ~ ( member @ SV22 @ SV6 ) )
= $true )
| ( ( ~ ( member @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(221,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
| ~ ( member @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(222,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) ) )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(223,plain,
! [SV26: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ! [SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ SY101 @ SV6 )
| ~ ( member @ SY102 @ SV11 ) )
| ~ ( member @ SY103 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ SY101 @ SY102 )
| ~ ( apply @ SV1 @ SY101 @ SY103 ) )
| ( SY102 = SY103 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) ) )
| ~ ( apply @ SV2 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV18 ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(225,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV27 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SV27 ) )
| ~ ( apply @ SV2 @ SV27 @ SV18 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(226,plain,
! [SV1: $i,SV25: $i,SV11: $i,SV24: $i,SV6: $i,SV22: $i] :
( ( ( member @ SV22 @ SV6 )
= $false )
| ( ( ~ ( member @ SV24 @ SV11 ) )
= $true )
| ( ( ~ ( member @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(227,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(228,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(229,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) )
| ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(230,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ! [SY138: $i,SY139: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ SY138 @ SV11 ) )
| ~ ( member @ SY139 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SY138 )
| ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SY139 ) )
| ( SY138 = SY139 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[223]) ).
thf(231,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) ) )
| ~ ( apply @ SV2 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV18 ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(232,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( member @ SV27 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SV27 ) )
| ~ ( apply @ SV2 @ SV27 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(233,plain,
! [SV1: $i,SV25: $i,SV6: $i,SV22: $i,SV11: $i,SV24: $i] :
( ( ( member @ SV24 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( ~ ( member @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(234,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) ) )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(235,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) @ SV11 )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(236,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(237,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(238,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ! [SY140: $i] :
( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
| ~ ( member @ SY140 @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) )
| ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SY140 ) )
| ( ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 )
= SY140 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[230]) ).
thf(239,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV18: $i,SV12: $i,SV16: $i,SV2: $i] :
( ( ( ~ ( apply @ SV2 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV18 ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(241,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( member @ SV27 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SV27 ) ) )
= $true )
| ( ( ~ ( apply @ SV2 @ SV27 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(242,plain,
! [SV1: $i,SV24: $i,SV6: $i,SV22: $i,SV11: $i,SV25: $i] :
( ( ( member @ SV25 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( member @ SV24 @ SV11 )
= $false )
| ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
| ( SV24 = SV25 ) )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(243,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(245,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ ( sK12_SY137 @ SV6 @ SV11 @ SV1 ) )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(246,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
| ~ ( member @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
| ~ ~ ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) )
| ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) )
| ( ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 )
= ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[238]) ).
thf(247,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( ~ ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) ) ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(248,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV18: $i,SV12: $i,SV16: $i,SV2: $i] :
( ( ( apply @ SV2 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV18 )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(249,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( ~ ( ~ ( member @ SV27 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SV27 ) ) )
= $false )
| ( ( ~ ( apply @ SV2 @ SV27 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(250,plain,
! [SV6: $i,SV11: $i,SV25: $i,SV24: $i,SV22: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) ) )
= $true )
| ( ( SV24 = SV25 )
= $true )
| ( ( member @ SV24 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( member @ SV25 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(251,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( ~ ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(252,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 ) )
= $false )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(253,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
| ~ ( member @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(254,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) )
| ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) )
| ( ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 )
= ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(255,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(256,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV15 )
| ~ ( apply @ SV7 @ SV17 @ SV27 ) )
= $true )
| ( ( ~ ( apply @ SV2 @ SV27 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(257,plain,
! [SV6: $i,SV11: $i,SV25: $i,SV24: $i,SV22: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) ) )
= $false )
| ( ( SV24 = SV25 )
= $true )
| ( ( member @ SV24 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( member @ SV25 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(258,plain,
! [SV6: $i,SV11: $i,SV1: $i] :
( ( ( member @ ( sK10_SY101 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(259,plain,
! [SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK11_SY135 @ SV6 @ SV11 @ SV1 ) @ SV11 )
= $true )
| ( ( member @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(260,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
| ~ ( member @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) ) )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(261,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) )
| ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(262,plain,
! [SV26: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 )
= ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(263,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(264,plain,
! [SV15: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) ) )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(265,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV15 ) )
= $true )
| ( ( ~ ( apply @ SV7 @ SV17 @ SV27 ) )
= $true )
| ( ( ~ ( apply @ SV2 @ SV27 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(266,plain,
! [SV6: $i,SV11: $i,SV25: $i,SV24: $i,SV22: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV22 @ SV24 )
| ~ ( apply @ SV1 @ SV22 @ SV25 ) )
= $true )
| ( ( SV24 = SV25 )
= $true )
| ( ( member @ SV24 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( member @ SV25 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(267,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
| ~ ( member @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(268,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( ~ ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) )
| ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) ) )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(269,plain,
! [SV15: $i,SV7: $i,SV17: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( member @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) @ SV15 )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(270,plain,
! [SV15: $i,SV2: $i,SV18: $i,SV12: $i,SV16: $i,SV17: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV17 @ ( sK13_SY126 @ SV16 @ SV12 @ SV18 @ SV2 @ SV17 @ SV7 @ SV15 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $false )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV17: $i,SV7: $i,SV15: $i,SV27: $i] :
( ( ( member @ SV27 @ SV15 )
= $false )
| ( ( ~ ( apply @ SV7 @ SV17 @ SV27 ) )
= $true )
| ( ( ~ ( apply @ SV2 @ SV27 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(272,plain,
! [SV6: $i,SV11: $i,SV25: $i,SV24: $i,SV22: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ SV22 @ SV24 ) )
= $true )
| ( ( ~ ( apply @ SV1 @ SV22 @ SV25 ) )
= $true )
| ( ( SV24 = SV25 )
= $true )
| ( ( member @ SV24 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( member @ SV25 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(273,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(274,plain,
! [SV26: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(275,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) )
| ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(276,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV2: $i,SV15: $i,SV27: $i,SV17: $i,SV7: $i] :
( ( ( apply @ SV7 @ SV17 @ SV27 )
= $false )
| ( ( member @ SV27 @ SV15 )
= $false )
| ( ( ~ ( apply @ SV2 @ SV27 @ SV18 ) )
= $true )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(277,plain,
! [SV6: $i,SV11: $i,SV25: $i,SV24: $i,SV22: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV22 @ SV24 )
= $false )
| ( ( ~ ( apply @ SV1 @ SV22 @ SV25 ) )
= $true )
| ( ( SV24 = SV25 )
= $true )
| ( ( member @ SV24 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( member @ SV25 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(278,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) ) )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(279,plain,
! [SV26: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(280,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(281,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( ~ ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(282,plain,
! [SV16: $i,SV12: $i,SV17: $i,SV7: $i,SV15: $i,SV18: $i,SV27: $i,SV2: $i] :
( ( ( apply @ SV2 @ SV27 @ SV18 )
= $false )
| ( ( member @ SV27 @ SV15 )
= $false )
| ( ( apply @ SV7 @ SV17 @ SV27 )
= $false )
| ( ( apply @ ( compose_function @ SV2 @ SV7 @ SV12 @ SV15 @ SV16 ) @ SV17 @ SV18 )
= $true )
| ( ( member @ SV17 @ SV12 )
= $false )
| ( ( member @ SV18 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(283,plain,
! [SV6: $i,SV11: $i,SV24: $i,SV25: $i,SV22: $i,SV1: $i] :
( ( ( apply @ SV1 @ SV22 @ SV25 )
= $false )
| ( ( apply @ SV1 @ SV22 @ SV24 )
= $false )
| ( ( SV24 = SV25 )
= $true )
| ( ( member @ SV24 @ SV11 )
= $false )
| ( ( member @ SV22 @ SV6 )
= $false )
| ( ( member @ SV25 @ SV11 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(284,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
| ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(285,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(286,plain,
! [SV6: $i,SV11: $i,SV26: $i,SV1: $i] :
( ( ( apply @ SV1 @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ ( sK16_SY140 @ SV6 @ SV11 @ SV1 @ SV26 ) )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(287,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( ~ ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(288,plain,
! [SV26: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 ) )
= $false )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(289,plain,
! [SV6: $i,SV11: $i,SV1: $i,SV26: $i] :
( ( ( member @ ( sK14_SY101 @ SV26 @ SV1 @ SV11 @ SV6 ) @ SV6 )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(290,plain,
! [SV26: $i,SV1: $i,SV11: $i,SV6: $i] :
( ( ( member @ ( sK15_SY138 @ SV6 @ SV11 @ SV1 @ SV26 ) @ SV11 )
= $true )
| ( ( member @ SV26 @ SV11 )
= $false )
| ( ( apply @ SV1 @ ( sK7_SY99 @ SV1 @ SV11 @ SV6 ) @ SV26 )
= $false )
| ( ( maps @ SV1 @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(291,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,290,289,286,285,283,282,279,270,269,262,259,258,248,245,244,235,216,212,211,196,195,194,156,148,147,145,133,132,123,60,53,52]) ).
thf(292,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET734+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n026.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Oct 6 14:53:31 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.78/0.59
% 1.78/0.59 No.of.Axioms: 5
% 1.78/0.59
% 1.78/0.59 Length.of.Defs: 0
% 1.78/0.59
% 1.78/0.59 Contains.Choice.Funs: false
% 1.78/0.59 ............
% 1.78/0.59
% 1.78/0.59 ********************************
% 1.78/0.59 * All subproblems solved! *
% 1.78/0.59 ********************************
% 1.78/0.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:291,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.78/0.59
% 1.78/0.59 %**** Beginning of derivation protocol ****
% 1.78/0.59 % SZS output start CNFRefutation
% See solution above
% 1.78/0.60
% 1.78/0.60 %**** End of derivation protocol ****
% 1.78/0.60 %**** no. of clauses in derivation: 269 ****
% 1.78/0.60 %**** clause counter: 291 ****
% 1.78/0.60
% 1.78/0.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:291,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------