TSTP Solution File: SEU212+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n009.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 12:08:16 EDT 2022
% Result : Theorem 0.44s 0.66s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 64
% Syntax : Number of formulae : 703 ( 399 unt; 29 typ; 0 def)
% Number of atoms : 4350 (1514 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 7269 (1306 ~;1274 |; 109 &;4525 @)
% ( 17 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 12 con; 0-3 aty)
% Number of variables : 1324 ( 0 ^1304 !; 20 ?;1324 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $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_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_D,type,
sK13_D: $i > $i > $i > $i ).
thf(tp_sK14_C,type,
sK14_C: $i > $i > $i ).
thf(tp_sK15_SY61,type,
sK15_SY61: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY57,type,
sK2_SY57: $i ).
thf(tp_sK3_SY59,type,
sK3_SY59: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $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_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(10,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(13,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(14,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(15,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(16,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(17,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(18,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(19,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(20,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(22,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(24,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(25,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(26,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(27,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(29,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(30,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(35,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(36,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(42,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(43,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(47,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(48,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(49,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(50,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(51,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(52,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(53,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(54,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(57,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(59,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(61,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(62,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(63,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(64,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(72,plain,
( ( ! [SY57: $i,SY58: $i] :
( ( ( relation @ SY58 )
& ( function @ SY58 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ SY57 ) @ SY58 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY58 ) )
& ( SY57
= ( apply @ SY58 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(73,plain,
( ( ! [SY59: $i] :
( ( ( relation @ SY59 )
& ( function @ SY59 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ SY59 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY59 ) )
& ( sK2_SY57
= ( apply @ SY59 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(74,plain,
( ( ( ( relation @ sK3_SY59 )
& ( function @ sK3_SY59 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(75,plain,
( ( relation @ sK3_SY59 )
= $true ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(76,plain,
( ( function @ sK3_SY59 )
= $true ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(77,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(78,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[77]) ).
thf(79,plain,
( ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[77]) ).
thf(80,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[78]) ).
thf(81,plain,
( ( ~ ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[79]) ).
thf(82,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
& ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(83,plain,
( ( ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) )
& ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(86,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(87,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(89,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)],[43]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(92,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(93,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(94,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(96,plain,
( ( ~ ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(97,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(98,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(99,plain,
( ( ( empty @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(100,plain,
( ( ( function @ sK11_A )
& ( relation @ sK11_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(101,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(102,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(103,plain,
( ( ! [A: $i] : ( element @ ( sK12_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(104,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY60: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ SY60 ) @ A )
| ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY61 @ B @ A ) ) @ A )
| ( in @ ( sK14_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK13_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(105,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(106,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(107,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(110,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(111,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(113,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(114,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY60: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ SY60 ) @ A )
| ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY61 @ B @ A ) ) @ A )
| ( in @ ( sK14_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK13_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(116,plain,
( ( ! [A: $i] : ( element @ ( sK12_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(117,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(118,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(119,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(121,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(123,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(124,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(125,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(126,plain,
( ( ( function @ sK11_A )
& ( relation @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(127,plain,
( ( ( empty @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(128,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(129,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(130,plain,
( ( ~ ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(131,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(132,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(133,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(134,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(137,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)],[89]) ).
thf(138,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(139,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(140,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(143,plain,
( ( function @ sK3_SY59 )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(144,plain,
( ( relation @ sK3_SY59 )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(145,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
& ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(146,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY61 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(147,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(148,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) ) )
| ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(149,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK9_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(150,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(151,plain,
( ( ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(152,plain,
( ( ~ ( ~ ( function @ sK11_A )
| ~ ( relation @ sK11_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(153,plain,
( ( ~ ( ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(154,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)],[137]) ).
thf(155,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(156,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(157,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK6_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK6_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(158,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
| ~ ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(159,plain,
! [SV1: $i] :
( ( ! [SY62: $i] :
( ~ ( in @ SV1 @ SY62 )
| ~ ( in @ SY62 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(160,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(161,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ( relation @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(162,plain,
! [SV4: $i] :
( ( ! [SY63: $i] :
( ( unordered_pair @ SV4 @ SY63 )
= ( unordered_pair @ SY63 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(163,plain,
! [SV5: $i] :
( ( ! [SY64: $i] :
( ( ordered_pair @ SV5 @ SY64 )
= ( unordered_pair @ ( unordered_pair @ SV5 @ SY64 ) @ ( singleton @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(164,plain,
! [SV6: $i] :
( ( element @ ( sK12_B @ SV6 ) @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(165,plain,
! [SV7: $i] :
( ( ~ ( empty @ ( powerset @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(166,plain,
! [SV8: $i] :
( ( ! [SY65: $i] :
~ ( empty @ ( ordered_pair @ SV8 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(167,plain,
! [SV9: $i] :
( ( ~ ( empty @ ( singleton @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(168,plain,
! [SV10: $i] :
( ( ! [SY66: $i] :
~ ( empty @ ( unordered_pair @ SV10 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(169,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
| ~ ( relation @ SV11 )
| ~ ( empty @ ( relation_dom @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(170,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(171,plain,
! [SV12: $i] :
( ( subset @ SV12 @ SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(172,plain,
! [SV13: $i] :
( ( ! [SY67: $i] :
( ~ ( in @ SV13 @ SY67 )
| ( element @ SV13 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(173,plain,
! [SV14: $i] :
( ( ! [SY68: $i] :
( ~ ( element @ SV14 @ SY68 )
| ( empty @ SY68 )
| ( in @ SV14 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(174,plain,
! [SV15: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( element @ SY69 @ ( powerset @ SY70 ) )
| ~ ( in @ SV15 @ SY69 )
| ( element @ SV15 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(175,plain,
! [SV16: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( element @ SY71 @ ( powerset @ SY72 ) )
| ~ ( in @ SV16 @ SY71 )
| ~ ( empty @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(176,plain,
! [SV17: $i] :
( ( ~ ( empty @ SV17 )
| ( SV17 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(177,plain,
! [SV18: $i] :
( ( ! [SY73: $i] :
( ~ ( empty @ SY73 )
| ~ ( in @ SV18 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(178,plain,
! [SV19: $i] :
( ( ! [SY74: $i] :
( ( SV19 = SY74 )
| ~ ( empty @ SV19 )
| ~ ( empty @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(179,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ~ ( ~ ! [SY75: $i] :
( ~ ( ~ ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ SY76 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ ( sK15_SY61 @ SY75 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) ) )
| ( SY75
= ( relation_dom @ SV20 ) ) )
| ~ ! [SY77: $i] :
( ( SY77
!= ( relation_dom @ SV20 ) )
| ~ ( ~ ! [SY78: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SV20 )
| ( in @ SY78 @ SY77 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SY77 )
| ( in @ ( ordered_pair @ SY80 @ ( sK13_D @ SY80 @ SY77 @ SV20 ) ) @ SV20 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(180,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(181,plain,
! [SV21: $i] :
( ( ~ ( function @ SV21 )
| ~ ( relation @ SV21 )
| ~ ( ~ ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
| ~ ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(182,plain,
! [SV22: $i] :
( ( ( empty @ SV22 )
| ~ ( ~ ( element @ ( sK9_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ~ ( empty @ ( sK9_B @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(183,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(184,plain,
( ( ~ ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(185,plain,
( ( ~ ( function @ sK11_A )
| ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(186,plain,
( ( ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(187,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)],[154]) ).
thf(188,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(189,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(190,plain,
! [SV23: $i] :
( ( ~ ( ~ ( element @ ( sK6_B @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ( empty @ ( sK6_B @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(191,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
| ~ ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(192,plain,
! [SV24: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV24 )
| ~ ( in @ SV24 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(193,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(194,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(195,plain,
! [SV25: $i,SV4: $i] :
( ( ( unordered_pair @ SV4 @ SV25 )
= ( unordered_pair @ SV25 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(196,plain,
! [SV26: $i,SV5: $i] :
( ( ( ordered_pair @ SV5 @ SV26 )
= ( unordered_pair @ ( unordered_pair @ SV5 @ SV26 ) @ ( singleton @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(197,plain,
! [SV7: $i] :
( ( empty @ ( powerset @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(198,plain,
! [SV27: $i,SV8: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV8 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(199,plain,
! [SV9: $i] :
( ( empty @ ( singleton @ SV9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(200,plain,
! [SV28: $i,SV10: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV10 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(201,plain,
! [SV11: $i] :
( ( ( ( empty @ SV11 )
| ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(202,plain,
! [SV29: $i,SV13: $i] :
( ( ~ ( in @ SV13 @ SV29 )
| ( element @ SV13 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(203,plain,
! [SV30: $i,SV14: $i] :
( ( ~ ( element @ SV14 @ SV30 )
| ( empty @ SV30 )
| ( in @ SV14 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(204,plain,
! [SV15: $i,SV31: $i] :
( ( ! [SY89: $i] :
( ~ ( element @ SV31 @ ( powerset @ SY89 ) )
| ~ ( in @ SV15 @ SV31 )
| ( element @ SV15 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(205,plain,
! [SV16: $i,SV32: $i] :
( ( ! [SY90: $i] :
( ~ ( element @ SV32 @ ( powerset @ SY90 ) )
| ~ ( in @ SV16 @ SV32 )
| ~ ( empty @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(206,plain,
! [SV17: $i] :
( ( ( ~ ( empty @ SV17 ) )
= $true )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(207,plain,
! [SV18: $i,SV33: $i] :
( ( ~ ( empty @ SV33 )
| ~ ( in @ SV18 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(208,plain,
! [SV34: $i,SV19: $i] :
( ( ( SV19 = SV34 )
| ~ ( empty @ SV19 )
| ~ ( empty @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(209,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY75: $i] :
( ~ ( ~ ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ SY76 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ ( sK15_SY61 @ SY75 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) ) )
| ( SY75
= ( relation_dom @ SV20 ) ) )
| ~ ! [SY77: $i] :
( ( SY77
!= ( relation_dom @ SV20 ) )
| ~ ( ~ ! [SY78: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SV20 )
| ( in @ SY78 @ SY77 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SY77 )
| ( in @ ( ordered_pair @ SY80 @ ( sK13_D @ SY80 @ SY77 @ SV20 ) ) @ SV20 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(210,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(211,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(212,plain,
! [SV21: $i] :
( ( ( ~ ( function @ SV21 )
| ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
| ~ ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(213,plain,
! [SV22: $i] :
( ( ( empty @ SV22 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK9_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ~ ( empty @ ( sK9_B @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(214,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(215,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(216,plain,
( ( ~ ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(217,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(218,plain,
( ( ~ ( function @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(219,plain,
( ( ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(220,plain,
( ( ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(221,plain,
( ( ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(222,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(223,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(224,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(225,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(226,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(227,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(228,plain,
! [SV23: $i] :
( ( ~ ( element @ ( sK6_B @ SV23 ) @ ( powerset @ SV23 ) )
| ~ ( empty @ ( sK6_B @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(229,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(230,plain,
( ( ~ ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(231,plain,
! [SV24: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV24 ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(232,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(233,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(234,plain,
! [SV27: $i,SV8: $i] :
( ( empty @ ( ordered_pair @ SV8 @ SV27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(235,plain,
! [SV28: $i,SV10: $i] :
( ( empty @ ( unordered_pair @ SV10 @ SV28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(236,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $true )
| ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(237,plain,
! [SV29: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV29 ) )
= $true )
| ( ( element @ SV13 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(238,plain,
! [SV30: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ SV30 ) )
= $true )
| ( ( ( empty @ SV30 )
| ( in @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(239,plain,
! [SV15: $i,SV35: $i,SV31: $i] :
( ( ~ ( element @ SV31 @ ( powerset @ SV35 ) )
| ~ ( in @ SV15 @ SV31 )
| ( element @ SV15 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(240,plain,
! [SV16: $i,SV36: $i,SV32: $i] :
( ( ~ ( element @ SV32 @ ( powerset @ SV36 ) )
| ~ ( in @ SV16 @ SV32 )
| ~ ( empty @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(241,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(242,plain,
! [SV18: $i,SV33: $i] :
( ( ( ~ ( empty @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(243,plain,
! [SV34: $i,SV19: $i] :
( ( ( ( SV19 = SV34 )
| ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(244,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ~ ( ~ ! [SY75: $i] :
( ~ ( ~ ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ SY76 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ ( sK15_SY61 @ SY75 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) ) )
| ( SY75
= ( relation_dom @ SV20 ) ) )
| ~ ! [SY77: $i] :
( ( SY77
!= ( relation_dom @ SV20 ) )
| ~ ( ~ ! [SY78: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SV20 )
| ( in @ SY78 @ SY77 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SY77 )
| ( in @ ( ordered_pair @ SY80 @ ( sK13_D @ SY80 @ SY77 @ SV20 ) ) @ SV20 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(245,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(246,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(247,plain,
! [SV21: $i] :
( ( ( ~ ( function @ SV21 ) )
= $true )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
| ~ ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(248,plain,
! [SV22: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ~ ( empty @ ( sK9_B @ SV22 ) ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(249,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(250,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(251,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(252,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(253,plain,
( ( function @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(254,plain,
( ( relation @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(255,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(256,plain,
( ( relation @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(257,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(258,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(259,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(260,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(261,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(262,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(263,plain,
! [SV23: $i] :
( ( ~ ( element @ ( sK6_B @ SV23 ) @ ( powerset @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(264,plain,
! [SV23: $i] :
( ( ~ ( empty @ ( sK6_B @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(265,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(266,plain,
( ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(267,plain,
! [SV24: $i,SV1: $i] :
( ( ( in @ SV1 @ SV24 )
= $false )
| ( ( ~ ( in @ SV24 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(268,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( empty @ SV11 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(269,plain,
! [SV29: $i,SV13: $i] :
( ( ( in @ SV13 @ SV29 )
= $false )
| ( ( element @ SV13 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(270,plain,
! [SV30: $i,SV14: $i] :
( ( ( element @ SV14 @ SV30 )
= $false )
| ( ( ( empty @ SV30 )
| ( in @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(271,plain,
! [SV15: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV35 ) )
| ~ ( in @ SV15 @ SV31 ) )
= $true )
| ( ( element @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(272,plain,
! [SV16: $i,SV36: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV36 ) )
| ~ ( in @ SV16 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(273,plain,
! [SV18: $i,SV33: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( ~ ( in @ SV18 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(274,plain,
! [SV34: $i,SV19: $i] :
( ( ( SV19 = SV34 )
= $true )
| ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(275,plain,
! [SV20: $i] :
( ( ( ~ ! [SY75: $i] :
( ~ ( ~ ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ SY76 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ ( sK15_SY61 @ SY75 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) ) )
| ( SY75
= ( relation_dom @ SV20 ) ) )
| ~ ! [SY77: $i] :
( ( SY77
!= ( relation_dom @ SV20 ) )
| ~ ( ~ ! [SY78: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SV20 )
| ( in @ SY78 @ SY77 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SY77 )
| ( in @ ( ordered_pair @ SY80 @ ( sK13_D @ SY80 @ SY77 @ SV20 ) ) @ SV20 ) ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(276,plain,
! [SV21: $i] :
( ( ( function @ SV21 )
= $false )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
| ~ ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(277,plain,
! [SV22: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV22 ) @ ( powerset @ SV22 ) ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(278,plain,
! [SV22: $i] :
( ( ( ~ ~ ( empty @ ( sK9_B @ SV22 ) ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(279,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(280,plain,
! [SV37: $i] :
( ( ! [SY91: $i] :
( ~ ( element @ SV37 @ ( powerset @ SY91 ) )
| ( subset @ SV37 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(281,plain,
! [SV38: $i] :
( ( ! [SY92: $i] :
( ~ ( subset @ SV38 @ SY92 )
| ( element @ SV38 @ ( powerset @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(282,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(283,plain,
! [SV39: $i] :
( ( ~ ( empty @ SV39 )
| ( empty @ ( relation_dom @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(284,plain,
! [SV40: $i] :
( ( ~ ( empty @ SV40 )
| ( relation @ ( relation_dom @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(285,plain,
! [SV23: $i] :
( ( element @ ( sK6_B @ SV23 ) @ ( powerset @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(286,plain,
! [SV23: $i] :
( ( empty @ ( sK6_B @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(287,plain,
( ( ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) ) )
= $true )
| ( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(288,plain,
! [SV1: $i,SV24: $i] :
( ( ( in @ SV24 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(289,plain,
! [SV11: $i] :
( ( ( empty @ ( relation_dom @ SV11 ) )
= $false )
| ( ( empty @ SV11 )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(290,plain,
! [SV14: $i,SV30: $i] :
( ( ( empty @ SV30 )
= $true )
| ( ( in @ SV14 @ SV30 )
= $true )
| ( ( element @ SV14 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(291,plain,
! [SV15: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV31 ) )
= $true )
| ( ( element @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(292,plain,
! [SV16: $i,SV36: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(293,plain,
! [SV33: $i,SV18: $i] :
( ( ( in @ SV18 @ SV33 )
= $false )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(294,plain,
! [SV34: $i,SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( SV19 = SV34 )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(295,plain,
! [SV20: $i] :
( ( ( ~ ! [SY75: $i] :
( ~ ( ~ ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ SY76 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ ( sK15_SY61 @ SY75 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) ) )
| ( SY75
= ( relation_dom @ SV20 ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(296,plain,
! [SV20: $i] :
( ( ( ~ ! [SY77: $i] :
( ( SY77
!= ( relation_dom @ SV20 ) )
| ~ ( ~ ! [SY78: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SV20 )
| ( in @ SY78 @ SY77 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SY77 )
| ( in @ ( ordered_pair @ SY80 @ ( sK13_D @ SY80 @ SY77 @ SV20 ) ) @ SV20 ) ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(297,plain,
! [SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
| ~ ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(298,plain,
! [SV22: $i] :
( ( ( element @ ( sK9_B @ SV22 ) @ ( powerset @ SV22 ) )
= $true )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(299,plain,
! [SV22: $i] :
( ( ( ~ ( empty @ ( sK9_B @ SV22 ) ) )
= $true )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(300,plain,
! [SV41: $i,SV37: $i] :
( ( ~ ( element @ SV37 @ ( powerset @ SV41 ) )
| ( subset @ SV37 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(301,plain,
! [SV42: $i,SV38: $i] :
( ( ~ ( subset @ SV38 @ SV42 )
| ( element @ SV38 @ ( powerset @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(302,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(303,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(304,plain,
! [SV39: $i] :
( ( ( ~ ( empty @ SV39 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(305,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ SV40 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(306,plain,
( ( ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) )
= $false )
| ( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(307,plain,
! [SV15: $i,SV35: $i,SV31: $i] :
( ( ( element @ SV31 @ ( powerset @ SV35 ) )
= $false )
| ( ( ~ ( in @ SV15 @ SV31 ) )
= $true )
| ( ( element @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(308,plain,
! [SV16: $i,SV36: $i,SV32: $i] :
( ( ( element @ SV32 @ ( powerset @ SV36 ) )
= $false )
| ( ( ~ ( in @ SV16 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(309,plain,
! [SV19: $i,SV34: $i] :
( ( ( empty @ SV34 )
= $false )
| ( ( SV19 = SV34 )
= $true )
| ( ( empty @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(310,plain,
! [SV20: $i] :
( ( ( ! [SY75: $i] :
( ~ ( ~ ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ SY76 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY75 @ SV20 ) @ ( sK15_SY61 @ SY75 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SY75 @ SV20 ) @ SY75 ) ) )
| ( SY75
= ( relation_dom @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(311,plain,
! [SV20: $i] :
( ( ( ! [SY77: $i] :
( ( SY77
!= ( relation_dom @ SV20 ) )
| ~ ( ~ ! [SY78: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SV20 )
| ( in @ SY78 @ SY77 ) )
| ~ ! [SY80: $i] :
( ~ ( in @ SY80 @ SY77 )
| ( in @ ( ordered_pair @ SY80 @ ( sK13_D @ SY80 @ SY77 @ SV20 ) ) @ SV20 ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(312,plain,
! [SV21: $i] :
( ( ( ~ ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
| ~ ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(313,plain,
! [SV22: $i] :
( ( ( empty @ ( sK9_B @ SV22 ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(314,plain,
! [SV41: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( subset @ SV37 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(315,plain,
! [SV42: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV42 ) )
= $true )
| ( ( element @ SV38 @ ( powerset @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(316,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(317,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(318,plain,
! [SV39: $i] :
( ( ( empty @ SV39 )
= $false )
| ( ( empty @ ( relation_dom @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(319,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
= $false )
| ( ( relation @ ( relation_dom @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(320,plain,
( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
= $false )
| ( ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(321,plain,
! [SV35: $i,SV31: $i,SV15: $i] :
( ( ( in @ SV15 @ SV31 )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV35 ) )
= $false )
| ( ( element @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(322,plain,
! [SV36: $i,SV32: $i,SV16: $i] :
( ( ( in @ SV16 @ SV32 )
= $false )
| ( ( element @ SV32 @ ( powerset @ SV36 ) )
= $false )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(323,plain,
! [SV20: $i,SV43: $i] :
( ( ( ~ ( ~ ( ! [SY93: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SY93 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ ( sK15_SY61 @ SV43 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) ) )
| ( SV43
= ( relation_dom @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(324,plain,
! [SV20: $i,SV44: $i] :
( ( ( ( SV44
!= ( relation_dom @ SV20 ) )
| ~ ( ~ ! [SY94: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY94 @ SY79 ) @ SV20 )
| ( in @ SY94 @ SV44 ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ SV44 )
| ( in @ ( ordered_pair @ SY96 @ ( sK13_D @ SY96 @ SV44 @ SV20 ) ) @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(325,plain,
! [SV21: $i] :
( ( ( ~ ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(326,plain,
! [SV21: $i] :
( ( ( ~ ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(327,plain,
! [SV41: $i,SV37: $i] :
( ( ( element @ SV37 @ ( powerset @ SV41 ) )
= $false )
| ( ( subset @ SV37 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(328,plain,
! [SV42: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV42 )
= $false )
| ( ( element @ SV38 @ ( powerset @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(329,plain,
! [SV16: $i,SV32: $i,SV36: $i] :
( ( ( empty @ SV36 )
= $false )
| ( ( element @ SV32 @ ( powerset @ SV36 ) )
= $false )
| ( ( in @ SV16 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(330,plain,
! [SV20: $i,SV43: $i] :
( ( ( ~ ( ~ ( ! [SY93: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SY93 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ ( sK15_SY61 @ SV43 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) ) ) )
= $true )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(331,plain,
! [SV20: $i,SV44: $i] :
( ( ( ( SV44
!= ( relation_dom @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY94: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY94 @ SY79 ) @ SV20 )
| ( in @ SY94 @ SV44 ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ SV44 )
| ( in @ ( ordered_pair @ SY96 @ ( sK13_D @ SY96 @ SV44 @ SV20 ) ) @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(332,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(333,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(334,plain,
! [SV20: $i,SV43: $i] :
( ( ( ~ ( ! [SY93: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SY93 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ ( sK15_SY61 @ SV43 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) ) )
= $false )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(335,plain,
! [SV20: $i,SV44: $i] :
( ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( ~ ( ~ ! [SY94: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY94 @ SY79 ) @ SV20 )
| ( in @ SY94 @ SV44 ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ SV44 )
| ( in @ ( ordered_pair @ SY96 @ ( sK13_D @ SY96 @ SV44 @ SV20 ) ) @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(336,plain,
! [SV21: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) )
| ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(337,plain,
! [SV21: $i] :
( ( ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) )
| ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(338,plain,
! [SV20: $i,SV43: $i] :
( ( ( ~ ( ! [SY93: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SY93 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) ) )
= $false )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(339,plain,
! [SV20: $i,SV43: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ ( sK15_SY61 @ SV43 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) ) )
= $false )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(340,plain,
! [SV44: $i,SV20: $i] :
( ( ( ~ ! [SY94: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY94 @ SY79 ) @ SV20 )
| ( in @ SY94 @ SV44 ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ SV44 )
| ( in @ ( ordered_pair @ SY96 @ ( sK13_D @ SY96 @ SV44 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(341,plain,
! [SV21: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(342,plain,
! [SV21: $i] :
( ( ( ~ ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(343,plain,
! [SV21: $i] :
( ( ( ~ ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(344,plain,
! [SV21: $i] :
( ( ( ~ ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(345,plain,
! [SV20: $i,SV43: $i] :
( ( ( ! [SY93: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SY93 ) @ SV20 )
| ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
= $true )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(346,plain,
! [SV20: $i,SV43: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ ( sK15_SY61 @ SV43 @ SV20 ) ) @ SV20 )
| ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
= $true )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(347,plain,
! [SV44: $i,SV20: $i] :
( ( ( ~ ! [SY94: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY94 @ SY79 ) @ SV20 )
| ( in @ SY94 @ SV44 ) ) )
= $false )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(348,plain,
! [SV20: $i,SV44: $i] :
( ( ( ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ SV44 )
| ( in @ ( ordered_pair @ SY96 @ ( sK13_D @ SY96 @ SV44 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(349,plain,
! [SV21: $i] :
( ( ( ! [SY81: $i] :
( ~ ( in @ SY81 @ ( relation_dom @ SV21 ) )
| ! [SY82: $i] :
( ( SY82
!= ( apply @ SV21 @ SY81 ) )
| ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV21 ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(350,plain,
! [SV21: $i] :
( ( ( ! [SY83: $i] :
( ~ ( in @ SY83 @ ( relation_dom @ SV21 ) )
| ! [SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV21 )
| ( SY84
= ( apply @ SV21 @ SY83 ) ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(351,plain,
! [SV21: $i] :
( ( ( ! [SY85: $i] :
( ( in @ SY85 @ ( relation_dom @ SV21 ) )
| ! [SY86: $i] :
( ( SY86
!= ( apply @ SV21 @ SY85 ) )
| ( SY86 = empty_set ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(352,plain,
! [SV21: $i] :
( ( ( ! [SY87: $i] :
( ( in @ SY87 @ ( relation_dom @ SV21 ) )
| ! [SY88: $i] :
( ( SY88 != empty_set )
| ( SY88
= ( apply @ SV21 @ SY87 ) ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(353,plain,
! [SV20: $i,SV43: $i] :
( ( ( ! [SY93: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SY93 ) @ SV20 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
= $true )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(354,plain,
! [SV20: $i,SV43: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ ( sK15_SY61 @ SV43 @ SV20 ) ) @ SV20 )
= $true )
| ( ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 )
= $true )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(355,plain,
! [SV44: $i,SV20: $i] :
( ( ( ! [SY94: $i] :
( ! [SY79: $i] :
~ ( in @ ( ordered_pair @ SY94 @ SY79 ) @ SV20 )
| ( in @ SY94 @ SV44 ) ) )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(356,plain,
! [SV20: $i,SV44: $i] :
( ( ( ! [SY96: $i] :
( ~ ( in @ SY96 @ SV44 )
| ( in @ ( ordered_pair @ SY96 @ ( sK13_D @ SY96 @ SV44 @ SV20 ) ) @ SV20 ) ) )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(357,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( relation_dom @ SV21 ) )
| ! [SY97: $i] :
( ( SY97
!= ( apply @ SV21 @ SV45 ) )
| ( in @ ( ordered_pair @ SV45 @ SY97 ) @ SV21 ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(358,plain,
! [SV21: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ ( relation_dom @ SV21 ) )
| ! [SY98: $i] :
( ~ ( in @ ( ordered_pair @ SV46 @ SY98 ) @ SV21 )
| ( SY98
= ( apply @ SV21 @ SV46 ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(359,plain,
! [SV21: $i,SV47: $i] :
( ( ( ( in @ SV47 @ ( relation_dom @ SV21 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV21 @ SV47 ) )
| ( SY99 = empty_set ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(360,plain,
! [SV21: $i,SV48: $i] :
( ( ( ( in @ SV48 @ ( relation_dom @ SV21 ) )
| ! [SY100: $i] :
( ( SY100 != empty_set )
| ( SY100
= ( apply @ SV21 @ SV48 ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(361,plain,
! [SV49: $i,SV20: $i,SV43: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SV49 ) @ SV20 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
= $true )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(362,plain,
! [SV44: $i,SV20: $i,SV50: $i] :
( ( ( ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SV50 @ SY101 ) @ SV20 )
| ( in @ SV50 @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(363,plain,
! [SV20: $i,SV44: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV44 )
| ( in @ ( ordered_pair @ SV51 @ ( sK13_D @ SV51 @ SV44 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(364,plain,
! [SV21: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ ( relation_dom @ SV21 ) ) )
= $true )
| ( ( ! [SY97: $i] :
( ( SY97
!= ( apply @ SV21 @ SV45 ) )
| ( in @ ( ordered_pair @ SV45 @ SY97 ) @ SV21 ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(365,plain,
! [SV21: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ ( relation_dom @ SV21 ) ) )
= $true )
| ( ( ! [SY98: $i] :
( ~ ( in @ ( ordered_pair @ SV46 @ SY98 ) @ SV21 )
| ( SY98
= ( apply @ SV21 @ SV46 ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(366,plain,
! [SV21: $i,SV47: $i] :
( ( ( in @ SV47 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( ! [SY99: $i] :
( ( SY99
!= ( apply @ SV21 @ SV47 ) )
| ( SY99 = empty_set ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(367,plain,
! [SV21: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( ! [SY100: $i] :
( ( SY100 != empty_set )
| ( SY100
= ( apply @ SV21 @ SV48 ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(368,plain,
! [SV49: $i,SV20: $i,SV43: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SV49 ) @ SV20 )
= $false )
| ( ( ~ ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 ) )
= $true )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(369,plain,
! [SV44: $i,SV20: $i,SV50: $i] :
( ( ( ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SV50 @ SY101 ) @ SV20 ) )
= $true )
| ( ( in @ SV50 @ SV44 )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(370,plain,
! [SV20: $i,SV44: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ SV44 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK13_D @ SV51 @ SV44 @ SV20 ) ) @ SV20 )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(371,plain,
! [SV21: $i,SV45: $i] :
( ( ( in @ SV45 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( ! [SY97: $i] :
( ( SY97
!= ( apply @ SV21 @ SV45 ) )
| ( in @ ( ordered_pair @ SV45 @ SY97 ) @ SV21 ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(372,plain,
! [SV21: $i,SV46: $i] :
( ( ( in @ SV46 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( ! [SY98: $i] :
( ~ ( in @ ( ordered_pair @ SV46 @ SY98 ) @ SV21 )
| ( SY98
= ( apply @ SV21 @ SV46 ) ) ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(373,plain,
! [SV47: $i,SV21: $i,SV52: $i] :
( ( ( ( SV52
!= ( apply @ SV21 @ SV47 ) )
| ( SV52 = empty_set ) )
= $true )
| ( ( in @ SV47 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(374,plain,
! [SV48: $i,SV21: $i,SV53: $i] :
( ( ( ( SV53 != empty_set )
| ( SV53
= ( apply @ SV21 @ SV48 ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(375,plain,
! [SV49: $i,SV20: $i,SV43: $i] :
( ( ( in @ ( sK14_C @ SV43 @ SV20 ) @ SV43 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_C @ SV43 @ SV20 ) @ SV49 ) @ SV20 )
= $false )
| ( ( SV43
= ( relation_dom @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(376,plain,
! [SV44: $i,SV20: $i,SV54: $i,SV50: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV50 @ SV54 ) @ SV20 ) )
= $true )
| ( ( in @ SV50 @ SV44 )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(377,plain,
! [SV20: $i,SV44: $i,SV51: $i] :
( ( ( in @ SV51 @ SV44 )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ ( sK13_D @ SV51 @ SV44 @ SV20 ) ) @ SV20 )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(378,plain,
! [SV45: $i,SV21: $i,SV55: $i] :
( ( ( ( SV55
!= ( apply @ SV21 @ SV45 ) )
| ( in @ ( ordered_pair @ SV45 @ SV55 ) @ SV21 ) )
= $true )
| ( ( in @ SV45 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(379,plain,
! [SV21: $i,SV56: $i,SV46: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV56 ) @ SV21 )
| ( SV56
= ( apply @ SV21 @ SV46 ) ) )
= $true )
| ( ( in @ SV46 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(380,plain,
! [SV47: $i,SV21: $i,SV52: $i] :
( ( ( ( SV52
!= ( apply @ SV21 @ SV47 ) ) )
= $true )
| ( ( SV52 = empty_set )
= $true )
| ( ( in @ SV47 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(381,plain,
! [SV48: $i,SV21: $i,SV53: $i] :
( ( ( ( SV53 != empty_set ) )
= $true )
| ( ( SV53
= ( apply @ SV21 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(382,plain,
! [SV44: $i,SV20: $i,SV54: $i,SV50: $i] :
( ( ( in @ ( ordered_pair @ SV50 @ SV54 ) @ SV20 )
= $false )
| ( ( in @ SV50 @ SV44 )
= $true )
| ( ( SV44
= ( relation_dom @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(383,plain,
! [SV45: $i,SV21: $i,SV55: $i] :
( ( ( ( SV55
!= ( apply @ SV21 @ SV45 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV45 @ SV55 ) @ SV21 )
= $true )
| ( ( in @ SV45 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(384,plain,
! [SV21: $i,SV56: $i,SV46: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV56 ) @ SV21 ) )
= $true )
| ( ( SV56
= ( apply @ SV21 @ SV46 ) )
= $true )
| ( ( in @ SV46 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(385,plain,
! [SV47: $i,SV21: $i,SV52: $i] :
( ( ( SV52
= ( apply @ SV21 @ SV47 ) )
= $false )
| ( ( SV52 = empty_set )
= $true )
| ( ( in @ SV47 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(386,plain,
! [SV48: $i,SV21: $i,SV53: $i] :
( ( ( SV53 = empty_set )
= $false )
| ( ( SV53
= ( apply @ SV21 @ SV48 ) )
= $true )
| ( ( in @ SV48 @ ( relation_dom @ SV21 ) )
= $true )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(387,plain,
! [SV45: $i,SV21: $i,SV55: $i] :
( ( ( SV55
= ( apply @ SV21 @ SV45 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV45 @ SV55 ) @ SV21 )
= $true )
| ( ( in @ SV45 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(388,plain,
! [SV21: $i,SV56: $i,SV46: $i] :
( ( ( in @ ( ordered_pair @ SV46 @ SV56 ) @ SV21 )
= $false )
| ( ( SV56
= ( apply @ SV21 @ SV46 ) )
= $true )
| ( ( in @ SV46 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(389,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[119,388,387,386,385,382,377,375,354,329,328,327,321,320,319,318,317,316,313,309,298,293,290,289,288,286,285,279,269,265,260,256,255,254,253,252,250,249,246,245,241,235,234,233,232,199,197,196,195,171,170,164,144,143,129]) ).
thf(390,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(391,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(392,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(393,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(394,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(395,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY60: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ SY60 ) @ A )
| ~ ( in @ ( sK14_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY61 @ B @ A ) ) @ A )
| ( in @ ( sK14_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK13_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(396,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(397,plain,
( ( ! [A: $i] : ( element @ ( sK12_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(398,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(399,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(400,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(402,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(403,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(404,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(405,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(406,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(407,plain,
( ( ( function @ sK11_A )
& ( relation @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(408,plain,
( ( ( empty @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(409,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(410,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(411,plain,
( ( ~ ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(412,plain,
( ( ! [A: $i] :
( ( element @ ( sK6_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK6_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(413,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(414,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(415,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(418,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)],[89]) ).
thf(419,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(420,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(421,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(422,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(423,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(424,plain,
( ( function @ sK3_SY59 )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(425,plain,
( ( relation @ sK3_SY59 )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(426,plain,
( ( ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) )
& ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
& ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(427,plain,
( ( ~ ( ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(428,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(429,plain,
( ( ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(430,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK9_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(431,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) ) )
| ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(432,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)],[418]) ).
thf(433,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK6_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK6_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(434,plain,
( ( ~ ( ~ ~ ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) )
| ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(435,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(436,plain,
( ( ~ ( ~ ( function @ sK11_A )
| ~ ( relation @ sK11_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(437,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(438,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY61 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(439,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(440,plain,
! [SV57: $i] :
( ( ! [SY102: $i] :
( ~ ( in @ SV57 @ SY102 )
| ~ ( in @ SY102 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(441,plain,
! [SV58: $i] :
( ( ~ ( empty @ SV58 )
| ( function @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(442,plain,
! [SV59: $i] :
( ( ~ ( empty @ SV59 )
| ( relation @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(443,plain,
! [SV60: $i] :
( ( ! [SY103: $i] :
( ( unordered_pair @ SV60 @ SY103 )
= ( unordered_pair @ SY103 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(444,plain,
! [SV61: $i] :
( ( ! [SY104: $i] :
( ( ordered_pair @ SV61 @ SY104 )
= ( unordered_pair @ ( unordered_pair @ SV61 @ SY104 ) @ ( singleton @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(445,plain,
! [SV62: $i] :
( ( element @ ( sK12_B @ SV62 ) @ SV62 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(446,plain,
! [SV63: $i] :
( ( ~ ( empty @ ( powerset @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(447,plain,
! [SV64: $i] :
( ( ! [SY105: $i] :
~ ( empty @ ( ordered_pair @ SV64 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(448,plain,
! [SV65: $i] :
( ( ~ ( empty @ ( singleton @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(449,plain,
! [SV66: $i] :
( ( ! [SY106: $i] :
~ ( empty @ ( unordered_pair @ SV66 @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(450,plain,
! [SV67: $i] :
( ( ( empty @ SV67 )
| ~ ( relation @ SV67 )
| ~ ( empty @ ( relation_dom @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(451,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(452,plain,
! [SV68: $i] :
( ( subset @ SV68 @ SV68 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(453,plain,
! [SV69: $i] :
( ( ! [SY107: $i] :
( ~ ( in @ SV69 @ SY107 )
| ( element @ SV69 @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(454,plain,
! [SV70: $i] :
( ( ! [SY108: $i] :
( ~ ( element @ SV70 @ SY108 )
| ( empty @ SY108 )
| ( in @ SV70 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(455,plain,
! [SV71: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( element @ SY109 @ ( powerset @ SY110 ) )
| ~ ( in @ SV71 @ SY109 )
| ( element @ SV71 @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(456,plain,
! [SV72: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( element @ SY111 @ ( powerset @ SY112 ) )
| ~ ( in @ SV72 @ SY111 )
| ~ ( empty @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(457,plain,
! [SV73: $i] :
( ( ~ ( empty @ SV73 )
| ( SV73 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(458,plain,
! [SV74: $i] :
( ( ! [SY113: $i] :
( ~ ( empty @ SY113 )
| ~ ( in @ SV74 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(459,plain,
! [SV75: $i] :
( ( ! [SY114: $i] :
( ( SV75 = SY114 )
| ~ ( empty @ SV75 )
| ~ ( empty @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(460,plain,
( ( ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(461,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(462,plain,
( ( ~ ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(463,plain,
! [SV76: $i] :
( ( ( empty @ SV76 )
| ~ ( ~ ( element @ ( sK9_B @ SV76 ) @ ( powerset @ SV76 ) )
| ~ ~ ( empty @ ( sK9_B @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(464,plain,
! [SV77: $i] :
( ( ~ ( function @ SV77 )
| ~ ( relation @ SV77 )
| ~ ( ~ ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(465,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)],[432]) ).
thf(466,plain,
! [SV78: $i] :
( ( ~ ( ~ ( element @ ( sK6_B @ SV78 ) @ ( powerset @ SV78 ) )
| ~ ( empty @ ( sK6_B @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(467,plain,
( ( ~ ~ ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) )
| ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(468,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(469,plain,
( ( ~ ( function @ sK11_A )
| ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(470,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(471,plain,
! [SV79: $i] :
( ( ~ ( relation @ SV79 )
| ~ ( ~ ! [SY123: $i] :
( ~ ( ~ ( ! [SY124: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ SY124 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ ( sK15_SY61 @ SY123 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) ) )
| ( SY123
= ( relation_dom @ SV79 ) ) )
| ~ ! [SY125: $i] :
( ( SY125
!= ( relation_dom @ SV79 ) )
| ~ ( ~ ! [SY126: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY126 @ SY127 ) @ SV79 )
| ( in @ SY126 @ SY125 ) )
| ~ ! [SY128: $i] :
( ~ ( in @ SY128 @ SY125 )
| ( in @ ( ordered_pair @ SY128 @ ( sK13_D @ SY128 @ SY125 @ SV79 ) ) @ SV79 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(472,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(473,plain,
! [SV80: $i,SV57: $i] :
( ( ~ ( in @ SV57 @ SV80 )
| ~ ( in @ SV80 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(474,plain,
! [SV58: $i] :
( ( ( ~ ( empty @ SV58 ) )
= $true )
| ( ( function @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(475,plain,
! [SV59: $i] :
( ( ( ~ ( empty @ SV59 ) )
= $true )
| ( ( relation @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(476,plain,
! [SV81: $i,SV60: $i] :
( ( ( unordered_pair @ SV60 @ SV81 )
= ( unordered_pair @ SV81 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(477,plain,
! [SV82: $i,SV61: $i] :
( ( ( ordered_pair @ SV61 @ SV82 )
= ( unordered_pair @ ( unordered_pair @ SV61 @ SV82 ) @ ( singleton @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(478,plain,
! [SV63: $i] :
( ( empty @ ( powerset @ SV63 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(479,plain,
! [SV83: $i,SV64: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV64 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(480,plain,
! [SV65: $i] :
( ( empty @ ( singleton @ SV65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(481,plain,
! [SV84: $i,SV66: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV66 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(482,plain,
! [SV67: $i] :
( ( ( ( empty @ SV67 )
| ~ ( relation @ SV67 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(483,plain,
! [SV85: $i,SV69: $i] :
( ( ~ ( in @ SV69 @ SV85 )
| ( element @ SV69 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(484,plain,
! [SV86: $i,SV70: $i] :
( ( ~ ( element @ SV70 @ SV86 )
| ( empty @ SV86 )
| ( in @ SV70 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(485,plain,
! [SV71: $i,SV87: $i] :
( ( ! [SY129: $i] :
( ~ ( element @ SV87 @ ( powerset @ SY129 ) )
| ~ ( in @ SV71 @ SV87 )
| ( element @ SV71 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(486,plain,
! [SV72: $i,SV88: $i] :
( ( ! [SY130: $i] :
( ~ ( element @ SV88 @ ( powerset @ SY130 ) )
| ~ ( in @ SV72 @ SV88 )
| ~ ( empty @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(487,plain,
! [SV73: $i] :
( ( ( ~ ( empty @ SV73 ) )
= $true )
| ( ( SV73 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(488,plain,
! [SV74: $i,SV89: $i] :
( ( ~ ( empty @ SV89 )
| ~ ( in @ SV74 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(489,plain,
! [SV90: $i,SV75: $i] :
( ( ( SV75 = SV90 )
| ~ ( empty @ SV75 )
| ~ ( empty @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(490,plain,
( ( ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(491,plain,
( ( ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(492,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(493,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(494,plain,
( ( ~ ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(495,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(496,plain,
! [SV76: $i] :
( ( ( empty @ SV76 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK9_B @ SV76 ) @ ( powerset @ SV76 ) )
| ~ ~ ( empty @ ( sK9_B @ SV76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(497,plain,
! [SV77: $i] :
( ( ( ~ ( function @ SV77 )
| ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(498,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(499,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(500,plain,
! [SV78: $i] :
( ( ~ ( element @ ( sK6_B @ SV78 ) @ ( powerset @ SV78 ) )
| ~ ( empty @ ( sK6_B @ SV78 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(501,plain,
( ( ~ ~ ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(502,plain,
( ( ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(503,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(504,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(505,plain,
( ( ~ ( function @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(506,plain,
( ( ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(507,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(508,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(509,plain,
! [SV79: $i] :
( ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( ~ ( ~ ! [SY123: $i] :
( ~ ( ~ ( ! [SY124: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ SY124 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ ( sK15_SY61 @ SY123 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) ) )
| ( SY123
= ( relation_dom @ SV79 ) ) )
| ~ ! [SY125: $i] :
( ( SY125
!= ( relation_dom @ SV79 ) )
| ~ ( ~ ! [SY126: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY126 @ SY127 ) @ SV79 )
| ( in @ SY126 @ SY125 ) )
| ~ ! [SY128: $i] :
( ~ ( in @ SY128 @ SY125 )
| ( in @ ( ordered_pair @ SY128 @ ( sK13_D @ SY128 @ SY125 @ SV79 ) ) @ SV79 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(510,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(511,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(512,plain,
! [SV80: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV80 ) )
= $true )
| ( ( ~ ( in @ SV80 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(513,plain,
! [SV58: $i] :
( ( ( empty @ SV58 )
= $false )
| ( ( function @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(514,plain,
! [SV59: $i] :
( ( ( empty @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(515,plain,
! [SV83: $i,SV64: $i] :
( ( empty @ ( ordered_pair @ SV64 @ SV83 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(516,plain,
! [SV84: $i,SV66: $i] :
( ( empty @ ( unordered_pair @ SV66 @ SV84 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(517,plain,
! [SV67: $i] :
( ( ( empty @ SV67 )
= $true )
| ( ( ~ ( relation @ SV67 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(518,plain,
! [SV85: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ SV85 ) )
= $true )
| ( ( element @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(519,plain,
! [SV86: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ SV86 ) )
= $true )
| ( ( ( empty @ SV86 )
| ( in @ SV70 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(520,plain,
! [SV71: $i,SV91: $i,SV87: $i] :
( ( ~ ( element @ SV87 @ ( powerset @ SV91 ) )
| ~ ( in @ SV71 @ SV87 )
| ( element @ SV71 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(521,plain,
! [SV72: $i,SV92: $i,SV88: $i] :
( ( ~ ( element @ SV88 @ ( powerset @ SV92 ) )
| ~ ( in @ SV72 @ SV88 )
| ~ ( empty @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(522,plain,
! [SV73: $i] :
( ( ( empty @ SV73 )
= $false )
| ( ( SV73 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(523,plain,
! [SV74: $i,SV89: $i] :
( ( ( ~ ( empty @ SV89 ) )
= $true )
| ( ( ~ ( in @ SV74 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(524,plain,
! [SV90: $i,SV75: $i] :
( ( ( ( SV75 = SV90 )
| ~ ( empty @ SV75 ) )
= $true )
| ( ( ~ ( empty @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(525,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(526,plain,
( ( relation @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(527,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(528,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(529,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(530,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(531,plain,
! [SV76: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV76 ) @ ( powerset @ SV76 ) )
| ~ ~ ( empty @ ( sK9_B @ SV76 ) ) )
= $false )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(532,plain,
! [SV77: $i] :
( ( ( ~ ( function @ SV77 ) )
= $true )
| ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(533,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(534,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(535,plain,
! [SV78: $i] :
( ( ~ ( element @ ( sK6_B @ SV78 ) @ ( powerset @ SV78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(536,plain,
! [SV78: $i] :
( ( ~ ( empty @ ( sK6_B @ SV78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(537,plain,
( ( ~ ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(538,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(539,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(540,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(541,plain,
( ( function @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(542,plain,
( ( relation @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(543,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(544,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(545,plain,
! [SV79: $i] :
( ( ( relation @ SV79 )
= $false )
| ( ( ~ ( ~ ! [SY123: $i] :
( ~ ( ~ ( ! [SY124: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ SY124 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ ( sK15_SY61 @ SY123 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) ) )
| ( SY123
= ( relation_dom @ SV79 ) ) )
| ~ ! [SY125: $i] :
( ( SY125
!= ( relation_dom @ SV79 ) )
| ~ ( ~ ! [SY126: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY126 @ SY127 ) @ SV79 )
| ( in @ SY126 @ SY125 ) )
| ~ ! [SY128: $i] :
( ~ ( in @ SY128 @ SY125 )
| ( in @ ( ordered_pair @ SY128 @ ( sK13_D @ SY128 @ SY125 @ SV79 ) ) @ SV79 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(546,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(547,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(548,plain,
! [SV80: $i,SV57: $i] :
( ( ( in @ SV57 @ SV80 )
= $false )
| ( ( ~ ( in @ SV80 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(549,plain,
! [SV67: $i] :
( ( ( relation @ SV67 )
= $false )
| ( ( empty @ SV67 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(550,plain,
! [SV85: $i,SV69: $i] :
( ( ( in @ SV69 @ SV85 )
= $false )
| ( ( element @ SV69 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(551,plain,
! [SV86: $i,SV70: $i] :
( ( ( element @ SV70 @ SV86 )
= $false )
| ( ( ( empty @ SV86 )
| ( in @ SV70 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(552,plain,
! [SV71: $i,SV91: $i,SV87: $i] :
( ( ( ~ ( element @ SV87 @ ( powerset @ SV91 ) )
| ~ ( in @ SV71 @ SV87 ) )
= $true )
| ( ( element @ SV71 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(553,plain,
! [SV72: $i,SV92: $i,SV88: $i] :
( ( ( ~ ( element @ SV88 @ ( powerset @ SV92 ) )
| ~ ( in @ SV72 @ SV88 ) )
= $true )
| ( ( ~ ( empty @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(554,plain,
! [SV74: $i,SV89: $i] :
( ( ( empty @ SV89 )
= $false )
| ( ( ~ ( in @ SV74 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(555,plain,
! [SV90: $i,SV75: $i] :
( ( ( SV75 = SV90 )
= $true )
| ( ( ~ ( empty @ SV75 ) )
= $true )
| ( ( ~ ( empty @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(556,plain,
! [SV93: $i] :
( ( ~ ( empty @ SV93 )
| ( empty @ ( relation_dom @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(557,plain,
! [SV94: $i] :
( ( ~ ( empty @ SV94 )
| ( relation @ ( relation_dom @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(558,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(559,plain,
! [SV76: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV76 ) @ ( powerset @ SV76 ) ) )
= $false )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(560,plain,
! [SV76: $i] :
( ( ( ~ ~ ( empty @ ( sK9_B @ SV76 ) ) )
= $false )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(561,plain,
! [SV77: $i] :
( ( ( function @ SV77 )
= $false )
| ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(562,plain,
! [SV95: $i] :
( ( ! [SY131: $i] :
( ~ ( element @ SV95 @ ( powerset @ SY131 ) )
| ( subset @ SV95 @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(563,plain,
! [SV96: $i] :
( ( ! [SY132: $i] :
( ~ ( subset @ SV96 @ SY132 )
| ( element @ SV96 @ ( powerset @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(564,plain,
! [SV78: $i] :
( ( element @ ( sK6_B @ SV78 ) @ ( powerset @ SV78 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(565,plain,
! [SV78: $i] :
( ( empty @ ( sK6_B @ SV78 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(566,plain,
( ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(567,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY57 ) @ sK3_SY59 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(568,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(569,plain,
! [SV79: $i] :
( ( ( ~ ! [SY123: $i] :
( ~ ( ~ ( ! [SY124: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ SY124 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ ( sK15_SY61 @ SY123 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) ) )
| ( SY123
= ( relation_dom @ SV79 ) ) )
| ~ ! [SY125: $i] :
( ( SY125
!= ( relation_dom @ SV79 ) )
| ~ ( ~ ! [SY126: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY126 @ SY127 ) @ SV79 )
| ( in @ SY126 @ SY125 ) )
| ~ ! [SY128: $i] :
( ~ ( in @ SY128 @ SY125 )
| ( in @ ( ordered_pair @ SY128 @ ( sK13_D @ SY128 @ SY125 @ SV79 ) ) @ SV79 ) ) ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(570,plain,
! [SV57: $i,SV80: $i] :
( ( ( in @ SV80 @ SV57 )
= $false )
| ( ( in @ SV57 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(571,plain,
! [SV67: $i] :
( ( ( empty @ ( relation_dom @ SV67 ) )
= $false )
| ( ( empty @ SV67 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(572,plain,
! [SV70: $i,SV86: $i] :
( ( ( empty @ SV86 )
= $true )
| ( ( in @ SV70 @ SV86 )
= $true )
| ( ( element @ SV70 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(573,plain,
! [SV71: $i,SV91: $i,SV87: $i] :
( ( ( ~ ( element @ SV87 @ ( powerset @ SV91 ) ) )
= $true )
| ( ( ~ ( in @ SV71 @ SV87 ) )
= $true )
| ( ( element @ SV71 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(574,plain,
! [SV72: $i,SV92: $i,SV88: $i] :
( ( ( ~ ( element @ SV88 @ ( powerset @ SV92 ) ) )
= $true )
| ( ( ~ ( in @ SV72 @ SV88 ) )
= $true )
| ( ( ~ ( empty @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(575,plain,
! [SV89: $i,SV74: $i] :
( ( ( in @ SV74 @ SV89 )
= $false )
| ( ( empty @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(576,plain,
! [SV90: $i,SV75: $i] :
( ( ( empty @ SV75 )
= $false )
| ( ( SV75 = SV90 )
= $true )
| ( ( ~ ( empty @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(577,plain,
! [SV93: $i] :
( ( ( ~ ( empty @ SV93 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(578,plain,
! [SV94: $i] :
( ( ( ~ ( empty @ SV94 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(579,plain,
! [SV76: $i] :
( ( ( element @ ( sK9_B @ SV76 ) @ ( powerset @ SV76 ) )
= $true )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(580,plain,
! [SV76: $i] :
( ( ( ~ ( empty @ ( sK9_B @ SV76 ) ) )
= $true )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(581,plain,
! [SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(582,plain,
! [SV97: $i,SV95: $i] :
( ( ~ ( element @ SV95 @ ( powerset @ SV97 ) )
| ( subset @ SV95 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(583,plain,
! [SV98: $i,SV96: $i] :
( ( ~ ( subset @ SV96 @ SV98 )
| ( element @ SV96 @ ( powerset @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(584,plain,
( ( ( sK2_SY57
!= ( apply @ sK3_SY59 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(585,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(586,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(587,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(588,plain,
! [SV79: $i] :
( ( ( ~ ! [SY123: $i] :
( ~ ( ~ ( ! [SY124: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ SY124 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ ( sK15_SY61 @ SY123 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) ) )
| ( SY123
= ( relation_dom @ SV79 ) ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(589,plain,
! [SV79: $i] :
( ( ( ~ ! [SY125: $i] :
( ( SY125
!= ( relation_dom @ SV79 ) )
| ~ ( ~ ! [SY126: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY126 @ SY127 ) @ SV79 )
| ( in @ SY126 @ SY125 ) )
| ~ ! [SY128: $i] :
( ~ ( in @ SY128 @ SY125 )
| ( in @ ( ordered_pair @ SY128 @ ( sK13_D @ SY128 @ SY125 @ SV79 ) ) @ SV79 ) ) ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(590,plain,
! [SV71: $i,SV91: $i,SV87: $i] :
( ( ( element @ SV87 @ ( powerset @ SV91 ) )
= $false )
| ( ( ~ ( in @ SV71 @ SV87 ) )
= $true )
| ( ( element @ SV71 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(591,plain,
! [SV72: $i,SV92: $i,SV88: $i] :
( ( ( element @ SV88 @ ( powerset @ SV92 ) )
= $false )
| ( ( ~ ( in @ SV72 @ SV88 ) )
= $true )
| ( ( ~ ( empty @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(592,plain,
! [SV75: $i,SV90: $i] :
( ( ( empty @ SV90 )
= $false )
| ( ( SV75 = SV90 )
= $true )
| ( ( empty @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(593,plain,
! [SV93: $i] :
( ( ( empty @ SV93 )
= $false )
| ( ( empty @ ( relation_dom @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(594,plain,
! [SV94: $i] :
( ( ( empty @ SV94 )
= $false )
| ( ( relation @ ( relation_dom @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(595,plain,
! [SV76: $i] :
( ( ( empty @ ( sK9_B @ SV76 ) )
= $false )
| ( ( empty @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(596,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
| ~ ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(597,plain,
! [SV97: $i,SV95: $i] :
( ( ( ~ ( element @ SV95 @ ( powerset @ SV97 ) ) )
= $true )
| ( ( subset @ SV95 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(598,plain,
! [SV98: $i,SV96: $i] :
( ( ( ~ ( subset @ SV96 @ SV98 ) )
= $true )
| ( ( element @ SV96 @ ( powerset @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(599,plain,
( ( sK2_SY57
= ( apply @ sK3_SY59 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(600,plain,
( ( in @ sK1_A @ ( relation_dom @ sK3_SY59 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(601,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(602,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(603,plain,
! [SV79: $i] :
( ( ( ! [SY123: $i] :
( ~ ( ~ ( ! [SY124: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ SY124 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SY123 @ SV79 ) @ ( sK15_SY61 @ SY123 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SY123 @ SV79 ) @ SY123 ) ) )
| ( SY123
= ( relation_dom @ SV79 ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(604,plain,
! [SV79: $i] :
( ( ( ! [SY125: $i] :
( ( SY125
!= ( relation_dom @ SV79 ) )
| ~ ( ~ ! [SY126: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY126 @ SY127 ) @ SV79 )
| ( in @ SY126 @ SY125 ) )
| ~ ! [SY128: $i] :
( ~ ( in @ SY128 @ SY125 )
| ( in @ ( ordered_pair @ SY128 @ ( sK13_D @ SY128 @ SY125 @ SV79 ) ) @ SV79 ) ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(605,plain,
! [SV91: $i,SV87: $i,SV71: $i] :
( ( ( in @ SV71 @ SV87 )
= $false )
| ( ( element @ SV87 @ ( powerset @ SV91 ) )
= $false )
| ( ( element @ SV71 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(606,plain,
! [SV92: $i,SV88: $i,SV72: $i] :
( ( ( in @ SV72 @ SV88 )
= $false )
| ( ( element @ SV88 @ ( powerset @ SV92 ) )
= $false )
| ( ( ~ ( empty @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(607,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(608,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(609,plain,
! [SV97: $i,SV95: $i] :
( ( ( element @ SV95 @ ( powerset @ SV97 ) )
= $false )
| ( ( subset @ SV95 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(610,plain,
! [SV98: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV98 )
= $false )
| ( ( element @ SV96 @ ( powerset @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(611,plain,
! [SV79: $i,SV99: $i] :
( ( ( ~ ( ~ ( ! [SY133: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SY133 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ ( sK15_SY61 @ SV99 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) ) )
| ( SV99
= ( relation_dom @ SV79 ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(612,plain,
! [SV79: $i,SV100: $i] :
( ( ( ( SV100
!= ( relation_dom @ SV79 ) )
| ~ ( ~ ! [SY134: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY134 @ SY127 ) @ SV79 )
| ( in @ SY134 @ SV100 ) )
| ~ ! [SY136: $i] :
( ~ ( in @ SY136 @ SV100 )
| ( in @ ( ordered_pair @ SY136 @ ( sK13_D @ SY136 @ SV100 @ SV79 ) ) @ SV79 ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(613,plain,
! [SV72: $i,SV88: $i,SV92: $i] :
( ( ( empty @ SV92 )
= $false )
| ( ( element @ SV88 @ ( powerset @ SV92 ) )
= $false )
| ( ( in @ SV72 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(614,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(615,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(616,plain,
! [SV79: $i,SV99: $i] :
( ( ( ~ ( ~ ( ! [SY133: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SY133 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ ( sK15_SY61 @ SV99 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) ) ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(617,plain,
! [SV79: $i,SV100: $i] :
( ( ( ( SV100
!= ( relation_dom @ SV79 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY134: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY134 @ SY127 ) @ SV79 )
| ( in @ SY134 @ SV100 ) )
| ~ ! [SY136: $i] :
( ~ ( in @ SY136 @ SV100 )
| ( in @ ( ordered_pair @ SY136 @ ( sK13_D @ SY136 @ SV100 @ SV79 ) ) @ SV79 ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(618,plain,
! [SV77: $i] :
( ( ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) )
| ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(619,plain,
! [SV77: $i] :
( ( ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) )
| ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(620,plain,
! [SV79: $i,SV99: $i] :
( ( ( ~ ( ! [SY133: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SY133 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ ( sK15_SY61 @ SV99 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(621,plain,
! [SV79: $i,SV100: $i] :
( ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( ~ ( ~ ! [SY134: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY134 @ SY127 ) @ SV79 )
| ( in @ SY134 @ SV100 ) )
| ~ ! [SY136: $i] :
( ~ ( in @ SY136 @ SV100 )
| ( in @ ( ordered_pair @ SY136 @ ( sK13_D @ SY136 @ SV100 @ SV79 ) ) @ SV79 ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(622,plain,
! [SV77: $i] :
( ( ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(623,plain,
! [SV77: $i] :
( ( ( ~ ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(624,plain,
! [SV77: $i] :
( ( ( ~ ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(625,plain,
! [SV77: $i] :
( ( ( ~ ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(626,plain,
! [SV79: $i,SV99: $i] :
( ( ( ~ ( ! [SY133: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SY133 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(627,plain,
! [SV79: $i,SV99: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ ( sK15_SY61 @ SV99 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) ) )
= $false )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(628,plain,
! [SV100: $i,SV79: $i] :
( ( ( ~ ! [SY134: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY134 @ SY127 ) @ SV79 )
| ( in @ SY134 @ SV100 ) )
| ~ ! [SY136: $i] :
( ~ ( in @ SY136 @ SV100 )
| ( in @ ( ordered_pair @ SY136 @ ( sK13_D @ SY136 @ SV100 @ SV79 ) ) @ SV79 ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(629,plain,
! [SV77: $i] :
( ( ( ! [SY115: $i] :
( ~ ( in @ SY115 @ ( relation_dom @ SV77 ) )
| ! [SY116: $i] :
( ( SY116
!= ( apply @ SV77 @ SY115 ) )
| ( in @ ( ordered_pair @ SY115 @ SY116 ) @ SV77 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(630,plain,
! [SV77: $i] :
( ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ ( relation_dom @ SV77 ) )
| ! [SY118: $i] :
( ~ ( in @ ( ordered_pair @ SY117 @ SY118 ) @ SV77 )
| ( SY118
= ( apply @ SV77 @ SY117 ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(631,plain,
! [SV77: $i] :
( ( ( ! [SY119: $i] :
( ( in @ SY119 @ ( relation_dom @ SV77 ) )
| ! [SY120: $i] :
( ( SY120
!= ( apply @ SV77 @ SY119 ) )
| ( SY120 = empty_set ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(632,plain,
! [SV77: $i] :
( ( ( ! [SY121: $i] :
( ( in @ SY121 @ ( relation_dom @ SV77 ) )
| ! [SY122: $i] :
( ( SY122 != empty_set )
| ( SY122
= ( apply @ SV77 @ SY121 ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(633,plain,
! [SV79: $i,SV99: $i] :
( ( ( ! [SY133: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SY133 ) @ SV79 )
| ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(634,plain,
! [SV79: $i,SV99: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ ( sK15_SY61 @ SV99 @ SV79 ) ) @ SV79 )
| ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(635,plain,
! [SV100: $i,SV79: $i] :
( ( ( ~ ! [SY134: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY134 @ SY127 ) @ SV79 )
| ( in @ SY134 @ SV100 ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(636,plain,
! [SV79: $i,SV100: $i] :
( ( ( ~ ! [SY136: $i] :
( ~ ( in @ SY136 @ SV100 )
| ( in @ ( ordered_pair @ SY136 @ ( sK13_D @ SY136 @ SV100 @ SV79 ) ) @ SV79 ) ) )
= $false )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(637,plain,
! [SV77: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ ( relation_dom @ SV77 ) )
| ! [SY137: $i] :
( ( SY137
!= ( apply @ SV77 @ SV101 ) )
| ( in @ ( ordered_pair @ SV101 @ SY137 ) @ SV77 ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(638,plain,
! [SV77: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ ( relation_dom @ SV77 ) )
| ! [SY138: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SY138 ) @ SV77 )
| ( SY138
= ( apply @ SV77 @ SV102 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(639,plain,
! [SV77: $i,SV103: $i] :
( ( ( ( in @ SV103 @ ( relation_dom @ SV77 ) )
| ! [SY139: $i] :
( ( SY139
!= ( apply @ SV77 @ SV103 ) )
| ( SY139 = empty_set ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(640,plain,
! [SV77: $i,SV104: $i] :
( ( ( ( in @ SV104 @ ( relation_dom @ SV77 ) )
| ! [SY140: $i] :
( ( SY140 != empty_set )
| ( SY140
= ( apply @ SV77 @ SV104 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(641,plain,
! [SV79: $i,SV99: $i] :
( ( ( ! [SY133: $i] :
~ ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SY133 ) @ SV79 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(642,plain,
! [SV79: $i,SV99: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ ( sK15_SY61 @ SV99 @ SV79 ) ) @ SV79 )
= $true )
| ( ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 )
= $true )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(643,plain,
! [SV100: $i,SV79: $i] :
( ( ( ! [SY134: $i] :
( ! [SY127: $i] :
~ ( in @ ( ordered_pair @ SY134 @ SY127 ) @ SV79 )
| ( in @ SY134 @ SV100 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(644,plain,
! [SV79: $i,SV100: $i] :
( ( ( ! [SY136: $i] :
( ~ ( in @ SY136 @ SV100 )
| ( in @ ( ordered_pair @ SY136 @ ( sK13_D @ SY136 @ SV100 @ SV79 ) ) @ SV79 ) ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(645,plain,
! [SV77: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ ( relation_dom @ SV77 ) ) )
= $true )
| ( ( ! [SY137: $i] :
( ( SY137
!= ( apply @ SV77 @ SV101 ) )
| ( in @ ( ordered_pair @ SV101 @ SY137 ) @ SV77 ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(646,plain,
! [SV77: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ ( relation_dom @ SV77 ) ) )
= $true )
| ( ( ! [SY138: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SY138 ) @ SV77 )
| ( SY138
= ( apply @ SV77 @ SV102 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(647,plain,
! [SV77: $i,SV103: $i] :
( ( ( in @ SV103 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( ! [SY139: $i] :
( ( SY139
!= ( apply @ SV77 @ SV103 ) )
| ( SY139 = empty_set ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(648,plain,
! [SV77: $i,SV104: $i] :
( ( ( in @ SV104 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( ! [SY140: $i] :
( ( SY140 != empty_set )
| ( SY140
= ( apply @ SV77 @ SV104 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(649,plain,
! [SV105: $i,SV79: $i,SV99: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SV105 ) @ SV79 ) )
= $true )
| ( ( ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(650,plain,
! [SV100: $i,SV79: $i,SV106: $i] :
( ( ( ! [SY141: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY141 ) @ SV79 )
| ( in @ SV106 @ SV100 ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(651,plain,
! [SV79: $i,SV100: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV100 )
| ( in @ ( ordered_pair @ SV107 @ ( sK13_D @ SV107 @ SV100 @ SV79 ) ) @ SV79 ) )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(652,plain,
! [SV77: $i,SV101: $i] :
( ( ( in @ SV101 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( ! [SY137: $i] :
( ( SY137
!= ( apply @ SV77 @ SV101 ) )
| ( in @ ( ordered_pair @ SV101 @ SY137 ) @ SV77 ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(653,plain,
! [SV77: $i,SV102: $i] :
( ( ( in @ SV102 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( in @ ( ordered_pair @ SV102 @ SY138 ) @ SV77 )
| ( SY138
= ( apply @ SV77 @ SV102 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(654,plain,
! [SV103: $i,SV77: $i,SV108: $i] :
( ( ( ( SV108
!= ( apply @ SV77 @ SV103 ) )
| ( SV108 = empty_set ) )
= $true )
| ( ( in @ SV103 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(655,plain,
! [SV104: $i,SV77: $i,SV109: $i] :
( ( ( ( SV109 != empty_set )
| ( SV109
= ( apply @ SV77 @ SV104 ) ) )
= $true )
| ( ( in @ SV104 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(656,plain,
! [SV105: $i,SV79: $i,SV99: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SV105 ) @ SV79 )
= $false )
| ( ( ~ ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 ) )
= $true )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(657,plain,
! [SV100: $i,SV79: $i,SV106: $i] :
( ( ( ! [SY141: $i] :
~ ( in @ ( ordered_pair @ SV106 @ SY141 ) @ SV79 ) )
= $true )
| ( ( in @ SV106 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(658,plain,
! [SV79: $i,SV100: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV100 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV107 @ ( sK13_D @ SV107 @ SV100 @ SV79 ) ) @ SV79 )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(659,plain,
! [SV101: $i,SV77: $i,SV110: $i] :
( ( ( ( SV110
!= ( apply @ SV77 @ SV101 ) )
| ( in @ ( ordered_pair @ SV101 @ SV110 ) @ SV77 ) )
= $true )
| ( ( in @ SV101 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(660,plain,
! [SV77: $i,SV111: $i,SV102: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV111 ) @ SV77 )
| ( SV111
= ( apply @ SV77 @ SV102 ) ) )
= $true )
| ( ( in @ SV102 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(661,plain,
! [SV103: $i,SV77: $i,SV108: $i] :
( ( ( ( SV108
!= ( apply @ SV77 @ SV103 ) ) )
= $true )
| ( ( SV108 = empty_set )
= $true )
| ( ( in @ SV103 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(662,plain,
! [SV104: $i,SV77: $i,SV109: $i] :
( ( ( ( SV109 != empty_set ) )
= $true )
| ( ( SV109
= ( apply @ SV77 @ SV104 ) )
= $true )
| ( ( in @ SV104 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(663,plain,
! [SV105: $i,SV79: $i,SV99: $i] :
( ( ( in @ ( sK14_C @ SV99 @ SV79 ) @ SV99 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_C @ SV99 @ SV79 ) @ SV105 ) @ SV79 )
= $false )
| ( ( SV99
= ( relation_dom @ SV79 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(664,plain,
! [SV100: $i,SV79: $i,SV112: $i,SV106: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV106 @ SV112 ) @ SV79 ) )
= $true )
| ( ( in @ SV106 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(665,plain,
! [SV79: $i,SV100: $i,SV107: $i] :
( ( ( in @ SV107 @ SV100 )
= $false )
| ( ( in @ ( ordered_pair @ SV107 @ ( sK13_D @ SV107 @ SV100 @ SV79 ) ) @ SV79 )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(666,plain,
! [SV101: $i,SV77: $i,SV110: $i] :
( ( ( ( SV110
!= ( apply @ SV77 @ SV101 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV101 @ SV110 ) @ SV77 )
= $true )
| ( ( in @ SV101 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(667,plain,
! [SV77: $i,SV111: $i,SV102: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV102 @ SV111 ) @ SV77 ) )
= $true )
| ( ( SV111
= ( apply @ SV77 @ SV102 ) )
= $true )
| ( ( in @ SV102 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(668,plain,
! [SV103: $i,SV77: $i,SV108: $i] :
( ( ( SV108
= ( apply @ SV77 @ SV103 ) )
= $false )
| ( ( SV108 = empty_set )
= $true )
| ( ( in @ SV103 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(669,plain,
! [SV104: $i,SV77: $i,SV109: $i] :
( ( ( SV109 = empty_set )
= $false )
| ( ( SV109
= ( apply @ SV77 @ SV104 ) )
= $true )
| ( ( in @ SV104 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(670,plain,
! [SV100: $i,SV79: $i,SV112: $i,SV106: $i] :
( ( ( in @ ( ordered_pair @ SV106 @ SV112 ) @ SV79 )
= $false )
| ( ( in @ SV106 @ SV100 )
= $true )
| ( ( SV100
= ( relation_dom @ SV79 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(671,plain,
! [SV101: $i,SV77: $i,SV110: $i] :
( ( ( SV110
= ( apply @ SV77 @ SV101 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV101 @ SV110 ) @ SV77 )
= $true )
| ( ( in @ SV101 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(672,plain,
! [SV77: $i,SV111: $i,SV102: $i] :
( ( ( in @ ( ordered_pair @ SV102 @ SV111 ) @ SV77 )
= $false )
| ( ( SV111
= ( apply @ SV77 @ SV102 ) )
= $true )
| ( ( in @ SV102 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(673,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[400,672,671,670,669,668,665,663,642,613,610,609,605,602,601,600,599,595,594,593,592,579,575,572,571,570,567,565,564,558,550,547,546,544,542,541,540,539,530,526,525,522,516,515,514,513,480,478,477,476,452,451,445,425,424,410]) ).
thf(674,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[673,389]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 15:30:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 34
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.36 .
% 0.12/0.37 (rf:0,axioms:34,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:36,loop_count:0,foatp_calls:0,translation:fof_full)..................................
% 0.44/0.66
% 0.44/0.66 ********************************
% 0.44/0.66 * All subproblems solved! *
% 0.44/0.66 ********************************
% 0.44/0.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:36,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:673,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.62/0.82
% 0.62/0.82 %**** Beginning of derivation protocol ****
% 0.62/0.82 % SZS output start CNFRefutation
% See solution above
% 0.62/0.82
% 0.62/0.82 %**** End of derivation protocol ****
% 0.62/0.82 %**** no. of clauses in derivation: 674 ****
% 0.62/0.82 %**** clause counter: 673 ****
% 0.62/0.82
% 0.62/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:36,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:673,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------