TSTP Solution File: SEU290+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU290+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:09:34 EDT 2022
% Result : Theorem 75.37s 76.06s
% Output : CNFRefutation 76.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 89
% Syntax : Number of formulae : 703 ( 429 unt; 42 typ; 0 def)
% Number of atoms : 4250 (1508 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 7538 (1446 ~;1312 |; 173 &;4535 @)
% ( 12 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 17 con; 0-3 aty)
% Number of variables : 1286 ( 0 ^1250 !; 36 ?;1286 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_as_subset,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_A,type,
sK12_A: $i ).
thf(tp_sK13_A,type,
sK13_A: $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK15_A,type,
sK15_A: $i ).
thf(tp_sK16_A,type,
sK16_A: $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_A,type,
sK18_A: $i ).
thf(tp_sK19_C,type,
sK19_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_B,type,
sK20_B: $i > $i ).
thf(tp_sK21_C,type,
sK21_C: $i > $i > $i ).
thf(tp_sK22_D,type,
sK22_D: $i > $i > $i > $i ).
thf(tp_sK23_C,type,
sK23_C: $i > $i > $i ).
thf(tp_sK24_SY92,type,
sK24_SY92: $i > $i > $i ).
thf(tp_sK2_SY85,type,
sK2_SY85: $i ).
thf(tp_sK3_SY88,type,
sK3_SY88: $i ).
thf(tp_sK4_SY90,type,
sK4_SY90: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_B,type,
sK9_B: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(13,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(14,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(15,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(17,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(19,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(20,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(21,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(22,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(23,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(24,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(26,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(27,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(28,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(29,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(31,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(32,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(33,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(34,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(36,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(37,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(48,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(50,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(52,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(53,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(55,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( in @ C @ A )
=> ( ( B = empty_set )
| ( in @ ( apply @ D @ C ) @ ( relation_rng @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_funct_2) ).
thf(56,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( in @ C @ A )
=> ( ( B = empty_set )
| ( in @ ( apply @ D @ C ) @ ( relation_rng @ D ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[55]) ).
thf(57,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( function @ D )
& ( quasi_total @ D @ A @ B )
& ( relation_of2_as_subset @ D @ A @ B ) )
=> ( ( in @ C @ A )
=> ( ( B = empty_set )
| ( in @ ( apply @ D @ C ) @ ( relation_rng @ D ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[56]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(69,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(70,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(71,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(72,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(73,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(74,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(76,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(77,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(78,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(79,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(80,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(82,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(84,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(85,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(86,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(88,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(89,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(90,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(91,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(93,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(95,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(98,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(105,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(107,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(108,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(109,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(110,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(112,plain,
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ( ( function @ SY87 )
& ( quasi_total @ SY87 @ sK1_A @ SY85 )
& ( relation_of2_as_subset @ SY87 @ sK1_A @ SY85 ) )
=> ( ( in @ SY86 @ sK1_A )
=> ( ( SY85 = empty_set )
| ( in @ ( apply @ SY87 @ SY86 ) @ ( relation_rng @ SY87 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(113,plain,
( ( ! [SY88: $i,SY89: $i] :
( ( ( function @ SY89 )
& ( quasi_total @ SY89 @ sK1_A @ sK2_SY85 )
& ( relation_of2_as_subset @ SY89 @ sK1_A @ sK2_SY85 ) )
=> ( ( in @ SY88 @ sK1_A )
=> ( ( sK2_SY85 = empty_set )
| ( in @ ( apply @ SY89 @ SY88 ) @ ( relation_rng @ SY89 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(114,plain,
( ( ! [SY90: $i] :
( ( ( function @ SY90 )
& ( quasi_total @ SY90 @ sK1_A @ sK2_SY85 )
& ( relation_of2_as_subset @ SY90 @ sK1_A @ sK2_SY85 ) )
=> ( ( in @ sK3_SY88 @ sK1_A )
=> ( ( sK2_SY85 = empty_set )
| ( in @ ( apply @ SY90 @ sK3_SY88 ) @ ( relation_rng @ SY90 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[113]) ).
thf(115,plain,
( ( ( ( function @ sK4_SY90 )
& ( quasi_total @ sK4_SY90 @ sK1_A @ sK2_SY85 )
& ( relation_of2_as_subset @ sK4_SY90 @ sK1_A @ sK2_SY85 ) )
=> ( ( in @ sK3_SY88 @ sK1_A )
=> ( ( sK2_SY85 = empty_set )
| ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(116,plain,
( ( function @ sK4_SY90 )
= $true ),
inference(standard_cnf,[status(thm)],[115]) ).
thf(117,plain,
( ( quasi_total @ sK4_SY90 @ sK1_A @ sK2_SY85 )
= $true ),
inference(standard_cnf,[status(thm)],[115]) ).
thf(118,plain,
( ( relation_of2_as_subset @ sK4_SY90 @ sK1_A @ sK2_SY85 )
= $true ),
inference(standard_cnf,[status(thm)],[115]) ).
thf(119,plain,
( ( in @ sK3_SY88 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[115]) ).
thf(120,plain,
( ( ( sK2_SY85 = empty_set )
| ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[115]) ).
thf(121,plain,
( ( ~ ( ( sK2_SY85 = empty_set )
| ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[120]) ).
thf(122,plain,
( ( ( sK2_SY85 != empty_set )
& ~ ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(125,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(128,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(131,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(132,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(134,plain,
( ( ( relation @ sK5_A )
& ( relation_empty_yielding @ sK5_A )
& ( function @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(135,plain,
( ( ( relation @ sK6_A )
& ( relation_empty_yielding @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(136,plain,
( ( ( function @ sK7_A )
& ( relation @ sK7_A )
& ( one_to_one @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(137,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(138,plain,
( ( ! [A: $i] :
( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK9_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(139,plain,
( ( ~ ( empty @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ ( sK11_C @ B @ A ) )
& ( relation_of2 @ ( sK11_C @ B @ A ) @ A @ B )
& ( function @ ( sK11_C @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(141,plain,
( ( ( empty @ sK12_A )
& ( relation @ sK12_A )
& ( function @ sK12_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(142,plain,
( ( empty @ sK13_A )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(143,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK14_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK14_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(144,plain,
( ( ( empty @ sK15_A )
& ( relation @ sK15_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(145,plain,
( ( ( function @ sK16_A )
& ( relation @ sK16_A )
& ( one_to_one @ sK16_A )
& ( empty @ sK16_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ ( sK17_C @ B @ A ) )
& ( relation_of2 @ ( sK17_C @ B @ A ) @ A @ B )
& ( function @ ( sK17_C @ B @ A ) )
& ( quasi_total @ ( sK17_C @ B @ A ) @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(147,plain,
( ( ( function @ sK18_A )
& ( relation @ sK18_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(148,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(149,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(150,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(151,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK19_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(154,plain,
( ( ! [A: $i] : ( element @ ( sK20_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK21_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(156,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(157,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(158,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY91: $i] :
( ( ( sK23_C @ B @ A )
!= ( apply @ A @ SY91 ) )
| ~ ( in @ SY91 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
& ( ( ( ( sK23_C @ B @ A )
= ( apply @ A @ ( sK24_SY92 @ B @ A ) ) )
& ( in @ ( sK24_SY92 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK23_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( C
= ( apply @ A @ ( sK22_D @ C @ B @ A ) ) )
& ( in @ ( sK22_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(159,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ( C != empty_set )
| ( quasi_total @ C @ A @ B )
| ( A = empty_set ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( C = empty_set )
| ( A = empty_set ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(160,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(161,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(162,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(163,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(164,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(166,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(167,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(168,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(169,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(170,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ( C != empty_set )
| ( quasi_total @ C @ A @ B )
| ( A = empty_set ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( C = empty_set )
| ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(171,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY91: $i] :
( ( ( sK23_C @ B @ A )
!= ( apply @ A @ SY91 ) )
| ~ ( in @ SY91 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
& ( ( ( ( sK23_C @ B @ A )
= ( apply @ A @ ( sK24_SY92 @ B @ A ) ) )
& ( in @ ( sK24_SY92 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK23_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( C
= ( apply @ A @ ( sK22_D @ C @ B @ A ) ) )
& ( in @ ( sK22_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(178,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK21_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(183,plain,
( ( ! [A: $i] : ( element @ ( sK20_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK19_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(185,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(186,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(187,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(188,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(190,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(191,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(192,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(193,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(194,plain,
( ( ( function @ sK18_A )
& ( relation @ sK18_A ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(195,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ ( sK17_C @ B @ A ) )
& ( relation_of2 @ ( sK17_C @ B @ A ) @ A @ B )
& ( function @ ( sK17_C @ B @ A ) )
& ( quasi_total @ ( sK17_C @ B @ A ) @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(196,plain,
( ( ( function @ sK16_A )
& ( relation @ sK16_A )
& ( one_to_one @ sK16_A )
& ( empty @ sK16_A ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(197,plain,
( ( ( empty @ sK15_A )
& ( relation @ sK15_A ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(198,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK14_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK14_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(199,plain,
( ( empty @ sK13_A )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(200,plain,
( ( ( empty @ sK12_A )
& ( relation @ sK12_A )
& ( function @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ ( sK11_C @ B @ A ) )
& ( relation_of2 @ ( sK11_C @ B @ A ) @ A @ B )
& ( function @ ( sK11_C @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(202,plain,
( ( ~ ( empty @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(203,plain,
( ( ! [A: $i] :
( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK9_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(204,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(205,plain,
( ( ( function @ sK7_A )
& ( relation @ sK7_A )
& ( one_to_one @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(206,plain,
( ( ( relation @ sK6_A )
& ( relation_empty_yielding @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(207,plain,
( ( ( relation @ sK5_A )
& ( relation_empty_yielding @ sK5_A )
& ( function @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(208,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(209,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(210,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(212,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(214,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(215,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(216,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(218,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(219,plain,
( ( in @ sK3_SY88 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(220,plain,
( ( relation_of2_as_subset @ sK4_SY90 @ sK1_A @ sK2_SY85 )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(221,plain,
( ( quasi_total @ sK4_SY90 @ sK1_A @ sK2_SY85 )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(222,plain,
( ( function @ sK4_SY90 )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(223,plain,
( ( ( sK2_SY85 != empty_set )
& ~ ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(224,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK14_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(225,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 = empty_set )
| ( SX0
!= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) )
| ( quasi_total @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 = empty_set )
| ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX0
= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX0 != empty_set )
| ( SX0
!= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) )
| ( quasi_total @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX0 != empty_set )
| ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX0
= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 != empty_set )
| ( SX2 != empty_set )
| ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX0 = empty_set ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 != empty_set )
| ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX2 = empty_set )
| ( SX0 = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(226,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( one_to_one @ sK16_A ) )
| ~ ( empty @ sK16_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(227,plain,
( ( ~ ( ~ ( ( sK2_SY85 != empty_set ) )
| ~ ~ ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(228,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(229,plain,
( ( ~ ( ~ ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(230,plain,
( ( ~ ( ~ ( empty @ sK15_A )
| ~ ( relation @ sK15_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(231,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK9_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(232,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ( relation @ ( sK11_C @ SX1 @ SX0 ) )
| ~ ( relation_of2 @ ( sK11_C @ SX1 @ SX0 ) @ SX0 @ SX1 ) )
| ~ ( function @ ( sK11_C @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(233,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(234,plain,
( ( ~ ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(235,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(236,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) )
| ~ ( function @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(237,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK5_A )
| ~ ( relation_empty_yielding @ sK5_A ) )
| ~ ( function @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(238,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(239,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ( ( sK23_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) ) )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK24_SY92 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK24_SY92 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ( SX2
!= ( apply @ SX0 @ ( sK22_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(240,plain,
( ( ~ ( ~ ( function @ sK18_A )
| ~ ( relation @ sK18_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(241,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(242,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(243,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ( relation @ ( sK17_C @ SX1 @ SX0 ) )
| ~ ( relation_of2 @ ( sK17_C @ SX1 @ SX0 ) @ SX0 @ SX1 ) )
| ~ ( function @ ( sK17_C @ SX1 @ SX0 ) ) )
| ~ ( quasi_total @ ( sK17_C @ SX1 @ SX0 ) @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(244,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( one_to_one @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(245,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(246,plain,
! [SV1: $i] :
( ( ! [SY93: $i] :
( ~ ( in @ SV1 @ SY93 )
| ~ ( in @ SY93 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(247,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(248,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ( relation @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(249,plain,
! [SV4: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( element @ SY95 @ ( powerset @ ( cartesian_product2 @ SV4 @ SY94 ) ) )
| ( relation @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(250,plain,
! [SV5: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( relation_of2 @ SY97 @ SV5 @ SY96 )
| ( element @ ( relation_dom_as_subset @ SV5 @ SY96 @ SY97 ) @ ( powerset @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(251,plain,
! [SV6: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ( relation_of2_as_subset @ SY99 @ SV6 @ SY98 )
| ( element @ SY99 @ ( powerset @ ( cartesian_product2 @ SV6 @ SY98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(252,plain,
! [SV7: $i] :
( ( ! [SY100: $i] : ( relation_of2 @ ( sK21_C @ SY100 @ SV7 ) @ SV7 @ SY100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(253,plain,
! [SV8: $i] :
( ( element @ ( sK20_B @ SV8 ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(254,plain,
! [SV9: $i] :
( ( ! [SY101: $i] : ( relation_of2_as_subset @ ( sK19_C @ SY101 @ SV9 ) @ SV9 @ SY101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(255,plain,
! [SV10: $i] :
( ( ~ ( empty @ ( powerset @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(256,plain,
! [SV11: $i] :
( ( ! [SY102: $i] :
( ( empty @ SV11 )
| ( empty @ SY102 )
| ~ ( empty @ ( cartesian_product2 @ SV11 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(257,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
| ~ ( relation @ SV12 )
| ~ ( empty @ ( relation_dom @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(258,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
| ~ ( relation @ SV13 )
| ~ ( empty @ ( relation_rng @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(259,plain,
( ( empty @ sK8_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(260,plain,
! [SV14: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( relation_of2 @ SY104 @ SV14 @ SY103 )
| ( ( relation_dom_as_subset @ SV14 @ SY103 @ SY104 )
= ( relation_dom @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(261,plain,
! [SV15: $i] :
( ( subset @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(262,plain,
! [SV16: $i] :
( ( ! [SY105: $i] :
( ~ ( in @ SV16 @ SY105 )
| ( element @ SV16 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(263,plain,
! [SV17: $i] :
( ( ! [SY106: $i] :
( ~ ( element @ SV17 @ SY106 )
| ( empty @ SY106 )
| ( in @ SV17 @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(264,plain,
! [SV18: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( element @ SY107 @ ( powerset @ SY108 ) )
| ~ ( in @ SV18 @ SY107 )
| ( element @ SV18 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(265,plain,
! [SV19: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( element @ SY109 @ ( powerset @ SY110 ) )
| ~ ( in @ SV19 @ SY109 )
| ~ ( empty @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(266,plain,
! [SV20: $i] :
( ( ~ ( empty @ SV20 )
| ( SV20 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(267,plain,
! [SV21: $i] :
( ( ! [SY111: $i] :
( ~ ( empty @ SY111 )
| ~ ( in @ SV21 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(268,plain,
! [SV22: $i] :
( ( ! [SY112: $i] :
( ( SV22 = SY112 )
| ~ ( empty @ SV22 )
| ~ ( empty @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(269,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
| ~ ( ~ ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ~ ( empty @ ( sK14_B @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(270,plain,
! [SV24: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
| ~ ~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) ) )
| ~ ~ ( ~ ! [SY121: $i,SY122: $i] :
( ~ ( relation_of2_as_subset @ SY122 @ SV24 @ SY121 )
| ( SY121 != empty_set )
| ( SY122 != empty_set )
| ( quasi_total @ SY122 @ SV24 @ SY121 )
| ( SV24 = empty_set ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( relation_of2_as_subset @ SY124 @ SV24 @ SY123 )
| ( SY123 != empty_set )
| ~ ( quasi_total @ SY124 @ SV24 @ SY123 )
| ( SY124 = empty_set )
| ( SV24 = empty_set ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(271,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( one_to_one @ sK16_A ) )
| ~ ( empty @ sK16_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(272,plain,
( ( ~ ( ( sK2_SY85 != empty_set ) )
| ~ ~ ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(273,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(274,plain,
( ( ~ ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(275,plain,
( ( ~ ( empty @ sK15_A )
| ~ ( relation @ sK15_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(276,plain,
! [SV25: $i] :
( ( ~ ( ~ ( element @ ( sK9_B @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ( empty @ ( sK9_B @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(277,plain,
! [SV26: $i] :
( ( ! [SY125: $i] :
~ ( ~ ~ ( ~ ( relation @ ( sK11_C @ SY125 @ SV26 ) )
| ~ ( relation_of2 @ ( sK11_C @ SY125 @ SV26 ) @ SV26 @ SY125 ) )
| ~ ( function @ ( sK11_C @ SY125 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(278,plain,
! [SV27: $i] :
( ( ~ ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( relation_of2 @ SY127 @ SV27 @ SY126 )
| ( relation_of2_as_subset @ SY127 @ SV27 @ SY126 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( relation_of2_as_subset @ SY129 @ SV27 @ SY128 )
| ( relation_of2 @ SY129 @ SV27 @ SY128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(279,plain,
( ( ~ ( relation @ sK6_A )
| ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(280,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(281,plain,
( ( ~ ~ ( ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) )
| ~ ( function @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(282,plain,
( ( ~ ~ ( ~ ( relation @ sK5_A )
| ~ ( relation_empty_yielding @ sK5_A ) )
| ~ ( function @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(283,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(284,plain,
! [SV28: $i] :
( ( ~ ( function @ SV28 )
| ~ ( relation @ SV28 )
| ~ ( ~ ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) )
| ~ ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(285,plain,
( ( ~ ( function @ sK18_A )
| ~ ( relation @ sK18_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(286,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(287,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(288,plain,
! [SV29: $i] :
( ( ! [SY136: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ( relation @ ( sK17_C @ SY136 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SY136 @ SV29 ) @ SV29 @ SY136 ) )
| ~ ( function @ ( sK17_C @ SY136 @ SV29 ) ) )
| ~ ( quasi_total @ ( sK17_C @ SY136 @ SV29 ) @ SV29 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(289,plain,
( ( ~ ~ ( ~ ( function @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( one_to_one @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(290,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(291,plain,
! [SV30: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV30 )
| ~ ( in @ SV30 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(292,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(293,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(294,plain,
! [SV31: $i,SV4: $i] :
( ( ! [SY137: $i] :
( ~ ( element @ SY137 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV31 ) ) )
| ( relation @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(295,plain,
! [SV32: $i,SV5: $i] :
( ( ! [SY138: $i] :
( ~ ( relation_of2 @ SY138 @ SV5 @ SV32 )
| ( element @ ( relation_dom_as_subset @ SV5 @ SV32 @ SY138 ) @ ( powerset @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(296,plain,
! [SV33: $i,SV6: $i] :
( ( ! [SY139: $i] :
( ~ ( relation_of2_as_subset @ SY139 @ SV6 @ SV33 )
| ( element @ SY139 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(297,plain,
! [SV7: $i,SV34: $i] :
( ( relation_of2 @ ( sK21_C @ SV34 @ SV7 ) @ SV7 @ SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(298,plain,
! [SV9: $i,SV35: $i] :
( ( relation_of2_as_subset @ ( sK19_C @ SV35 @ SV9 ) @ SV9 @ SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(299,plain,
! [SV10: $i] :
( ( empty @ ( powerset @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(300,plain,
! [SV36: $i,SV11: $i] :
( ( ( empty @ SV11 )
| ( empty @ SV36 )
| ~ ( empty @ ( cartesian_product2 @ SV11 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(301,plain,
! [SV12: $i] :
( ( ( ( empty @ SV12 )
| ~ ( relation @ SV12 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(302,plain,
! [SV13: $i] :
( ( ( ( empty @ SV13 )
| ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(303,plain,
! [SV37: $i,SV14: $i] :
( ( ! [SY140: $i] :
( ~ ( relation_of2 @ SY140 @ SV14 @ SV37 )
| ( ( relation_dom_as_subset @ SV14 @ SV37 @ SY140 )
= ( relation_dom @ SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(304,plain,
! [SV38: $i,SV16: $i] :
( ( ~ ( in @ SV16 @ SV38 )
| ( element @ SV16 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(305,plain,
! [SV39: $i,SV17: $i] :
( ( ~ ( element @ SV17 @ SV39 )
| ( empty @ SV39 )
| ( in @ SV17 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(306,plain,
! [SV18: $i,SV40: $i] :
( ( ! [SY141: $i] :
( ~ ( element @ SV40 @ ( powerset @ SY141 ) )
| ~ ( in @ SV18 @ SV40 )
| ( element @ SV18 @ SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(307,plain,
! [SV19: $i,SV41: $i] :
( ( ! [SY142: $i] :
( ~ ( element @ SV41 @ ( powerset @ SY142 ) )
| ~ ( in @ SV19 @ SV41 )
| ~ ( empty @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(308,plain,
! [SV20: $i] :
( ( ( ~ ( empty @ SV20 ) )
= $true )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(309,plain,
! [SV21: $i,SV42: $i] :
( ( ~ ( empty @ SV42 )
| ~ ( in @ SV21 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(310,plain,
! [SV43: $i,SV22: $i] :
( ( ( SV22 = SV43 )
| ~ ( empty @ SV22 )
| ~ ( empty @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(311,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ~ ( empty @ ( sK14_B @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(312,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
| ~ ~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) ) )
| ~ ~ ( ~ ! [SY121: $i,SY122: $i] :
( ~ ( relation_of2_as_subset @ SY122 @ SV24 @ SY121 )
| ( SY121 != empty_set )
| ( SY122 != empty_set )
| ( quasi_total @ SY122 @ SV24 @ SY121 )
| ( SV24 = empty_set ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( relation_of2_as_subset @ SY124 @ SV24 @ SY123 )
| ( SY123 != empty_set )
| ~ ( quasi_total @ SY124 @ SV24 @ SY123 )
| ( SY124 = empty_set )
| ( SV24 = empty_set ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(313,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( one_to_one @ sK16_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(314,plain,
( ( ~ ( empty @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(315,plain,
( ( ~ ( ( sK2_SY85 != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(316,plain,
( ( ~ ~ ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(317,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(318,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(319,plain,
( ( ~ ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(320,plain,
( ( ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(321,plain,
( ( ~ ( empty @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(322,plain,
( ( ~ ( relation @ sK15_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(323,plain,
! [SV25: $i] :
( ( ~ ( element @ ( sK9_B @ SV25 ) @ ( powerset @ SV25 ) )
| ~ ( empty @ ( sK9_B @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(324,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ( ~ ~ ( ~ ( relation @ ( sK11_C @ SV44 @ SV26 ) )
| ~ ( relation_of2 @ ( sK11_C @ SV44 @ SV26 ) @ SV26 @ SV44 ) )
| ~ ( function @ ( sK11_C @ SV44 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(325,plain,
! [SV27: $i] :
( ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( relation_of2 @ SY127 @ SV27 @ SY126 )
| ( relation_of2_as_subset @ SY127 @ SV27 @ SY126 ) )
| ~ ! [SY128: $i,SY129: $i] :
( ~ ( relation_of2_as_subset @ SY129 @ SV27 @ SY128 )
| ( relation_of2 @ SY129 @ SV27 @ SY128 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(326,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(327,plain,
( ( ~ ( relation_empty_yielding @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(328,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(329,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(330,plain,
( ( ~ ~ ( ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(331,plain,
( ( ~ ( function @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(332,plain,
( ( ~ ~ ( ~ ( relation @ sK5_A )
| ~ ( relation_empty_yielding @ sK5_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(333,plain,
( ( ~ ( function @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(335,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(336,plain,
! [SV28: $i] :
( ( ( ~ ( function @ SV28 )
| ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) )
| ~ ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(337,plain,
( ( ~ ( function @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(338,plain,
( ( ~ ( relation @ sK18_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(339,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(340,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(341,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(342,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(343,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
| ~ ( function @ ( sK17_C @ SV45 @ SV29 ) ) )
| ~ ( quasi_total @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(344,plain,
( ( ~ ~ ( ~ ( function @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(345,plain,
( ( ~ ( one_to_one @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(346,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(347,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(348,plain,
! [SV30: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV30 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(349,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(350,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(351,plain,
! [SV31: $i,SV4: $i,SV46: $i] :
( ( ~ ( element @ SV46 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV31 ) ) )
| ( relation @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(352,plain,
! [SV32: $i,SV5: $i,SV47: $i] :
( ( ~ ( relation_of2 @ SV47 @ SV5 @ SV32 )
| ( element @ ( relation_dom_as_subset @ SV5 @ SV32 @ SV47 ) @ ( powerset @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(353,plain,
! [SV33: $i,SV6: $i,SV48: $i] :
( ( ~ ( relation_of2_as_subset @ SV48 @ SV6 @ SV33 )
| ( element @ SV48 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(354,plain,
! [SV36: $i,SV11: $i] :
( ( ( ( empty @ SV11 )
| ( empty @ SV36 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV11 @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(355,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $true )
| ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(356,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(357,plain,
! [SV37: $i,SV14: $i,SV49: $i] :
( ( ~ ( relation_of2 @ SV49 @ SV14 @ SV37 )
| ( ( relation_dom_as_subset @ SV14 @ SV37 @ SV49 )
= ( relation_dom @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(358,plain,
! [SV38: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV38 ) )
= $true )
| ( ( element @ SV16 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(359,plain,
! [SV39: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ SV39 ) )
= $true )
| ( ( ( empty @ SV39 )
| ( in @ SV17 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(360,plain,
! [SV18: $i,SV50: $i,SV40: $i] :
( ( ~ ( element @ SV40 @ ( powerset @ SV50 ) )
| ~ ( in @ SV18 @ SV40 )
| ( element @ SV18 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(361,plain,
! [SV19: $i,SV51: $i,SV41: $i] :
( ( ~ ( element @ SV41 @ ( powerset @ SV51 ) )
| ~ ( in @ SV19 @ SV41 )
| ~ ( empty @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(362,plain,
! [SV20: $i] :
( ( ( empty @ SV20 )
= $false )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(363,plain,
! [SV21: $i,SV42: $i] :
( ( ( ~ ( empty @ SV42 ) )
= $true )
| ( ( ~ ( in @ SV21 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(364,plain,
! [SV43: $i,SV22: $i] :
( ( ( ( SV22 = SV43 )
| ~ ( empty @ SV22 ) )
= $true )
| ( ( ~ ( empty @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(365,plain,
! [SV23: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ~ ( empty @ ( sK14_B @ SV23 ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(366,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
| ~ ~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(367,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY121: $i,SY122: $i] :
( ~ ( relation_of2_as_subset @ SY122 @ SV24 @ SY121 )
| ( SY121 != empty_set )
| ( SY122 != empty_set )
| ( quasi_total @ SY122 @ SV24 @ SY121 )
| ( SV24 = empty_set ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( relation_of2_as_subset @ SY124 @ SV24 @ SY123 )
| ( SY123 != empty_set )
| ~ ( quasi_total @ SY124 @ SV24 @ SY123 )
| ( SY124 = empty_set )
| ( SV24 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(368,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( one_to_one @ sK16_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(369,plain,
( ( empty @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(370,plain,
( ( ( sK2_SY85 != empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(371,plain,
( ( ~ ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(372,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(373,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(374,plain,
( ( ~ ( empty @ sK10_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(375,plain,
( ( relation @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(376,plain,
( ( empty @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(377,plain,
( ( relation @ sK15_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(378,plain,
! [SV25: $i] :
( ( ~ ( element @ ( sK9_B @ SV25 ) @ ( powerset @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(379,plain,
! [SV25: $i] :
( ( ~ ( empty @ ( sK9_B @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(380,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ~ ( ~ ( relation @ ( sK11_C @ SV44 @ SV26 ) )
| ~ ( relation_of2 @ ( sK11_C @ SV44 @ SV26 ) @ SV26 @ SV44 ) )
| ~ ( function @ ( sK11_C @ SV44 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(381,plain,
! [SV27: $i] :
( ( ~ ! [SY126: $i,SY127: $i] :
( ~ ( relation_of2 @ SY127 @ SV27 @ SY126 )
| ( relation_of2_as_subset @ SY127 @ SV27 @ SY126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(382,plain,
! [SV27: $i] :
( ( ~ ! [SY128: $i,SY129: $i] :
( ~ ( relation_of2_as_subset @ SY129 @ SV27 @ SY128 )
| ( relation_of2 @ SY129 @ SV27 @ SY128 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(383,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(384,plain,
( ( relation_empty_yielding @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(385,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(386,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(387,plain,
( ( ~ ( ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(388,plain,
( ( function @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(389,plain,
( ( ~ ( ~ ( relation @ sK5_A )
| ~ ( relation_empty_yielding @ sK5_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(390,plain,
( ( function @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(392,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(393,plain,
! [SV28: $i] :
( ( ( ~ ( function @ SV28 ) )
= $true )
| ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) )
| ~ ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(394,plain,
( ( function @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(395,plain,
( ( relation @ sK18_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(396,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(397,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(398,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(399,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(400,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
| ~ ( function @ ( sK17_C @ SV45 @ SV29 ) ) )
| ~ ( quasi_total @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(401,plain,
( ( ~ ( ~ ( function @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(402,plain,
( ( one_to_one @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(403,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(404,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(405,plain,
! [SV30: $i,SV1: $i] :
( ( ( in @ SV1 @ SV30 )
= $false )
| ( ( ~ ( in @ SV30 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(406,plain,
! [SV31: $i,SV4: $i,SV46: $i] :
( ( ( ~ ( element @ SV46 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV31 ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(407,plain,
! [SV32: $i,SV5: $i,SV47: $i] :
( ( ( ~ ( relation_of2 @ SV47 @ SV5 @ SV32 ) )
= $true )
| ( ( element @ ( relation_dom_as_subset @ SV5 @ SV32 @ SV47 ) @ ( powerset @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(408,plain,
! [SV33: $i,SV6: $i,SV48: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV48 @ SV6 @ SV33 ) )
= $true )
| ( ( element @ SV48 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(409,plain,
! [SV36: $i,SV11: $i] :
( ( ( empty @ SV11 )
= $true )
| ( ( empty @ SV36 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV11 @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(410,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( empty @ SV12 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(411,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(412,plain,
! [SV37: $i,SV14: $i,SV49: $i] :
( ( ( ~ ( relation_of2 @ SV49 @ SV14 @ SV37 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV14 @ SV37 @ SV49 )
= ( relation_dom @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(413,plain,
! [SV38: $i,SV16: $i] :
( ( ( in @ SV16 @ SV38 )
= $false )
| ( ( element @ SV16 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(414,plain,
! [SV39: $i,SV17: $i] :
( ( ( element @ SV17 @ SV39 )
= $false )
| ( ( ( empty @ SV39 )
| ( in @ SV17 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(415,plain,
! [SV18: $i,SV50: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ SV50 ) )
| ~ ( in @ SV18 @ SV40 ) )
= $true )
| ( ( element @ SV18 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(416,plain,
! [SV19: $i,SV51: $i,SV41: $i] :
( ( ( ~ ( element @ SV41 @ ( powerset @ SV51 ) )
| ~ ( in @ SV19 @ SV41 ) )
= $true )
| ( ( ~ ( empty @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(417,plain,
! [SV21: $i,SV42: $i] :
( ( ( empty @ SV42 )
= $false )
| ( ( ~ ( in @ SV21 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(418,plain,
! [SV43: $i,SV22: $i] :
( ( ( SV22 = SV43 )
= $true )
| ( ( ~ ( empty @ SV22 ) )
= $true )
| ( ( ~ ( empty @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(419,plain,
! [SV23: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(420,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ ( sK14_B @ SV23 ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(421,plain,
! [SV24: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
| ~ ~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(422,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY121: $i,SY122: $i] :
( ~ ( relation_of2_as_subset @ SY122 @ SV24 @ SY121 )
| ( SY121 != empty_set )
| ( SY122 != empty_set )
| ( quasi_total @ SY122 @ SV24 @ SY121 )
| ( SV24 = empty_set ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( relation_of2_as_subset @ SY124 @ SV24 @ SY123 )
| ( SY123 != empty_set )
| ~ ( quasi_total @ SY124 @ SV24 @ SY123 )
| ( SY124 = empty_set )
| ( SV24 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(423,plain,
( ( ~ ~ ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) )
| ~ ( one_to_one @ sK16_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(424,plain,
( ( sK2_SY85 = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(425,plain,
( ( in @ ( apply @ sK4_SY90 @ sK3_SY88 ) @ ( relation_rng @ sK4_SY90 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(426,plain,
! [SV52: $i] :
( ( ~ ( empty @ SV52 )
| ( empty @ ( relation_rng @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(427,plain,
! [SV53: $i] :
( ( ~ ( empty @ SV53 )
| ( relation @ ( relation_rng @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(428,plain,
( ( empty @ sK10_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(429,plain,
! [SV25: $i] :
( ( element @ ( sK9_B @ SV25 ) @ ( powerset @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(430,plain,
! [SV25: $i] :
( ( empty @ ( sK9_B @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(431,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ~ ( ~ ( relation @ ( sK11_C @ SV44 @ SV26 ) )
| ~ ( relation_of2 @ ( sK11_C @ SV44 @ SV26 ) @ SV26 @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(432,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ( function @ ( sK11_C @ SV44 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(433,plain,
! [SV27: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ~ ( relation_of2 @ SY127 @ SV27 @ SY126 )
| ( relation_of2_as_subset @ SY127 @ SV27 @ SY126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(434,plain,
! [SV27: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( relation_of2_as_subset @ SY129 @ SV27 @ SY128 )
| ( relation_of2 @ SY129 @ SV27 @ SY128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(435,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(436,plain,
( ( ~ ( empty @ sK12_A )
| ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(437,plain,
( ( ~ ( relation @ sK5_A )
| ~ ( relation_empty_yielding @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(439,plain,
! [SV54: $i] :
( ( ~ ( empty @ SV54 )
| ~ ( relation @ SV54 )
| ~ ( function @ SV54 )
| ( one_to_one @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(440,plain,
! [SV28: $i] :
( ( ( function @ SV28 )
= $false )
| ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( ~ ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) )
| ~ ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(441,plain,
! [SV55: $i] :
( ( ~ ( empty @ SV55 )
| ( empty @ ( relation_dom @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(442,plain,
! [SV56: $i] :
( ( ~ ( empty @ SV56 )
| ( relation @ ( relation_dom @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(443,plain,
! [SV57: $i] :
( ( ! [SY143: $i] :
( ~ ( element @ SV57 @ ( powerset @ SY143 ) )
| ( subset @ SV57 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(444,plain,
! [SV58: $i] :
( ( ! [SY144: $i] :
( ~ ( subset @ SV58 @ SY144 )
| ( element @ SV58 @ ( powerset @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(445,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
| ~ ( function @ ( sK17_C @ SV45 @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(446,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( quasi_total @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(447,plain,
( ( ~ ( function @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(448,plain,
! [SV1: $i,SV30: $i] :
( ( ( in @ SV30 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(449,plain,
! [SV31: $i,SV4: $i,SV46: $i] :
( ( ( element @ SV46 @ ( powerset @ ( cartesian_product2 @ SV4 @ SV31 ) ) )
= $false )
| ( ( relation @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(450,plain,
! [SV32: $i,SV5: $i,SV47: $i] :
( ( ( relation_of2 @ SV47 @ SV5 @ SV32 )
= $false )
| ( ( element @ ( relation_dom_as_subset @ SV5 @ SV32 @ SV47 ) @ ( powerset @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(451,plain,
! [SV33: $i,SV6: $i,SV48: $i] :
( ( ( relation_of2_as_subset @ SV48 @ SV6 @ SV33 )
= $false )
| ( ( element @ SV48 @ ( powerset @ ( cartesian_product2 @ SV6 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(452,plain,
! [SV36: $i,SV11: $i] :
( ( ( empty @ ( cartesian_product2 @ SV11 @ SV36 ) )
= $false )
| ( ( empty @ SV36 )
= $true )
| ( ( empty @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(453,plain,
! [SV12: $i] :
( ( ( empty @ ( relation_dom @ SV12 ) )
= $false )
| ( ( empty @ SV12 )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(454,plain,
! [SV13: $i] :
( ( ( empty @ ( relation_rng @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(455,plain,
! [SV37: $i,SV14: $i,SV49: $i] :
( ( ( relation_of2 @ SV49 @ SV14 @ SV37 )
= $false )
| ( ( ( relation_dom_as_subset @ SV14 @ SV37 @ SV49 )
= ( relation_dom @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(456,plain,
! [SV17: $i,SV39: $i] :
( ( ( empty @ SV39 )
= $true )
| ( ( in @ SV17 @ SV39 )
= $true )
| ( ( element @ SV17 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(457,plain,
! [SV18: $i,SV50: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ SV50 ) ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV40 ) )
= $true )
| ( ( element @ SV18 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(458,plain,
! [SV19: $i,SV51: $i,SV41: $i] :
( ( ( ~ ( element @ SV41 @ ( powerset @ SV51 ) ) )
= $true )
| ( ( ~ ( in @ SV19 @ SV41 ) )
= $true )
| ( ( ~ ( empty @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(459,plain,
! [SV42: $i,SV21: $i] :
( ( ( in @ SV21 @ SV42 )
= $false )
| ( ( empty @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(460,plain,
! [SV43: $i,SV22: $i] :
( ( ( empty @ SV22 )
= $false )
| ( ( SV22 = SV43 )
= $true )
| ( ( ~ ( empty @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(461,plain,
! [SV23: $i] :
( ( ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(462,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ ( sK14_B @ SV23 ) ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(463,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
| ~ ~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(464,plain,
! [SV24: $i] :
( ( ~ ! [SY121: $i,SY122: $i] :
( ~ ( relation_of2_as_subset @ SY122 @ SV24 @ SY121 )
| ( SY121 != empty_set )
| ( SY122 != empty_set )
| ( quasi_total @ SY122 @ SV24 @ SY121 )
| ( SV24 = empty_set ) )
| ~ ! [SY123: $i,SY124: $i] :
( ~ ( relation_of2_as_subset @ SY124 @ SV24 @ SY123 )
| ( SY123 != empty_set )
| ~ ( quasi_total @ SY124 @ SV24 @ SY123 )
| ( SY124 = empty_set )
| ( SV24 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(465,plain,
( ( ~ ~ ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(466,plain,
( ( ~ ( one_to_one @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(467,plain,
! [SV52: $i] :
( ( ( ~ ( empty @ SV52 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(468,plain,
! [SV53: $i] :
( ( ( ~ ( empty @ SV53 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(469,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ( ~ ( relation @ ( sK11_C @ SV44 @ SV26 ) )
| ~ ( relation_of2 @ ( sK11_C @ SV44 @ SV26 ) @ SV26 @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(470,plain,
! [SV26: $i,SV44: $i] :
( ( function @ ( sK11_C @ SV44 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(471,plain,
! [SV59: $i,SV27: $i] :
( ( ! [SY145: $i] :
( ~ ( relation_of2 @ SY145 @ SV27 @ SV59 )
| ( relation_of2_as_subset @ SY145 @ SV27 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(472,plain,
! [SV60: $i,SV27: $i] :
( ( ! [SY146: $i] :
( ~ ( relation_of2_as_subset @ SY146 @ SV27 @ SV60 )
| ( relation_of2 @ SY146 @ SV27 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(473,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(474,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(475,plain,
( ( ~ ( empty @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(476,plain,
( ( ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(477,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(478,plain,
( ( ~ ( relation_empty_yielding @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(481,plain,
! [SV54: $i] :
( ( ( ~ ( empty @ SV54 )
| ~ ( relation @ SV54 )
| ~ ( function @ SV54 ) )
= $true )
| ( ( one_to_one @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(482,plain,
! [SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( ~ ( ~ ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) )
| ~ ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(483,plain,
! [SV55: $i] :
( ( ( ~ ( empty @ SV55 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(484,plain,
! [SV56: $i] :
( ( ( ~ ( empty @ SV56 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(485,plain,
! [SV61: $i,SV57: $i] :
( ( ~ ( element @ SV57 @ ( powerset @ SV61 ) )
| ( subset @ SV57 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(486,plain,
! [SV62: $i,SV58: $i] :
( ( ~ ( subset @ SV58 @ SV62 )
| ( element @ SV58 @ ( powerset @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(487,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( ~ ~ ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
| ~ ( function @ ( sK17_C @ SV45 @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(488,plain,
! [SV29: $i,SV45: $i] :
( ( quasi_total @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(489,plain,
( ( ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(490,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(491,plain,
! [SV18: $i,SV50: $i,SV40: $i] :
( ( ( element @ SV40 @ ( powerset @ SV50 ) )
= $false )
| ( ( ~ ( in @ SV18 @ SV40 ) )
= $true )
| ( ( element @ SV18 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(492,plain,
! [SV19: $i,SV51: $i,SV41: $i] :
( ( ( element @ SV41 @ ( powerset @ SV51 ) )
= $false )
| ( ( ~ ( in @ SV19 @ SV41 ) )
= $true )
| ( ( ~ ( empty @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(493,plain,
! [SV22: $i,SV43: $i] :
( ( ( empty @ SV43 )
= $false )
| ( ( SV22 = SV43 )
= $true )
| ( ( empty @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(494,plain,
! [SV23: $i] :
( ( ( empty @ ( sK14_B @ SV23 ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(495,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(496,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(497,plain,
! [SV24: $i] :
( ( ~ ! [SY121: $i,SY122: $i] :
( ~ ( relation_of2_as_subset @ SY122 @ SV24 @ SY121 )
| ( SY121 != empty_set )
| ( SY122 != empty_set )
| ( quasi_total @ SY122 @ SV24 @ SY121 )
| ( SV24 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(498,plain,
! [SV24: $i] :
( ( ~ ! [SY123: $i,SY124: $i] :
( ~ ( relation_of2_as_subset @ SY124 @ SV24 @ SY123 )
| ( SY123 != empty_set )
| ~ ( quasi_total @ SY124 @ SV24 @ SY123 )
| ( SY124 = empty_set )
| ( SV24 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(499,plain,
( ( ~ ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(500,plain,
( ( one_to_one @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(501,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
= $false )
| ( ( empty @ ( relation_rng @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(502,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
= $false )
| ( ( relation @ ( relation_rng @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(503,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ( relation @ ( sK11_C @ SV44 @ SV26 ) )
| ~ ( relation_of2 @ ( sK11_C @ SV44 @ SV26 ) @ SV26 @ SV44 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(504,plain,
! [SV59: $i,SV27: $i,SV63: $i] :
( ( ~ ( relation_of2 @ SV63 @ SV27 @ SV59 )
| ( relation_of2_as_subset @ SV63 @ SV27 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(505,plain,
! [SV60: $i,SV27: $i,SV64: $i] :
( ( ~ ( relation_of2_as_subset @ SV64 @ SV27 @ SV60 )
| ( relation_of2 @ SV64 @ SV27 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(506,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(507,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(508,plain,
( ( empty @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(509,plain,
( ( relation @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(510,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(511,plain,
( ( relation_empty_yielding @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(514,plain,
! [SV54: $i] :
( ( ( ~ ( empty @ SV54 )
| ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( function @ SV54 ) )
= $true )
| ( ( one_to_one @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(515,plain,
! [SV28: $i] :
( ( ( ~ ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) )
| ~ ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(516,plain,
! [SV55: $i] :
( ( ( empty @ SV55 )
= $false )
| ( ( empty @ ( relation_dom @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(517,plain,
! [SV56: $i] :
( ( ( empty @ SV56 )
= $false )
| ( ( relation @ ( relation_dom @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(518,plain,
! [SV61: $i,SV57: $i] :
( ( ( ~ ( element @ SV57 @ ( powerset @ SV61 ) ) )
= $true )
| ( ( subset @ SV57 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(519,plain,
! [SV62: $i,SV58: $i] :
( ( ( ~ ( subset @ SV58 @ SV62 ) )
= $true )
| ( ( element @ SV58 @ ( powerset @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(520,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ~ ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
| ~ ( function @ ( sK17_C @ SV45 @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(521,plain,
( ( function @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(522,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(523,plain,
! [SV50: $i,SV40: $i,SV18: $i] :
( ( ( in @ SV18 @ SV40 )
= $false )
| ( ( element @ SV40 @ ( powerset @ SV50 ) )
= $false )
| ( ( element @ SV18 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(524,plain,
! [SV51: $i,SV41: $i,SV19: $i] :
( ( ( in @ SV19 @ SV41 )
= $false )
| ( ( element @ SV41 @ ( powerset @ SV51 ) )
= $false )
| ( ( ~ ( empty @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(525,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(526,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(527,plain,
! [SV24: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ~ ( relation_of2_as_subset @ SY122 @ SV24 @ SY121 )
| ( SY121 != empty_set )
| ( SY122 != empty_set )
| ( quasi_total @ SY122 @ SV24 @ SY121 )
| ( SV24 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(528,plain,
! [SV24: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( relation_of2_as_subset @ SY124 @ SV24 @ SY123 )
| ( SY123 != empty_set )
| ~ ( quasi_total @ SY124 @ SV24 @ SY123 )
| ( SY124 = empty_set )
| ( SV24 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(529,plain,
( ( ~ ( function @ sK16_A )
| ~ ( relation @ sK16_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(530,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ( relation @ ( sK11_C @ SV44 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(531,plain,
! [SV26: $i,SV44: $i] :
( ( ~ ( relation_of2 @ ( sK11_C @ SV44 @ SV26 ) @ SV26 @ SV44 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(532,plain,
! [SV59: $i,SV27: $i,SV63: $i] :
( ( ( ~ ( relation_of2 @ SV63 @ SV27 @ SV59 ) )
= $true )
| ( ( relation_of2_as_subset @ SV63 @ SV27 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(533,plain,
! [SV60: $i,SV27: $i,SV64: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV64 @ SV27 @ SV60 ) )
= $true )
| ( ( relation_of2 @ SV64 @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(536,plain,
! [SV54: $i] :
( ( ( ~ ( empty @ SV54 ) )
= $true )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( function @ SV54 ) )
= $true )
| ( ( one_to_one @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(537,plain,
! [SV28: $i] :
( ( ( ~ ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(538,plain,
! [SV28: $i] :
( ( ( ~ ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(539,plain,
! [SV61: $i,SV57: $i] :
( ( ( element @ SV57 @ ( powerset @ SV61 ) )
= $false )
| ( ( subset @ SV57 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(540,plain,
! [SV62: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV62 )
= $false )
| ( ( element @ SV58 @ ( powerset @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(541,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ~ ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(542,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( function @ ( sK17_C @ SV45 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[520]) ).
thf(543,plain,
! [SV19: $i,SV41: $i,SV51: $i] :
( ( ( empty @ SV51 )
= $false )
| ( ( element @ SV41 @ ( powerset @ SV51 ) )
= $false )
| ( ( in @ SV19 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(544,plain,
! [SV24: $i] :
( ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) )
| ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(545,plain,
! [SV24: $i] :
( ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) )
| ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(546,plain,
! [SV67: $i,SV24: $i] :
( ( ! [SY147: $i] :
( ~ ( relation_of2_as_subset @ SY147 @ SV24 @ SV67 )
| ( SV67 != empty_set )
| ( SY147 != empty_set )
| ( quasi_total @ SY147 @ SV24 @ SV67 )
| ( SV24 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(547,plain,
! [SV68: $i,SV24: $i] :
( ( ! [SY148: $i] :
( ~ ( relation_of2_as_subset @ SY148 @ SV24 @ SV68 )
| ( SV68 != empty_set )
| ~ ( quasi_total @ SY148 @ SV24 @ SV68 )
| ( SY148 = empty_set )
| ( SV24 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(548,plain,
( ( ~ ( function @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(549,plain,
( ( ~ ( relation @ sK16_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(550,plain,
! [SV26: $i,SV44: $i] :
( ( relation @ ( sK11_C @ SV44 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(551,plain,
! [SV26: $i,SV44: $i] :
( ( relation_of2 @ ( sK11_C @ SV44 @ SV26 ) @ SV26 @ SV44 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(552,plain,
! [SV59: $i,SV27: $i,SV63: $i] :
( ( ( relation_of2 @ SV63 @ SV27 @ SV59 )
= $false )
| ( ( relation_of2_as_subset @ SV63 @ SV27 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(553,plain,
! [SV60: $i,SV27: $i,SV64: $i] :
( ( ( relation_of2_as_subset @ SV64 @ SV27 @ SV60 )
= $false )
| ( ( relation_of2 @ SV64 @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(556,plain,
! [SV54: $i] :
( ( ( empty @ SV54 )
= $false )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( function @ SV54 ) )
= $true )
| ( ( one_to_one @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(557,plain,
! [SV28: $i] :
( ( ( ! [SY130: $i] :
( ~ ( ~ ( ! [SY131: $i] :
( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ SY131 ) )
| ~ ( in @ SY131 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) )
| ~ ( ~ ( ( ( sK23_C @ SY130 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SY130 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SY130 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SY130 @ SV28 ) @ SY130 ) ) )
| ( SY130
= ( relation_rng @ SV28 ) ) ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(558,plain,
! [SV28: $i] :
( ( ( ! [SY132: $i] :
( ( SY132
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY133: $i] :
( ! [SY134: $i] :
( ( SY133
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY133 @ SY132 ) )
| ~ ! [SY135: $i] :
( ~ ( in @ SY135 @ SY132 )
| ~ ( ( SY135
!= ( apply @ SV28 @ ( sK22_D @ SY135 @ SY132 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY135 @ SY132 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(559,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(560,plain,
! [SV29: $i,SV45: $i] :
( ( function @ ( sK17_C @ SV45 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(561,plain,
! [SV24: $i] :
( ( ~ ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(562,plain,
! [SV24: $i] :
( ( ~ ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(563,plain,
! [SV24: $i] :
( ( ~ ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(564,plain,
! [SV24: $i] :
( ( ~ ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(565,plain,
! [SV67: $i,SV24: $i,SV69: $i] :
( ( ~ ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 )
| ( SV67 != empty_set )
| ( SV69 != empty_set )
| ( quasi_total @ SV69 @ SV24 @ SV67 )
| ( SV24 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(566,plain,
! [SV68: $i,SV24: $i,SV70: $i] :
( ( ~ ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 )
| ( SV68 != empty_set )
| ~ ( quasi_total @ SV70 @ SV24 @ SV68 )
| ( SV70 = empty_set )
| ( SV24 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(567,plain,
( ( function @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(568,plain,
( ( relation @ sK16_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(571,plain,
! [SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( empty @ SV54 )
= $false )
| ( ( ~ ( function @ SV54 ) )
= $true )
| ( ( one_to_one @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(572,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( ~ ( ! [SY149: $i] :
( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SY149 ) )
| ~ ( in @ SY149 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
| ~ ( ~ ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) ) )
| ( SV71
= ( relation_rng @ SV28 ) ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(573,plain,
! [SV28: $i,SV72: $i] :
( ( ( ( SV72
!= ( relation_rng @ SV28 ) )
| ~ ( ~ ! [SY150: $i] :
( ! [SY134: $i] :
( ( SY150
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY150 @ SV72 ) )
| ~ ! [SY152: $i] :
( ~ ( in @ SY152 @ SV72 )
| ~ ( ( SY152
!= ( apply @ SV28 @ ( sK22_D @ SY152 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY152 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(574,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) )
| ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(575,plain,
! [SV24: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( relation_of2_as_subset @ SY114 @ SV24 @ SY113 )
| ( SY113 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY113 @ SY114 ) )
| ( quasi_total @ SY114 @ SV24 @ SY113 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(576,plain,
! [SV24: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( relation_of2_as_subset @ SY116 @ SV24 @ SY115 )
| ( SY115 = empty_set )
| ~ ( quasi_total @ SY116 @ SV24 @ SY115 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY115 @ SY116 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(577,plain,
! [SV24: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SY117 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SY117 @ SY118 ) )
| ( quasi_total @ SY118 @ SV24 @ SY117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(578,plain,
! [SV24: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( relation_of2_as_subset @ SY120 @ SV24 @ SY119 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY120 @ SV24 @ SY119 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SY119 @ SY120 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(579,plain,
! [SV67: $i,SV24: $i,SV69: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 ) )
= $true )
| ( ( ( SV67 != empty_set )
| ( SV69 != empty_set )
| ( quasi_total @ SV69 @ SV24 @ SV67 )
| ( SV24 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(580,plain,
! [SV68: $i,SV24: $i,SV70: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 ) )
= $true )
| ( ( ( SV68 != empty_set )
| ~ ( quasi_total @ SV70 @ SV24 @ SV68 )
| ( SV70 = empty_set )
| ( SV24 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(583,plain,
! [SV54: $i] :
( ( ( function @ SV54 )
= $false )
| ( ( empty @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false )
| ( ( one_to_one @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(584,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( ~ ( ! [SY149: $i] :
( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SY149 ) )
| ~ ( in @ SY149 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
| ~ ( ~ ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) ) ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(585,plain,
! [SV28: $i,SV72: $i] :
( ( ( ( SV72
!= ( relation_rng @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY150: $i] :
( ! [SY134: $i] :
( ( SY150
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY150 @ SV72 ) )
| ~ ! [SY152: $i] :
( ~ ( in @ SY152 @ SV72 )
| ~ ( ( SY152
!= ( apply @ SV28 @ ( sK22_D @ SY152 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY152 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(586,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( relation @ ( sK17_C @ SV45 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(587,plain,
! [SV29: $i,SV45: $i] :
( ( ~ ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(588,plain,
! [SV73: $i,SV24: $i] :
( ( ! [SY153: $i] :
( ~ ( relation_of2_as_subset @ SY153 @ SV24 @ SV73 )
| ( SV73 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV73 @ SY153 ) )
| ( quasi_total @ SY153 @ SV24 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(589,plain,
! [SV74: $i,SV24: $i] :
( ( ! [SY154: $i] :
( ~ ( relation_of2_as_subset @ SY154 @ SV24 @ SV74 )
| ( SV74 = empty_set )
| ~ ( quasi_total @ SY154 @ SV24 @ SV74 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV74 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(590,plain,
! [SV75: $i,SV24: $i] :
( ( ! [SY155: $i] :
( ~ ( relation_of2_as_subset @ SY155 @ SV24 @ SV75 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV75 @ SY155 ) )
| ( quasi_total @ SY155 @ SV24 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(591,plain,
! [SV76: $i,SV24: $i] :
( ( ! [SY156: $i] :
( ~ ( relation_of2_as_subset @ SY156 @ SV24 @ SV76 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SY156 @ SV24 @ SV76 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(592,plain,
! [SV67: $i,SV24: $i,SV69: $i] :
( ( ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 )
= $false )
| ( ( ( SV67 != empty_set )
| ( SV69 != empty_set )
| ( quasi_total @ SV69 @ SV24 @ SV67 )
| ( SV24 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(593,plain,
! [SV68: $i,SV24: $i,SV70: $i] :
( ( ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 )
= $false )
| ( ( ( SV68 != empty_set )
| ~ ( quasi_total @ SV70 @ SV24 @ SV68 )
| ( SV70 = empty_set )
| ( SV24 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(596,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( ! [SY149: $i] :
( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SY149 ) )
| ~ ( in @ SY149 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
| ~ ( ~ ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) ) )
= $false )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(597,plain,
! [SV28: $i,SV72: $i] :
( ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( ~ ( ~ ! [SY150: $i] :
( ! [SY134: $i] :
( ( SY150
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY150 @ SV72 ) )
| ~ ! [SY152: $i] :
( ~ ( in @ SY152 @ SV72 )
| ~ ( ( SY152
!= ( apply @ SV28 @ ( sK22_D @ SY152 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY152 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(598,plain,
! [SV29: $i,SV45: $i] :
( ( relation @ ( sK17_C @ SV45 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(599,plain,
! [SV29: $i,SV45: $i] :
( ( relation_of2 @ ( sK17_C @ SV45 @ SV29 ) @ SV29 @ SV45 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(600,plain,
! [SV73: $i,SV24: $i,SV77: $i] :
( ( ~ ( relation_of2_as_subset @ SV77 @ SV24 @ SV73 )
| ( SV73 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV73 @ SV77 ) )
| ( quasi_total @ SV77 @ SV24 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(601,plain,
! [SV74: $i,SV24: $i,SV78: $i] :
( ( ~ ( relation_of2_as_subset @ SV78 @ SV24 @ SV74 )
| ( SV74 = empty_set )
| ~ ( quasi_total @ SV78 @ SV24 @ SV74 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV74 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(602,plain,
! [SV75: $i,SV24: $i,SV79: $i] :
( ( ~ ( relation_of2_as_subset @ SV79 @ SV24 @ SV75 )
| ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV75 @ SV79 ) )
| ( quasi_total @ SV79 @ SV24 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(603,plain,
! [SV76: $i,SV24: $i,SV80: $i] :
( ( ~ ( relation_of2_as_subset @ SV80 @ SV24 @ SV76 )
| ( SV24 != empty_set )
| ~ ( quasi_total @ SV80 @ SV24 @ SV76 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(604,plain,
! [SV24: $i,SV69: $i,SV67: $i] :
( ( ( ( SV67 != empty_set ) )
= $true )
| ( ( ( SV69 != empty_set )
| ( quasi_total @ SV69 @ SV24 @ SV67 )
| ( SV24 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(605,plain,
! [SV24: $i,SV70: $i,SV68: $i] :
( ( ( ( SV68 != empty_set ) )
= $true )
| ( ( ~ ( quasi_total @ SV70 @ SV24 @ SV68 )
| ( SV70 = empty_set )
| ( SV24 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(608,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( ! [SY149: $i] :
( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SY149 ) )
| ~ ( in @ SY149 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) ) )
= $false )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(609,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( ~ ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) ) )
= $false )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(610,plain,
! [SV72: $i,SV28: $i] :
( ( ( ~ ! [SY150: $i] :
( ! [SY134: $i] :
( ( SY150
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY150 @ SV72 ) )
| ~ ! [SY152: $i] :
( ~ ( in @ SY152 @ SV72 )
| ~ ( ( SY152
!= ( apply @ SV28 @ ( sK22_D @ SY152 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY152 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(611,plain,
! [SV73: $i,SV24: $i,SV77: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV77 @ SV24 @ SV73 ) )
= $true )
| ( ( ( SV73 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV73 @ SV77 ) )
| ( quasi_total @ SV77 @ SV24 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(612,plain,
! [SV74: $i,SV24: $i,SV78: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV78 @ SV24 @ SV74 ) )
= $true )
| ( ( ( SV74 = empty_set )
| ~ ( quasi_total @ SV78 @ SV24 @ SV74 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV74 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(613,plain,
! [SV75: $i,SV24: $i,SV79: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV79 @ SV24 @ SV75 ) )
= $true )
| ( ( ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV75 @ SV79 ) )
| ( quasi_total @ SV79 @ SV24 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(614,plain,
! [SV76: $i,SV24: $i,SV80: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV80 @ SV24 @ SV76 ) )
= $true )
| ( ( ( SV24 != empty_set )
| ~ ( quasi_total @ SV80 @ SV24 @ SV76 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(615,plain,
! [SV24: $i,SV69: $i,SV67: $i] :
( ( ( SV67 = empty_set )
= $false )
| ( ( ( SV69 != empty_set )
| ( quasi_total @ SV69 @ SV24 @ SV67 )
| ( SV24 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(616,plain,
! [SV24: $i,SV70: $i,SV68: $i] :
( ( ( SV68 = empty_set )
= $false )
| ( ( ~ ( quasi_total @ SV70 @ SV24 @ SV68 )
| ( SV70 = empty_set )
| ( SV24 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(619,plain,
! [SV28: $i,SV71: $i] :
( ( ( ! [SY149: $i] :
( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SY149 ) )
| ~ ( in @ SY149 @ ( relation_dom @ SV28 ) ) )
| ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(620,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
| ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(621,plain,
! [SV72: $i,SV28: $i] :
( ( ( ~ ! [SY150: $i] :
( ! [SY134: $i] :
( ( SY150
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY150 @ SV72 ) ) )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(622,plain,
! [SV28: $i,SV72: $i] :
( ( ( ~ ! [SY152: $i] :
( ~ ( in @ SY152 @ SV72 )
| ~ ( ( SY152
!= ( apply @ SV28 @ ( sK22_D @ SY152 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY152 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(623,plain,
! [SV73: $i,SV24: $i,SV77: $i] :
( ( ( relation_of2_as_subset @ SV77 @ SV24 @ SV73 )
= $false )
| ( ( ( SV73 = empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV73 @ SV77 ) )
| ( quasi_total @ SV77 @ SV24 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(624,plain,
! [SV74: $i,SV24: $i,SV78: $i] :
( ( ( relation_of2_as_subset @ SV78 @ SV24 @ SV74 )
= $false )
| ( ( ( SV74 = empty_set )
| ~ ( quasi_total @ SV78 @ SV24 @ SV74 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV74 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(625,plain,
! [SV75: $i,SV24: $i,SV79: $i] :
( ( ( relation_of2_as_subset @ SV79 @ SV24 @ SV75 )
= $false )
| ( ( ( SV24 != empty_set )
| ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV75 @ SV79 ) )
| ( quasi_total @ SV79 @ SV24 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(626,plain,
! [SV76: $i,SV24: $i,SV80: $i] :
( ( ( relation_of2_as_subset @ SV80 @ SV24 @ SV76 )
= $false )
| ( ( ( SV24 != empty_set )
| ~ ( quasi_total @ SV80 @ SV24 @ SV76 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(627,plain,
! [SV67: $i,SV24: $i,SV69: $i] :
( ( ( ( SV69 != empty_set )
| ( quasi_total @ SV69 @ SV24 @ SV67 ) )
= $true )
| ( ( SV24 = empty_set )
= $true )
| ( ( SV67 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(628,plain,
! [SV68: $i,SV24: $i,SV70: $i] :
( ( ( ~ ( quasi_total @ SV70 @ SV24 @ SV68 )
| ( SV70 = empty_set ) )
= $true )
| ( ( SV24 = empty_set )
= $true )
| ( ( SV68 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(629,plain,
! [SV28: $i,SV71: $i] :
( ( ( ! [SY149: $i] :
( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SY149 ) )
| ~ ( in @ SY149 @ ( relation_dom @ SV28 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(630,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) )
= $true )
| ( ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(631,plain,
! [SV72: $i,SV28: $i] :
( ( ( ! [SY150: $i] :
( ! [SY134: $i] :
( ( SY150
!= ( apply @ SV28 @ SY134 ) )
| ~ ( in @ SY134 @ ( relation_dom @ SV28 ) ) )
| ( in @ SY150 @ SV72 ) ) )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(632,plain,
! [SV28: $i,SV72: $i] :
( ( ( ! [SY152: $i] :
( ~ ( in @ SY152 @ SV72 )
| ~ ( ( SY152
!= ( apply @ SV28 @ ( sK22_D @ SY152 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SY152 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) ) )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(633,plain,
! [SV77: $i,SV24: $i,SV73: $i] :
( ( ( SV73 = empty_set )
= $true )
| ( ( ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV73 @ SV77 ) )
| ( quasi_total @ SV77 @ SV24 @ SV73 ) )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV24 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(634,plain,
! [SV24: $i,SV78: $i,SV74: $i] :
( ( ( SV74 = empty_set )
= $true )
| ( ( ~ ( quasi_total @ SV78 @ SV24 @ SV74 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV74 @ SV78 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV78 @ SV24 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(635,plain,
! [SV79: $i,SV75: $i,SV24: $i] :
( ( ( ( SV24 != empty_set ) )
= $true )
| ( ( ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV75 @ SV79 ) )
| ( quasi_total @ SV79 @ SV24 @ SV75 ) )
= $true )
| ( ( relation_of2_as_subset @ SV79 @ SV24 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(636,plain,
! [SV76: $i,SV80: $i,SV24: $i] :
( ( ( ( SV24 != empty_set ) )
= $true )
| ( ( ~ ( quasi_total @ SV80 @ SV24 @ SV76 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SV80 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV80 @ SV24 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(637,plain,
! [SV67: $i,SV24: $i,SV69: $i] :
( ( ( ( SV69 != empty_set ) )
= $true )
| ( ( quasi_total @ SV69 @ SV24 @ SV67 )
= $true )
| ( ( SV24 = empty_set )
= $true )
| ( ( SV67 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(638,plain,
! [SV68: $i,SV24: $i,SV70: $i] :
( ( ( ~ ( quasi_total @ SV70 @ SV24 @ SV68 ) )
= $true )
| ( ( SV70 = empty_set )
= $true )
| ( ( SV24 = empty_set )
= $true )
| ( ( SV68 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(639,plain,
! [SV81: $i,SV28: $i,SV71: $i] :
( ( ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SV81 ) )
| ~ ( in @ SV81 @ ( relation_dom @ SV28 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(640,plain,
! [SV28: $i,SV71: $i] :
( ( ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
| ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
= $false )
| ( ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(641,plain,
! [SV72: $i,SV28: $i,SV82: $i] :
( ( ( ! [SY157: $i] :
( ( SV82
!= ( apply @ SV28 @ SY157 ) )
| ~ ( in @ SY157 @ ( relation_dom @ SV28 ) ) )
| ( in @ SV82 @ SV72 ) )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(642,plain,
! [SV28: $i,SV72: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV72 )
| ~ ( ( SV83
!= ( apply @ SV28 @ ( sK22_D @ SV83 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SV83 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(643,plain,
! [SV77: $i,SV73: $i,SV24: $i] :
( ( ( ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV73 @ SV77 ) ) )
= $true )
| ( ( quasi_total @ SV77 @ SV24 @ SV73 )
= $true )
| ( ( SV73 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV24 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(644,plain,
! [SV74: $i,SV24: $i,SV78: $i] :
( ( ( ~ ( quasi_total @ SV78 @ SV24 @ SV74 ) )
= $true )
| ( ( SV24
= ( relation_dom_as_subset @ SV24 @ SV74 @ SV78 ) )
= $true )
| ( ( SV74 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV78 @ SV24 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(645,plain,
! [SV79: $i,SV75: $i,SV24: $i] :
( ( ( SV24 = empty_set )
= $false )
| ( ( ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV75 @ SV79 ) )
| ( quasi_total @ SV79 @ SV24 @ SV75 ) )
= $true )
| ( ( relation_of2_as_subset @ SV79 @ SV24 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(646,plain,
! [SV76: $i,SV80: $i,SV24: $i] :
( ( ( SV24 = empty_set )
= $false )
| ( ( ~ ( quasi_total @ SV80 @ SV24 @ SV76 )
| ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SV80 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV80 @ SV24 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(647,plain,
! [SV67: $i,SV24: $i,SV69: $i] :
( ( ( SV69 = empty_set )
= $false )
| ( ( quasi_total @ SV69 @ SV24 @ SV67 )
= $true )
| ( ( SV24 = empty_set )
= $true )
| ( ( SV67 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV69 @ SV24 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(648,plain,
! [SV68: $i,SV24: $i,SV70: $i] :
( ( ( quasi_total @ SV70 @ SV24 @ SV68 )
= $false )
| ( ( SV70 = empty_set )
= $true )
| ( ( SV24 = empty_set )
= $true )
| ( ( SV68 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV70 @ SV24 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(649,plain,
! [SV81: $i,SV28: $i,SV71: $i] :
( ( ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ SV81 ) ) )
= $true )
| ( ( ~ ( in @ SV81 @ ( relation_dom @ SV28 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(650,plain,
! [SV28: $i,SV71: $i] :
( ( ( ( ( sK23_C @ SV71 @ SV28 )
!= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) ) )
= $false )
| ( ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(651,plain,
! [SV28: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
= $false )
| ( ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(652,plain,
! [SV72: $i,SV28: $i,SV82: $i] :
( ( ( ! [SY157: $i] :
( ( SV82
!= ( apply @ SV28 @ SY157 ) )
| ~ ( in @ SY157 @ ( relation_dom @ SV28 ) ) ) )
= $true )
| ( ( in @ SV82 @ SV72 )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(653,plain,
! [SV28: $i,SV72: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV72 ) )
= $true )
| ( ( ~ ( ( SV83
!= ( apply @ SV28 @ ( sK22_D @ SV83 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SV83 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(654,plain,
! [SV77: $i,SV73: $i,SV24: $i] :
( ( ( SV24
= ( relation_dom_as_subset @ SV24 @ SV73 @ SV77 ) )
= $false )
| ( ( quasi_total @ SV77 @ SV24 @ SV73 )
= $true )
| ( ( SV73 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV24 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(655,plain,
! [SV74: $i,SV24: $i,SV78: $i] :
( ( ( quasi_total @ SV78 @ SV24 @ SV74 )
= $false )
| ( ( SV24
= ( relation_dom_as_subset @ SV24 @ SV74 @ SV78 ) )
= $true )
| ( ( SV74 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV78 @ SV24 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(656,plain,
! [SV79: $i,SV75: $i,SV24: $i] :
( ( ( ( SV24
!= ( relation_dom_as_subset @ SV24 @ SV75 @ SV79 ) ) )
= $true )
| ( ( quasi_total @ SV79 @ SV24 @ SV75 )
= $true )
| ( ( SV24 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV79 @ SV24 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(657,plain,
! [SV76: $i,SV24: $i,SV80: $i] :
( ( ( ~ ( quasi_total @ SV80 @ SV24 @ SV76 ) )
= $true )
| ( ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SV80 ) )
= $true )
| ( ( SV24 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV80 @ SV24 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(658,plain,
! [SV81: $i,SV28: $i,SV71: $i] :
( ( ( ( sK23_C @ SV71 @ SV28 )
= ( apply @ SV28 @ SV81 ) )
= $false )
| ( ( ~ ( in @ SV81 @ ( relation_dom @ SV28 ) ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(659,plain,
! [SV28: $i,SV71: $i] :
( ( ( ( sK23_C @ SV71 @ SV28 )
= ( apply @ SV28 @ ( sK24_SY92 @ SV71 @ SV28 ) ) )
= $true )
| ( ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(660,plain,
! [SV28: $i,SV71: $i] :
( ( ( in @ ( sK24_SY92 @ SV71 @ SV28 ) @ ( relation_dom @ SV28 ) )
= $true )
| ( ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(661,plain,
! [SV72: $i,SV84: $i,SV28: $i,SV82: $i] :
( ( ( ( SV82
!= ( apply @ SV28 @ SV84 ) )
| ~ ( in @ SV84 @ ( relation_dom @ SV28 ) ) )
= $true )
| ( ( in @ SV82 @ SV72 )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(662,plain,
! [SV28: $i,SV72: $i,SV83: $i] :
( ( ( in @ SV83 @ SV72 )
= $false )
| ( ( ~ ( ( SV83
!= ( apply @ SV28 @ ( sK22_D @ SV83 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SV83 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) ) )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(663,plain,
! [SV79: $i,SV75: $i,SV24: $i] :
( ( ( SV24
= ( relation_dom_as_subset @ SV24 @ SV75 @ SV79 ) )
= $false )
| ( ( quasi_total @ SV79 @ SV24 @ SV75 )
= $true )
| ( ( SV24 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV79 @ SV24 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(664,plain,
! [SV76: $i,SV24: $i,SV80: $i] :
( ( ( quasi_total @ SV80 @ SV24 @ SV76 )
= $false )
| ( ( SV24
= ( relation_dom_as_subset @ SV24 @ SV76 @ SV80 ) )
= $true )
| ( ( SV24 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV80 @ SV24 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(665,plain,
! [SV71: $i,SV28: $i,SV81: $i] :
( ( ( in @ SV81 @ ( relation_dom @ SV28 ) )
= $false )
| ( ( ( sK23_C @ SV71 @ SV28 )
= ( apply @ SV28 @ SV81 ) )
= $false )
| ( ( ~ ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(666,plain,
! [SV72: $i,SV84: $i,SV28: $i,SV82: $i] :
( ( ( ( SV82
!= ( apply @ SV28 @ SV84 ) ) )
= $true )
| ( ( ~ ( in @ SV84 @ ( relation_dom @ SV28 ) ) )
= $true )
| ( ( in @ SV82 @ SV72 )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(667,plain,
! [SV72: $i,SV28: $i,SV83: $i] :
( ( ( ( SV83
!= ( apply @ SV28 @ ( sK22_D @ SV83 @ SV72 @ SV28 ) ) )
| ~ ( in @ ( sK22_D @ SV83 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
= $false )
| ( ( in @ SV83 @ SV72 )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(668,plain,
! [SV81: $i,SV28: $i,SV71: $i] :
( ( ( in @ ( sK23_C @ SV71 @ SV28 ) @ SV71 )
= $false )
| ( ( ( sK23_C @ SV71 @ SV28 )
= ( apply @ SV28 @ SV81 ) )
= $false )
| ( ( in @ SV81 @ ( relation_dom @ SV28 ) )
= $false )
| ( ( SV71
= ( relation_rng @ SV28 ) )
= $true )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(669,plain,
! [SV72: $i,SV84: $i,SV28: $i,SV82: $i] :
( ( ( SV82
= ( apply @ SV28 @ SV84 ) )
= $false )
| ( ( ~ ( in @ SV84 @ ( relation_dom @ SV28 ) ) )
= $true )
| ( ( in @ SV82 @ SV72 )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(670,plain,
! [SV72: $i,SV28: $i,SV83: $i] :
( ( ( ( SV83
!= ( apply @ SV28 @ ( sK22_D @ SV83 @ SV72 @ SV28 ) ) ) )
= $false )
| ( ( in @ SV83 @ SV72 )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(671,plain,
! [SV28: $i,SV72: $i,SV83: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV83 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) ) )
= $false )
| ( ( in @ SV83 @ SV72 )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(672,plain,
! [SV72: $i,SV82: $i,SV28: $i,SV84: $i] :
( ( ( in @ SV84 @ ( relation_dom @ SV28 ) )
= $false )
| ( ( SV82
= ( apply @ SV28 @ SV84 ) )
= $false )
| ( ( in @ SV82 @ SV72 )
= $true )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(673,plain,
! [SV72: $i,SV28: $i,SV83: $i] :
( ( ( SV83
= ( apply @ SV28 @ ( sK22_D @ SV83 @ SV72 @ SV28 ) ) )
= $true )
| ( ( in @ SV83 @ SV72 )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(674,plain,
! [SV28: $i,SV72: $i,SV83: $i] :
( ( ( in @ ( sK22_D @ SV83 @ SV72 @ SV28 ) @ ( relation_dom @ SV28 ) )
= $true )
| ( ( in @ SV83 @ SV72 )
= $false )
| ( ( SV72
= ( relation_rng @ SV28 ) )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(675,plain,
! [SV1: $i,SV30: $i] :
( ( ( in @ SV1 @ SV30 )
= $false )
| ( ( ( in @ SV30 @ SV1 )
= ( in @ SV1 @ SV30 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[448]) ).
thf(676,plain,
! [SV42: $i,SV21: $i] :
( ( ( empty @ SV42 )
= $false )
| ( ( ( in @ SV21 @ SV42 )
= ( empty @ SV42 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[459]) ).
thf(677,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
= ( empty @ SV23 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[461]) ).
thf(678,plain,
! [SV1: $i,SV30: $i] :
( ( ( ~ ( ( in @ SV30 @ SV1 )
| ( in @ SV1 @ SV30 ) )
| ~ ( ~ ( in @ SV30 @ SV1 )
| ~ ( in @ SV1 @ SV30 ) ) )
= $false )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[675]) ).
thf(679,plain,
! [SV1: $i,SV30: $i] :
( ( ( ( in @ SV30 @ SV1 )
= ( in @ SV1 @ SV30 ) )
= $false )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[675]) ).
thf(680,plain,
! [SV42: $i,SV21: $i] :
( ( ( ~ ( ( in @ SV21 @ SV42 )
| ( empty @ SV42 ) )
| ~ ( ~ ( in @ SV21 @ SV42 )
| ~ ( empty @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[676]) ).
thf(682,plain,
! [SV23: $i] :
( ( ( ~ ( ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
| ( empty @ SV23 ) )
| ~ ( ~ ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ( empty @ SV23 ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[677]) ).
thf(685,plain,
! [SV1: $i,SV30: $i] :
( ( ( ~ ( ~ ( in @ SV30 @ SV1 )
| ~ ( in @ SV1 @ SV30 ) ) )
= $false )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(687,plain,
! [SV42: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ SV42 )
| ~ ( empty @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(688,plain,
! [SV23: $i] :
( ( ( ~ ( ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
| ( empty @ SV23 ) ) )
= $false )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(691,plain,
! [SV1: $i,SV30: $i] :
( ( ( ~ ( in @ SV30 @ SV1 )
| ~ ( in @ SV1 @ SV30 ) )
= $true )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(693,plain,
! [SV42: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV42 )
| ~ ( empty @ SV42 ) )
= $true )
| ( ( empty @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(694,plain,
! [SV23: $i] :
( ( ( ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
| ( empty @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(697,plain,
! [SV1: $i,SV30: $i] :
( ( ( ~ ( in @ SV30 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV1 @ SV30 ) )
= $true )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(699,plain,
! [SV42: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV42 ) )
= $true )
| ( ( ~ ( empty @ SV42 ) )
= $true )
| ( ( empty @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(700,plain,
! [SV23: $i] :
( ( ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(702,plain,
! [SV1: $i,SV30: $i] :
( ( ( in @ SV30 @ SV1 )
= $false )
| ( ( ~ ( in @ SV1 @ SV30 ) )
= $true )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(703,plain,
! [SV42: $i,SV21: $i] :
( ( ( in @ SV21 @ SV42 )
= $false )
| ( ( ~ ( empty @ SV42 ) )
= $true )
| ( ( empty @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(705,plain,
! [SV30: $i,SV1: $i] :
( ( ( in @ SV1 @ SV30 )
= $false )
| ( ( in @ SV30 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(706,plain,
! [SV21: $i,SV42: $i] :
( ( ( empty @ SV42 )
= $false )
| ( ( in @ SV21 @ SV42 )
= $false )
| ( ( empty @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(708,plain,
! [SV1: $i] :
( ( in @ SV1 @ SV1 )
= $false ),
inference(extuni,[status(esa)],[679:[bind(SV30,$thf( SV1 ))]]) ).
thf(709,plain,
! [SV24: $i] :
( ( ( relation_of2_as_subset @ empty_set @ SV24 @ empty_set )
= $false )
| ( ( SV24 = empty_set )
= $true )
| ( ( quasi_total @ empty_set @ SV24 @ empty_set )
= $true ) ),
inference(extuni,[status(esa)],[647:[bind(SV67,$thf( empty_set )),bind(SV69,$thf( empty_set ))]]) ).
thf(710,plain,
! [SV24: $i,SV70: $i] :
( ( ( relation_of2_as_subset @ SV70 @ SV24 @ empty_set )
= $false )
| ( ( SV24 = empty_set )
= $true )
| ( ( SV70 = empty_set )
= $true )
| ( ( quasi_total @ SV70 @ SV24 @ empty_set )
= $false ) ),
inference(extuni,[status(esa)],[648:[bind(SV68,$thf( empty_set ))]]) ).
thf(711,plain,
! [SV76: $i,SV80: $i] :
( ( ( relation_of2_as_subset @ SV80 @ empty_set @ SV76 )
= $false )
| ( ( empty_set
= ( relation_dom_as_subset @ empty_set @ SV76 @ SV80 ) )
= $true )
| ( ( quasi_total @ SV80 @ empty_set @ SV76 )
= $false ) ),
inference(extuni,[status(esa)],[664:[bind(SV24,$thf( empty_set ))]]) ).
thf(712,plain,
! [SV84: $i,SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( in @ ( apply @ SV28 @ SV84 ) @ ( relation_rng @ SV28 ) )
= $true )
| ( ( in @ SV84 @ ( relation_dom @ SV28 ) )
= $false ) ),
inference(extuni,[status(esa)],[672:[bind(SV72,$thf( relation_rng @ SV28 )),bind(SV82,$thf( apply @ SV28 @ SV84 ))]]) ).
thf(713,plain,
! [SV83: $i,SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( in @ SV83 @ ( relation_rng @ SV28 ) )
= $false )
| ( ( SV83
= ( apply @ SV28 @ ( sK22_D @ SV83 @ ( relation_rng @ SV28 ) @ SV28 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[673:[bind(SV72,$thf( relation_rng @ SV28 ))]]) ).
thf(714,plain,
! [SV83: $i,SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( in @ SV83 @ ( relation_rng @ SV28 ) )
= $false )
| ( ( in @ ( sK22_D @ SV83 @ ( relation_rng @ SV28 ) @ SV28 ) @ ( relation_dom @ SV28 ) )
= $true ) ),
inference(extuni,[status(esa)],[674:[bind(SV72,$thf( relation_rng @ SV28 ))]]) ).
thf(715,plain,
! [SV30: $i,SV1: $i] :
( ( ( in @ SV1 @ SV30 )
= $false )
| ( ( in @ SV30 @ SV1 )
= $false ) ),
inference(sim,[status(thm)],[705]) ).
thf(716,plain,
! [SV21: $i,SV42: $i] :
( ( ( empty @ SV42 )
= $false )
| ( ( in @ SV21 @ SV42 )
= $false ) ),
inference(sim,[status(thm)],[706]) ).
thf(717,plain,
! [SV23: $i] :
( ( ( element @ ( sK14_B @ SV23 ) @ ( powerset @ SV23 ) )
= $true )
| ( ( empty @ SV23 )
= $true ) ),
inference(sim,[status(thm)],[700]) ).
thf(718,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[187,717,716,715,714,713,712,711,710,709,708,674,673,672,668,664,663,660,659,655,654,648,647,599,598,583,568,567,560,553,552,551,550,543,540,539,523,522,521,517,516,511,510,509,508,507,506,502,501,500,494,493,488,470,461,459,456,455,454,453,452,451,450,449,448,430,429,428,425,424,413,404,403,402,395,394,390,388,386,384,383,377,376,375,369,362,350,349,299,298,297,261,259,253,222,221,220,219,199]) ).
thf(719,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU290+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 23:31:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.38
% 0.14/0.38 No.of.Axioms: 54
% 0.14/0.38
% 0.14/0.38 Length.of.Defs: 0
% 0.14/0.38
% 0.14/0.38 Contains.Choice.Funs: false
% 0.14/0.39 .
% 0.14/0.41 (rf:0,axioms:54,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:56,loop_count:0,foatp_calls:0,translation:fof_full).................................eprover: CPU time limit exceeded, terminating
% 74.40/74.67 .....
% 75.37/76.06
% 75.37/76.06 ********************************
% 75.37/76.06 * All subproblems solved! *
% 75.37/76.06 ********************************
% 75.37/76.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:58,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:718,loop_count:0,foatp_calls:2,translation:fof_full)
% 76.03/76.25
% 76.03/76.25 %**** Beginning of derivation protocol ****
% 76.03/76.25 % SZS output start CNFRefutation
% See solution above
% 76.03/76.25
% 76.03/76.25 %**** End of derivation protocol ****
% 76.03/76.25 %**** no. of clauses in derivation: 661 ****
% 76.03/76.25 %**** clause counter: 718 ****
% 76.03/76.25
% 76.03/76.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:58,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:718,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------