TSTP Solution File: SEU240+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n013.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 12:08:53 EDT 2022
% Result : Theorem 0.60s 0.87s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 66
% Syntax : Number of formulae : 650 ( 375 unt; 29 typ; 0 def)
% Number of atoms : 4217 (1132 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 7998 (1602 ~;1334 |; 96 &;4912 @)
% ( 9 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 12 con; 0-2 aty)
% Number of variables : 1074 ( 0 ^1062 !; 12 ?;1074 :)
% Comments :
%------------------------------------------------------------------------------
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_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_SY55,type,
sK12_SY55: $i > $i > $i ).
thf(tp_sK13_SY57,type,
sK13_SY57: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY49,type,
sK2_SY49: $i ).
thf(tp_sK3_SY52,type,
sK3_SY52: $i ).
thf(tp_sK4_SY54,type,
sK4_SY54: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_transitive,type,
transitive: $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] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(7,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(8,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(9,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(10,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(11,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(17,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(18,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(28,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_transitive_in @ A @ B )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
thf(29,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(30,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(31,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(34,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(35,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(37,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_wellord1) ).
thf(38,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(47,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(48,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(49,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(50,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(51,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(56,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(57,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(62,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(64,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(65,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(66,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_transitive_in @ A @ B )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(73,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(76,plain,
( ( ( relation @ sK1_A )
=> ( ( transitive @ sK1_A )
<=> ! [SY49: $i,SY50: $i,SY51: $i] :
( ( ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A ) )
=> ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(77,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[76]) ).
thf(78,plain,
( ( ( transitive @ sK1_A )
<=> ! [SY49: $i,SY50: $i,SY51: $i] :
( ( ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A ) )
=> ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[76]) ).
thf(79,plain,
( ( ( transitive @ sK1_A )
=> ! [SY49: $i,SY50: $i,SY51: $i] :
( ( ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A ) )
=> ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[78]) ).
thf(80,plain,
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ( ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A ) )
=> ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) )
=> ( transitive @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[78]) ).
thf(81,plain,
( ( ~ ( ( transitive @ sK1_A )
=> ! [SY49: $i,SY50: $i,SY51: $i] :
( ( ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A ) )
=> ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[79]) ).
thf(82,plain,
( ( ~ ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ( ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A ) )
=> ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) )
=> ( transitive @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[80]) ).
thf(83,plain,
( ( ( transitive @ sK1_A )
& ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
& ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A )
& ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(84,plain,
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A )
| ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) )
& ~ ( transitive @ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(87,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(88,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(91,plain,
( ( ( function @ sK5_A )
& ( relation @ sK5_A )
& ( one_to_one @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(92,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(93,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A )
& ( function @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(94,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(95,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(97,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(98,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(99,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(100,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK11_C @ B @ A ) @ B )
& ( in @ ( sK12_SY55 @ B @ A ) @ B )
& ( in @ ( sK13_SY57 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY55 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY55 @ B @ A ) @ ( sK13_SY57 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK13_SY57 @ B @ A ) ) @ A ) )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_transitive_in @ A @ B )
| ! [C: $i,D: $i,E: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ E @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(101,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(102,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_transitive_in @ A @ ( relation_field @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ( is_transitive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(103,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(104,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(107,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(108,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(111,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_transitive_in @ A @ ( relation_field @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ( is_transitive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(113,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(114,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK11_C @ B @ A ) @ B )
& ( in @ ( sK12_SY55 @ B @ A ) @ B )
& ( in @ ( sK13_SY57 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY55 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY55 @ B @ A ) @ ( sK13_SY57 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK13_SY57 @ B @ A ) ) @ A ) )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_transitive_in @ A @ B )
| ! [C: $i,D: $i,E: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ E @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(115,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(116,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(117,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(118,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(119,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(120,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(121,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(122,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(123,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(124,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(125,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(127,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(128,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(129,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(130,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(131,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(132,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A )
& ( function @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(133,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(134,plain,
( ( ( function @ sK5_A )
& ( relation @ sK5_A )
& ( one_to_one @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(135,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(137,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(138,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(139,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(142,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(143,plain,
( ( ( transitive @ sK1_A )
& ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
& ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A )
& ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(144,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK12_SY55 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK13_SY57 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY55 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_transitive_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX4 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(145,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(146,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(147,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) )
| ~ ( one_to_one @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(148,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(149,plain,
( ( ~ ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(150,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(151,plain,
( ( ~ ( ~ ( transitive @ sK1_A )
| ~ ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) )
| ~ ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(152,plain,
! [SV1: $i] :
( ( ! [SY58: $i] :
( ~ ( in @ SV1 @ SY58 )
| ~ ( in @ SY58 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(153,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(154,plain,
! [SV3: $i] :
( ( ! [SY59: $i] :
( ( unordered_pair @ SV3 @ SY59 )
= ( unordered_pair @ SY59 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(155,plain,
! [SV4: $i] :
( ( ! [SY60: $i] :
( ( set_union2 @ SV4 @ SY60 )
= ( set_union2 @ SY60 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(156,plain,
! [SV5: $i] :
( ( ! [SY61: $i] :
( ( ordered_pair @ SV5 @ SY61 )
= ( unordered_pair @ ( unordered_pair @ SV5 @ SY61 ) @ ( singleton @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(157,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ( ( relation_field @ SV6 )
= ( set_union2 @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(158,plain,
! [SV7: $i] :
( ( element @ ( sK10_B @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(159,plain,
! [SV8: $i] :
( ( ! [SY62: $i] :
~ ( empty @ ( ordered_pair @ SV8 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(160,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
| ! [SY63: $i] :
~ ( empty @ ( set_union2 @ SV9 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(161,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
| ! [SY64: $i] :
~ ( empty @ ( set_union2 @ SY64 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(162,plain,
! [SV11: $i] :
( ( ( set_union2 @ SV11 @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(163,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(164,plain,
! [SV12: $i] :
( ( ( set_union2 @ SV12 @ empty_set )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(165,plain,
! [SV13: $i] :
( ( ! [SY65: $i] :
( ~ ( in @ SV13 @ SY65 )
| ( element @ SV13 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(166,plain,
! [SV14: $i] :
( ( ! [SY66: $i] :
( ~ ( element @ SV14 @ SY66 )
| ( empty @ SY66 )
| ( in @ SV14 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(167,plain,
! [SV15: $i] :
( ( ~ ( empty @ SV15 )
| ( SV15 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(168,plain,
! [SV16: $i] :
( ( ! [SY67: $i] :
( ~ ( empty @ SY67 )
| ~ ( in @ SV16 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(169,plain,
! [SV17: $i] :
( ( ! [SY68: $i] :
( ( SV17 = SY68 )
| ~ ( empty @ SV17 )
| ~ ( empty @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(170,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ~ ( ~ ! [SY69: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY69 @ SV18 ) @ SY69 )
| ~ ( in @ ( sK12_SY55 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( sK13_SY57 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK12_SY55 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ( is_transitive_in @ SV18 @ SY69 ) )
| ~ ! [SY70: $i] :
( ~ ( is_transitive_in @ SV18 @ SY70 )
| ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( in @ SY71 @ SY70 )
| ~ ( in @ SY72 @ SY70 )
| ~ ( in @ SY73 @ SY70 )
| ~ ( in @ ( ordered_pair @ SY71 @ SY72 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY72 @ SY73 ) @ SV18 )
| ( in @ ( ordered_pair @ SY71 @ SY73 ) @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(171,plain,
! [SV19: $i] :
( ( ~ ( ~ ! [SY74: $i,SY75: $i] :
( ~ ( relation @ SY75 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY74 ) @ SY75 )
| ( in @ SV19 @ ( relation_field @ SY75 ) ) )
| ~ ! [SY76: $i,SY77: $i] :
( ~ ( relation @ SY77 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY76 ) @ SY77 )
| ( in @ SY76 @ ( relation_field @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(172,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(173,plain,
( ( ~ ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) )
| ~ ( one_to_one @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(174,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(175,plain,
( ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(176,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(177,plain,
( ( ~ ( transitive @ sK1_A )
| ~ ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) )
| ~ ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(178,plain,
! [SV20: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV20 )
| ~ ( in @ SV20 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(179,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(180,plain,
! [SV21: $i,SV3: $i] :
( ( ( unordered_pair @ SV3 @ SV21 )
= ( unordered_pair @ SV21 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(181,plain,
! [SV22: $i,SV4: $i] :
( ( ( set_union2 @ SV4 @ SV22 )
= ( set_union2 @ SV22 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(182,plain,
! [SV23: $i,SV5: $i] :
( ( ( ordered_pair @ SV5 @ SV23 )
= ( unordered_pair @ ( unordered_pair @ SV5 @ SV23 ) @ ( singleton @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(183,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ( relation_field @ SV6 )
= ( set_union2 @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(184,plain,
! [SV24: $i,SV8: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV8 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(185,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( ! [SY63: $i] :
~ ( empty @ ( set_union2 @ SV9 @ SY63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(186,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ! [SY64: $i] :
~ ( empty @ ( set_union2 @ SY64 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(187,plain,
! [SV25: $i,SV13: $i] :
( ( ~ ( in @ SV13 @ SV25 )
| ( element @ SV13 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(188,plain,
! [SV26: $i,SV14: $i] :
( ( ~ ( element @ SV14 @ SV26 )
| ( empty @ SV26 )
| ( in @ SV14 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(189,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(190,plain,
! [SV16: $i,SV27: $i] :
( ( ~ ( empty @ SV27 )
| ~ ( in @ SV16 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(191,plain,
! [SV28: $i,SV17: $i] :
( ( ( SV17 = SV28 )
| ~ ( empty @ SV17 )
| ~ ( empty @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(192,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( ~ ! [SY69: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY69 @ SV18 ) @ SY69 )
| ~ ( in @ ( sK12_SY55 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( sK13_SY57 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK12_SY55 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ( is_transitive_in @ SV18 @ SY69 ) )
| ~ ! [SY70: $i] :
( ~ ( is_transitive_in @ SV18 @ SY70 )
| ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( in @ SY71 @ SY70 )
| ~ ( in @ SY72 @ SY70 )
| ~ ( in @ SY73 @ SY70 )
| ~ ( in @ ( ordered_pair @ SY71 @ SY72 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY72 @ SY73 ) @ SV18 )
| ( in @ ( ordered_pair @ SY71 @ SY73 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(193,plain,
! [SV19: $i] :
( ( ~ ! [SY74: $i,SY75: $i] :
( ~ ( relation @ SY75 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY74 ) @ SY75 )
| ( in @ SV19 @ ( relation_field @ SY75 ) ) )
| ~ ! [SY76: $i,SY77: $i] :
( ~ ( relation @ SY77 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY76 ) @ SY77 )
| ( in @ SY76 @ ( relation_field @ SY77 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(194,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(195,plain,
( ( ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(196,plain,
( ( ~ ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(197,plain,
( ( ~ ( one_to_one @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(198,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(199,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(200,plain,
( ( ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(201,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(202,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(203,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(204,plain,
( ( ~ ( transitive @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(205,plain,
( ( ~ ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) )
| ~ ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(206,plain,
! [SV20: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV20 ) )
= $true )
| ( ( ~ ( in @ SV20 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(207,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(208,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ( relation_field @ SV6 )
= ( set_union2 @ ( relation_dom @ SV6 ) @ ( relation_rng @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(209,plain,
! [SV24: $i,SV8: $i] :
( ( empty @ ( ordered_pair @ SV8 @ SV24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(210,plain,
! [SV29: $i,SV9: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV9 @ SV29 ) ) )
= $true )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(211,plain,
! [SV10: $i,SV30: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV30 @ SV10 ) ) )
= $true )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(212,plain,
! [SV25: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV25 ) )
= $true )
| ( ( element @ SV13 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(213,plain,
! [SV26: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ SV26 ) )
= $true )
| ( ( ( empty @ SV26 )
| ( in @ SV14 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(214,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(215,plain,
! [SV16: $i,SV27: $i] :
( ( ( ~ ( empty @ SV27 ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(216,plain,
! [SV28: $i,SV17: $i] :
( ( ( ( SV17 = SV28 )
| ~ ( empty @ SV17 ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(217,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( ~ ! [SY69: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY69 @ SV18 ) @ SY69 )
| ~ ( in @ ( sK12_SY55 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( sK13_SY57 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK12_SY55 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ( is_transitive_in @ SV18 @ SY69 ) )
| ~ ! [SY70: $i] :
( ~ ( is_transitive_in @ SV18 @ SY70 )
| ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( in @ SY71 @ SY70 )
| ~ ( in @ SY72 @ SY70 )
| ~ ( in @ SY73 @ SY70 )
| ~ ( in @ ( ordered_pair @ SY71 @ SY72 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY72 @ SY73 ) @ SV18 )
| ( in @ ( ordered_pair @ SY71 @ SY73 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(218,plain,
! [SV19: $i] :
( ( ~ ! [SY74: $i,SY75: $i] :
( ~ ( relation @ SY75 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY74 ) @ SY75 )
| ( in @ SV19 @ ( relation_field @ SY75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(219,plain,
! [SV19: $i] :
( ( ~ ! [SY76: $i,SY77: $i] :
( ~ ( relation @ SY77 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY76 ) @ SY77 )
| ( in @ SY76 @ ( relation_field @ SY77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(220,plain,
( ( ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(221,plain,
( ( function @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(222,plain,
( ( ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(223,plain,
( ( one_to_one @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(224,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(225,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(226,plain,
( ( function @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(227,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(228,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(229,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(230,plain,
( ( transitive @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(231,plain,
( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) )
| ~ ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(232,plain,
! [SV20: $i,SV1: $i] :
( ( ( in @ SV1 @ SV20 )
= $false )
| ( ( ~ ( in @ SV20 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(233,plain,
! [SV29: $i,SV9: $i] :
( ( ( empty @ ( set_union2 @ SV9 @ SV29 ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(234,plain,
! [SV10: $i,SV30: $i] :
( ( ( empty @ ( set_union2 @ SV30 @ SV10 ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(235,plain,
! [SV25: $i,SV13: $i] :
( ( ( in @ SV13 @ SV25 )
= $false )
| ( ( element @ SV13 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(236,plain,
! [SV26: $i,SV14: $i] :
( ( ( element @ SV14 @ SV26 )
= $false )
| ( ( ( empty @ SV26 )
| ( in @ SV14 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(237,plain,
! [SV16: $i,SV27: $i] :
( ( ( empty @ SV27 )
= $false )
| ( ( ~ ( in @ SV16 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(238,plain,
! [SV28: $i,SV17: $i] :
( ( ( SV17 = SV28 )
= $true )
| ( ( ~ ( empty @ SV17 ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(239,plain,
! [SV18: $i] :
( ( ( ~ ! [SY69: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY69 @ SV18 ) @ SY69 )
| ~ ( in @ ( sK12_SY55 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( sK13_SY57 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK12_SY55 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ( is_transitive_in @ SV18 @ SY69 ) )
| ~ ! [SY70: $i] :
( ~ ( is_transitive_in @ SV18 @ SY70 )
| ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( in @ SY71 @ SY70 )
| ~ ( in @ SY72 @ SY70 )
| ~ ( in @ SY73 @ SY70 )
| ~ ( in @ ( ordered_pair @ SY71 @ SY72 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY72 @ SY73 ) @ SV18 )
| ( in @ ( ordered_pair @ SY71 @ SY73 ) @ SV18 ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(240,plain,
! [SV19: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ( relation @ SY75 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY74 ) @ SY75 )
| ( in @ SV19 @ ( relation_field @ SY75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(241,plain,
! [SV19: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( relation @ SY77 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY76 ) @ SY77 )
| ( in @ SY76 @ ( relation_field @ SY77 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(242,plain,
( ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(243,plain,
( ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(244,plain,
! [SV31: $i] :
( ( ~ ( relation @ SV31 )
| ~ ( is_transitive_in @ SV31 @ ( relation_field @ SV31 ) )
| ( transitive @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(245,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ~ ( transitive @ SV32 )
| ( is_transitive_in @ SV32 @ ( relation_field @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(246,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(247,plain,
! [SV33: $i] :
( ( ~ ( empty @ SV33 )
| ~ ( relation @ SV33 )
| ~ ( function @ SV33 )
| ( one_to_one @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(248,plain,
( ( ~ ~ ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) )
| ~ ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(249,plain,
! [SV1: $i,SV20: $i] :
( ( ( in @ SV20 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(250,plain,
! [SV14: $i,SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( in @ SV14 @ SV26 )
= $true )
| ( ( element @ SV14 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(251,plain,
! [SV27: $i,SV16: $i] :
( ( ( in @ SV16 @ SV27 )
= $false )
| ( ( empty @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(252,plain,
! [SV28: $i,SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( SV17 = SV28 )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(253,plain,
! [SV18: $i] :
( ( ( ~ ! [SY69: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY69 @ SV18 ) @ SY69 )
| ~ ( in @ ( sK12_SY55 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( sK13_SY57 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK12_SY55 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ( is_transitive_in @ SV18 @ SY69 ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(254,plain,
! [SV18: $i] :
( ( ( ~ ! [SY70: $i] :
( ~ ( is_transitive_in @ SV18 @ SY70 )
| ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( in @ SY71 @ SY70 )
| ~ ( in @ SY72 @ SY70 )
| ~ ( in @ SY73 @ SY70 )
| ~ ( in @ ( ordered_pair @ SY71 @ SY72 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY72 @ SY73 ) @ SV18 )
| ( in @ ( ordered_pair @ SY71 @ SY73 ) @ SV18 ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(255,plain,
! [SV34: $i,SV19: $i] :
( ( ! [SY78: $i] :
( ~ ( relation @ SY78 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ SY78 )
| ( in @ SV19 @ ( relation_field @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(256,plain,
! [SV35: $i,SV19: $i] :
( ( ! [SY79: $i] :
( ~ ( relation @ SY79 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV35 ) @ SY79 )
| ( in @ SV35 @ ( relation_field @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(257,plain,
( ( ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(258,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(259,plain,
( ( ~ ( function @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(260,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(261,plain,
! [SV31: $i] :
( ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV31 @ ( relation_field @ SV31 ) )
| ( transitive @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(262,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( transitive @ SV32 )
| ( is_transitive_in @ SV32 @ ( relation_field @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(263,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(264,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(265,plain,
! [SV33: $i] :
( ( ( ~ ( empty @ SV33 )
| ~ ( relation @ SV33 )
| ~ ( function @ SV33 ) )
= $true )
| ( ( one_to_one @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(266,plain,
( ( ~ ~ ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(267,plain,
( ( ~ ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(268,plain,
! [SV17: $i,SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( SV17 = SV28 )
= $true )
| ( ( empty @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(269,plain,
! [SV18: $i] :
( ( ( ! [SY69: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY69 @ SV18 ) @ SY69 )
| ~ ( in @ ( sK12_SY55 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( sK13_SY57 @ SY69 @ SV18 ) @ SY69 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK12_SY55 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY69 @ SV18 ) @ ( sK13_SY57 @ SY69 @ SV18 ) ) @ SV18 ) )
| ( is_transitive_in @ SV18 @ SY69 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(270,plain,
! [SV18: $i] :
( ( ( ! [SY70: $i] :
( ~ ( is_transitive_in @ SV18 @ SY70 )
| ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( in @ SY71 @ SY70 )
| ~ ( in @ SY72 @ SY70 )
| ~ ( in @ SY73 @ SY70 )
| ~ ( in @ ( ordered_pair @ SY71 @ SY72 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY72 @ SY73 ) @ SV18 )
| ( in @ ( ordered_pair @ SY71 @ SY73 ) @ SV18 ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(271,plain,
! [SV34: $i,SV19: $i,SV36: $i] :
( ( ~ ( relation @ SV36 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ SV36 )
| ( in @ SV19 @ ( relation_field @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(272,plain,
! [SV35: $i,SV19: $i,SV37: $i] :
( ( ~ ( relation @ SV37 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV35 ) @ SV37 )
| ( in @ SV35 @ ( relation_field @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(273,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(274,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(275,plain,
( ( function @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(276,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(277,plain,
! [SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( ~ ( is_transitive_in @ SV31 @ ( relation_field @ SV31 ) )
| ( transitive @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(278,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ~ ( transitive @ SV32 )
| ( is_transitive_in @ SV32 @ ( relation_field @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(279,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(280,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(281,plain,
! [SV33: $i] :
( ( ( ~ ( empty @ SV33 )
| ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( function @ SV33 ) )
= $true )
| ( ( one_to_one @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(282,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(283,plain,
( ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(284,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
| ( is_transitive_in @ SV18 @ SV38 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(285,plain,
! [SV39: $i,SV18: $i] :
( ( ( ~ ( is_transitive_in @ SV18 @ SV39 )
| ! [SY80: $i,SY81: $i,SY82: $i] :
( ~ ( in @ SY80 @ SV39 )
| ~ ( in @ SY81 @ SV39 )
| ~ ( in @ SY82 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY80 @ SY81 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV18 )
| ( in @ ( ordered_pair @ SY80 @ SY82 ) @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(286,plain,
! [SV34: $i,SV19: $i,SV36: $i] :
( ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ SV36 )
| ( in @ SV19 @ ( relation_field @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(287,plain,
! [SV35: $i,SV19: $i,SV37: $i] :
( ( ( ~ ( relation @ SV37 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV35 ) @ SV37 )
| ( in @ SV35 @ ( relation_field @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(288,plain,
! [SV31: $i] :
( ( ( ~ ( is_transitive_in @ SV31 @ ( relation_field @ SV31 ) ) )
= $true )
| ( ( transitive @ SV31 )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(289,plain,
! [SV32: $i] :
( ( ( ~ ( transitive @ SV32 ) )
= $true )
| ( ( is_transitive_in @ SV32 @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(290,plain,
! [SV40: $i] :
( ( ~ ( empty @ SV40 )
| ~ ( relation @ SV40 )
| ~ ( function @ SV40 )
| ( function @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(291,plain,
! [SV41: $i] :
( ( ~ ( empty @ SV41 )
| ~ ( relation @ SV41 )
| ~ ( function @ SV41 )
| ( relation @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(292,plain,
! [SV33: $i] :
( ( ( ~ ( empty @ SV33 ) )
= $true )
| ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( function @ SV33 ) )
= $true )
| ( ( one_to_one @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(293,plain,
( ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(294,plain,
( ( in @ ( ordered_pair @ sK2_SY49 @ sK4_SY54 ) @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(295,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(296,plain,
! [SV39: $i,SV18: $i] :
( ( ( ~ ( is_transitive_in @ SV18 @ SV39 ) )
= $true )
| ( ( ! [SY80: $i,SY81: $i,SY82: $i] :
( ~ ( in @ SY80 @ SV39 )
| ~ ( in @ SY81 @ SV39 )
| ~ ( in @ SY82 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY80 @ SY81 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV18 )
| ( in @ ( ordered_pair @ SY80 @ SY82 ) @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(297,plain,
! [SV34: $i,SV19: $i,SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ SV36 )
| ( in @ SV19 @ ( relation_field @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(298,plain,
! [SV35: $i,SV19: $i,SV37: $i] :
( ( ( relation @ SV37 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV35 ) @ SV37 )
| ( in @ SV35 @ ( relation_field @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(299,plain,
! [SV31: $i] :
( ( ( is_transitive_in @ SV31 @ ( relation_field @ SV31 ) )
= $false )
| ( ( transitive @ SV31 )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(300,plain,
! [SV32: $i] :
( ( ( transitive @ SV32 )
= $false )
| ( ( is_transitive_in @ SV32 @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(301,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ SV40 )
| ~ ( relation @ SV40 )
| ~ ( function @ SV40 ) )
= $true )
| ( ( function @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(302,plain,
! [SV41: $i] :
( ( ( ~ ( empty @ SV41 )
| ~ ( relation @ SV41 )
| ~ ( function @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(303,plain,
! [SV33: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( function @ SV33 ) )
= $true )
| ( ( one_to_one @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(304,plain,
( ( ~ ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(305,plain,
( ( ~ ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(306,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(307,plain,
! [SV39: $i,SV18: $i] :
( ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( ! [SY80: $i,SY81: $i,SY82: $i] :
( ~ ( in @ SY80 @ SV39 )
| ~ ( in @ SY81 @ SV39 )
| ~ ( in @ SY82 @ SV39 )
| ~ ( in @ ( ordered_pair @ SY80 @ SY81 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY81 @ SY82 ) @ SV18 )
| ( in @ ( ordered_pair @ SY80 @ SY82 ) @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(308,plain,
! [SV36: $i,SV34: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ SV36 ) )
= $true )
| ( ( in @ SV19 @ ( relation_field @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(309,plain,
! [SV37: $i,SV35: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV35 ) @ SV37 ) )
= $true )
| ( ( in @ SV35 @ ( relation_field @ SV37 ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(310,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ SV40 )
| ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( function @ SV40 ) )
= $true )
| ( ( function @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(311,plain,
! [SV41: $i] :
( ( ( ~ ( empty @ SV41 )
| ~ ( relation @ SV41 ) )
= $true )
| ( ( ~ ( function @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(312,plain,
! [SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( empty @ SV33 )
= $false )
| ( ( ~ ( function @ SV33 ) )
= $true )
| ( ( one_to_one @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(313,plain,
( ( in @ ( ordered_pair @ sK2_SY49 @ sK3_SY52 ) @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(314,plain,
( ( in @ ( ordered_pair @ sK3_SY52 @ sK4_SY54 ) @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(315,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(316,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(317,plain,
! [SV18: $i,SV39: $i,SV42: $i] :
( ( ( ! [SY83: $i,SY84: $i] :
( ~ ( in @ SV42 @ SV39 )
| ~ ( in @ SY83 @ SV39 )
| ~ ( in @ SY84 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV42 @ SY83 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV18 )
| ( in @ ( ordered_pair @ SV42 @ SY84 ) @ SV18 ) ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(318,plain,
! [SV36: $i,SV34: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ SV34 ) @ SV36 )
= $false )
| ( ( in @ SV19 @ ( relation_field @ SV36 ) )
= $true )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(319,plain,
! [SV37: $i,SV35: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ SV35 ) @ SV37 )
= $false )
| ( ( in @ SV35 @ ( relation_field @ SV37 ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(320,plain,
! [SV40: $i] :
( ( ( ~ ( empty @ SV40 ) )
= $true )
| ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( function @ SV40 ) )
= $true )
| ( ( function @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(321,plain,
! [SV41: $i] :
( ( ( ~ ( empty @ SV41 ) )
= $true )
| ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ~ ( function @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(322,plain,
! [SV33: $i] :
( ( ( function @ SV33 )
= $false )
| ( ( empty @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false )
| ( ( one_to_one @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(323,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(324,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(325,plain,
! [SV18: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( ! [SY85: $i] :
( ~ ( in @ SV42 @ SV39 )
| ~ ( in @ SV43 @ SV39 )
| ~ ( in @ SY85 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SV43 @ SY85 ) @ SV18 )
| ( in @ ( ordered_pair @ SV42 @ SY85 ) @ SV18 ) ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(326,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
= $false )
| ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( function @ SV40 ) )
= $true )
| ( ( function @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(327,plain,
! [SV41: $i] :
( ( ( empty @ SV41 )
= $false )
| ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ~ ( function @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(328,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(329,plain,
! [SV18: $i,SV38: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(330,plain,
! [SV18: $i,SV44: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV39 )
| ~ ( in @ SV43 @ SV39 )
| ~ ( in @ SV44 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 )
| ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(331,plain,
! [SV40: $i] :
( ( ( relation @ SV40 )
= $false )
| ( ( empty @ SV40 )
= $false )
| ( ( ~ ( function @ SV40 ) )
= $true )
| ( ( function @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(332,plain,
! [SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( empty @ SV41 )
= $false )
| ( ( ~ ( function @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(333,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(334,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(335,plain,
! [SV18: $i,SV44: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV39 )
| ~ ( in @ SV43 @ SV39 )
| ~ ( in @ SV44 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 )
| ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(336,plain,
! [SV40: $i] :
( ( ( function @ SV40 )
= $false )
| ( ( empty @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( function @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(337,plain,
! [SV41: $i] :
( ( ( function @ SV41 )
= $false )
| ( ( empty @ SV41 )
= $false )
| ( ( relation @ SV41 )
= $false )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(338,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(339,plain,
! [SV18: $i,SV38: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY55 @ SV38 @ SV18 ) @ ( sK13_SY57 @ SV38 @ SV18 ) ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(340,plain,
! [SV18: $i,SV44: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV39 )
| ~ ( in @ SV43 @ SV39 )
| ~ ( in @ SV44 @ SV39 )
| ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(341,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(342,plain,
! [SV18: $i,SV44: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV39 )
| ~ ( in @ SV43 @ SV39 )
| ~ ( in @ SV44 @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(343,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(344,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(345,plain,
! [SV18: $i,SV44: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV39 )
| ~ ( in @ SV43 @ SV39 ) )
= $true )
| ( ( ~ ( in @ SV44 @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(346,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(347,plain,
! [SV18: $i,SV38: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV38 @ SV18 ) @ ( sK12_SY55 @ SV38 @ SV18 ) ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(348,plain,
! [SV18: $i,SV44: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV39 ) )
= $true )
| ( ( ~ ( in @ SV43 @ SV39 ) )
= $true )
| ( ( ~ ( in @ SV44 @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(349,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
| ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(350,plain,
! [SV18: $i,SV44: $i,SV43: $i,SV39: $i,SV42: $i] :
( ( ( in @ SV42 @ SV39 )
= $false )
| ( ( ~ ( in @ SV43 @ SV39 ) )
= $true )
| ( ( ~ ( in @ SV44 @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(351,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(352,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(353,plain,
! [SV18: $i,SV44: $i,SV42: $i,SV39: $i,SV43: $i] :
( ( ( in @ SV43 @ SV39 )
= $false )
| ( ( in @ SV42 @ SV39 )
= $false )
| ( ( ~ ( in @ SV44 @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(354,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) ) )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(355,plain,
! [SV18: $i,SV38: $i] :
( ( ( in @ ( sK13_SY57 @ SV38 @ SV18 ) @ SV38 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(356,plain,
! [SV18: $i,SV43: $i,SV42: $i,SV39: $i,SV44: $i] :
( ( ( in @ SV44 @ SV39 )
= $false )
| ( ( in @ SV42 @ SV39 )
= $false )
| ( ( in @ SV43 @ SV39 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(357,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
| ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(358,plain,
! [SV44: $i,SV39: $i,SV18: $i,SV43: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 )
= $false )
| ( ( in @ SV43 @ SV39 )
= $false )
| ( ( in @ SV42 @ SV39 )
= $false )
| ( ( in @ SV44 @ SV39 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(359,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(360,plain,
! [SV18: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 ) )
= $false )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(361,plain,
! [SV42: $i,SV39: $i,SV18: $i,SV44: $i,SV43: $i] :
( ( ( in @ ( ordered_pair @ SV43 @ SV44 ) @ SV18 )
= $false )
| ( ( in @ SV44 @ SV39 )
= $false )
| ( ( in @ SV42 @ SV39 )
= $false )
| ( ( in @ SV43 @ SV39 )
= $false )
| ( ( in @ ( ordered_pair @ SV42 @ SV43 ) @ SV18 )
= $false )
| ( ( in @ ( ordered_pair @ SV42 @ SV44 ) @ SV18 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV39 )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(362,plain,
! [SV18: $i,SV38: $i] :
( ( ( in @ ( sK11_C @ SV38 @ SV18 ) @ SV38 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(363,plain,
! [SV18: $i,SV38: $i] :
( ( ( in @ ( sK12_SY55 @ SV38 @ SV18 ) @ SV38 )
= $true )
| ( ( is_transitive_in @ SV18 @ SV38 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(364,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[115,363,362,361,355,347,339,337,336,329,322,319,318,314,313,300,299,294,276,275,274,273,268,251,250,249,235,234,233,230,227,226,223,221,214,209,208,207,182,181,180,164,163,162,158,142,131,125,123,122,121,120,119,118,117,116]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(366,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(367,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(370,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_transitive_in @ A @ ( relation_field @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ( is_transitive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(371,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(372,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(373,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK11_C @ B @ A ) @ B )
& ( in @ ( sK12_SY55 @ B @ A ) @ B )
& ( in @ ( sK13_SY57 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK12_SY55 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK12_SY55 @ B @ A ) @ ( sK13_SY57 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK11_C @ B @ A ) @ ( sK13_SY57 @ B @ A ) ) @ A ) )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_transitive_in @ A @ B )
| ! [C: $i,D: $i,E: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ E @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(374,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(375,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(376,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(377,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(378,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(379,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(380,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(381,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(382,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(383,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(384,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(385,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(386,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(387,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(388,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(389,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(390,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(391,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A )
& ( function @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(392,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(393,plain,
( ( ( function @ sK5_A )
& ( relation @ sK5_A )
& ( one_to_one @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(394,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(395,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(396,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(397,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(398,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(399,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(401,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(402,plain,
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ( in @ ( ordered_pair @ SY49 @ SY50 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ sK1_A )
| ( in @ ( ordered_pair @ SY49 @ SY51 ) @ sK1_A ) )
& ~ ( transitive @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(403,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) )
| ~ ( one_to_one @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(404,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(405,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(406,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ sK1_A )
| ( in @ ( ordered_pair @ SX0 @ SX2 ) @ sK1_A ) )
| ~ ~ ( transitive @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(407,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(408,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK12_SY55 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK13_SY57 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK12_SY55 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_transitive_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX4 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(409,plain,
( ( ~ ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(410,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(411,plain,
! [SV45: $i] :
( ( ! [SY86: $i] :
( ~ ( in @ SV45 @ SY86 )
| ~ ( in @ SY86 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(412,plain,
! [SV46: $i] :
( ( ~ ( empty @ SV46 )
| ( function @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(413,plain,
! [SV47: $i] :
( ( ! [SY87: $i] :
( ( unordered_pair @ SV47 @ SY87 )
= ( unordered_pair @ SY87 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(414,plain,
! [SV48: $i] :
( ( ! [SY88: $i] :
( ( set_union2 @ SV48 @ SY88 )
= ( set_union2 @ SY88 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(415,plain,
! [SV49: $i] :
( ( ! [SY89: $i] :
( ( ordered_pair @ SV49 @ SY89 )
= ( unordered_pair @ ( unordered_pair @ SV49 @ SY89 ) @ ( singleton @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(416,plain,
! [SV50: $i] :
( ( ~ ( relation @ SV50 )
| ( ( relation_field @ SV50 )
= ( set_union2 @ ( relation_dom @ SV50 ) @ ( relation_rng @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(417,plain,
! [SV51: $i] :
( ( element @ ( sK10_B @ SV51 ) @ SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(418,plain,
! [SV52: $i] :
( ( ! [SY90: $i] :
~ ( empty @ ( ordered_pair @ SV52 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(419,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
| ! [SY91: $i] :
~ ( empty @ ( set_union2 @ SV53 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(420,plain,
! [SV54: $i] :
( ( ( empty @ SV54 )
| ! [SY92: $i] :
~ ( empty @ ( set_union2 @ SY92 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(421,plain,
! [SV55: $i] :
( ( ( set_union2 @ SV55 @ SV55 )
= SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(422,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(423,plain,
! [SV56: $i] :
( ( ( set_union2 @ SV56 @ empty_set )
= SV56 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(424,plain,
! [SV57: $i] :
( ( ! [SY93: $i] :
( ~ ( in @ SV57 @ SY93 )
| ( element @ SV57 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(425,plain,
! [SV58: $i] :
( ( ! [SY94: $i] :
( ~ ( element @ SV58 @ SY94 )
| ( empty @ SY94 )
| ( in @ SV58 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(426,plain,
! [SV59: $i] :
( ( ~ ( empty @ SV59 )
| ( SV59 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(427,plain,
! [SV60: $i] :
( ( ! [SY95: $i] :
( ~ ( empty @ SY95 )
| ~ ( in @ SV60 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(428,plain,
! [SV61: $i] :
( ( ! [SY96: $i] :
( ( SV61 = SY96 )
| ~ ( empty @ SV61 )
| ~ ( empty @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(429,plain,
( ( ~ ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) )
| ~ ( one_to_one @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(430,plain,
! [SV62: $i] :
( ( ~ ( ~ ! [SY97: $i,SY98: $i] :
( ~ ( relation @ SY98 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY97 ) @ SY98 )
| ( in @ SV62 @ ( relation_field @ SY98 ) ) )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ( relation @ SY100 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY99 ) @ SY100 )
| ( in @ SY99 @ ( relation_field @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(431,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(432,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ sK1_A )
| ( in @ ( ordered_pair @ SX0 @ SX2 ) @ sK1_A ) )
| ~ ~ ( transitive @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(433,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(434,plain,
! [SV63: $i] :
( ( ~ ( relation @ SV63 )
| ~ ( ~ ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY101 @ SV63 ) @ SY101 )
| ~ ( in @ ( sK12_SY55 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( sK13_SY57 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK12_SY55 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ( is_transitive_in @ SV63 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( is_transitive_in @ SV63 @ SY102 )
| ! [SY103: $i,SY104: $i,SY105: $i] :
( ~ ( in @ SY103 @ SY102 )
| ~ ( in @ SY104 @ SY102 )
| ~ ( in @ SY105 @ SY102 )
| ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY104 @ SY105 ) @ SV63 )
| ( in @ ( ordered_pair @ SY103 @ SY105 ) @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(435,plain,
( ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(436,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(437,plain,
! [SV64: $i,SV45: $i] :
( ( ~ ( in @ SV45 @ SV64 )
| ~ ( in @ SV64 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(438,plain,
! [SV46: $i] :
( ( ( ~ ( empty @ SV46 ) )
= $true )
| ( ( function @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(439,plain,
! [SV65: $i,SV47: $i] :
( ( ( unordered_pair @ SV47 @ SV65 )
= ( unordered_pair @ SV65 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(440,plain,
! [SV66: $i,SV48: $i] :
( ( ( set_union2 @ SV48 @ SV66 )
= ( set_union2 @ SV66 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(441,plain,
! [SV67: $i,SV49: $i] :
( ( ( ordered_pair @ SV49 @ SV67 )
= ( unordered_pair @ ( unordered_pair @ SV49 @ SV67 ) @ ( singleton @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(442,plain,
! [SV50: $i] :
( ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( ( relation_field @ SV50 )
= ( set_union2 @ ( relation_dom @ SV50 ) @ ( relation_rng @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(443,plain,
! [SV68: $i,SV52: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV52 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(444,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
= $true )
| ( ( ! [SY91: $i] :
~ ( empty @ ( set_union2 @ SV53 @ SY91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(445,plain,
! [SV54: $i] :
( ( ( empty @ SV54 )
= $true )
| ( ( ! [SY92: $i] :
~ ( empty @ ( set_union2 @ SY92 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(446,plain,
! [SV69: $i,SV57: $i] :
( ( ~ ( in @ SV57 @ SV69 )
| ( element @ SV57 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(447,plain,
! [SV70: $i,SV58: $i] :
( ( ~ ( element @ SV58 @ SV70 )
| ( empty @ SV70 )
| ( in @ SV58 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(448,plain,
! [SV59: $i] :
( ( ( ~ ( empty @ SV59 ) )
= $true )
| ( ( SV59 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(449,plain,
! [SV60: $i,SV71: $i] :
( ( ~ ( empty @ SV71 )
| ~ ( in @ SV60 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(450,plain,
! [SV72: $i,SV61: $i] :
( ( ( SV61 = SV72 )
| ~ ( empty @ SV61 )
| ~ ( empty @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(451,plain,
( ( ~ ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(452,plain,
( ( ~ ( one_to_one @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(453,plain,
! [SV62: $i] :
( ( ~ ! [SY97: $i,SY98: $i] :
( ~ ( relation @ SY98 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY97 ) @ SY98 )
| ( in @ SV62 @ ( relation_field @ SY98 ) ) )
| ~ ! [SY99: $i,SY100: $i] :
( ~ ( relation @ SY100 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY99 ) @ SY100 )
| ( in @ SY99 @ ( relation_field @ SY100 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(454,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(455,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(456,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ sK1_A )
| ( in @ ( ordered_pair @ SX0 @ SX2 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(457,plain,
( ( ~ ~ ( transitive @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(458,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(459,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(460,plain,
! [SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY101 @ SV63 ) @ SY101 )
| ~ ( in @ ( sK12_SY55 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( sK13_SY57 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK12_SY55 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ( is_transitive_in @ SV63 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( is_transitive_in @ SV63 @ SY102 )
| ! [SY103: $i,SY104: $i,SY105: $i] :
( ~ ( in @ SY103 @ SY102 )
| ~ ( in @ SY104 @ SY102 )
| ~ ( in @ SY105 @ SY102 )
| ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY104 @ SY105 ) @ SV63 )
| ( in @ ( ordered_pair @ SY103 @ SY105 ) @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(461,plain,
( ( ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(462,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(463,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(464,plain,
( ( ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(465,plain,
! [SV64: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV64 ) )
= $true )
| ( ( ~ ( in @ SV64 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(466,plain,
! [SV46: $i] :
( ( ( empty @ SV46 )
= $false )
| ( ( function @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(467,plain,
! [SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( ( relation_field @ SV50 )
= ( set_union2 @ ( relation_dom @ SV50 ) @ ( relation_rng @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(468,plain,
! [SV68: $i,SV52: $i] :
( ( empty @ ( ordered_pair @ SV52 @ SV68 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(469,plain,
! [SV73: $i,SV53: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV53 @ SV73 ) ) )
= $true )
| ( ( empty @ SV53 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(470,plain,
! [SV54: $i,SV74: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV74 @ SV54 ) ) )
= $true )
| ( ( empty @ SV54 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(471,plain,
! [SV69: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV69 ) )
= $true )
| ( ( element @ SV57 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(472,plain,
! [SV70: $i,SV58: $i] :
( ( ( ~ ( element @ SV58 @ SV70 ) )
= $true )
| ( ( ( empty @ SV70 )
| ( in @ SV58 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(473,plain,
! [SV59: $i] :
( ( ( empty @ SV59 )
= $false )
| ( ( SV59 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(474,plain,
! [SV60: $i,SV71: $i] :
( ( ( ~ ( empty @ SV71 ) )
= $true )
| ( ( ~ ( in @ SV60 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(475,plain,
! [SV72: $i,SV61: $i] :
( ( ( ( SV61 = SV72 )
| ~ ( empty @ SV61 ) )
= $true )
| ( ( ~ ( empty @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(476,plain,
( ( ~ ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(477,plain,
( ( one_to_one @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(478,plain,
! [SV62: $i] :
( ( ~ ! [SY97: $i,SY98: $i] :
( ~ ( relation @ SY98 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY97 ) @ SY98 )
| ( in @ SV62 @ ( relation_field @ SY98 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(479,plain,
! [SV62: $i] :
( ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( relation @ SY100 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY99 ) @ SY100 )
| ( in @ SY99 @ ( relation_field @ SY100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(480,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(481,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(482,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ sK1_A )
| ( in @ ( ordered_pair @ SX0 @ SX2 ) @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(483,plain,
( ( ~ ( transitive @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(484,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(485,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(486,plain,
! [SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( ~ ( ~ ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY101 @ SV63 ) @ SY101 )
| ~ ( in @ ( sK12_SY55 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( sK13_SY57 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK12_SY55 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ( is_transitive_in @ SV63 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( is_transitive_in @ SV63 @ SY102 )
| ! [SY103: $i,SY104: $i,SY105: $i] :
( ~ ( in @ SY103 @ SY102 )
| ~ ( in @ SY104 @ SY102 )
| ~ ( in @ SY105 @ SY102 )
| ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY104 @ SY105 ) @ SV63 )
| ( in @ ( ordered_pair @ SY103 @ SY105 ) @ SV63 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(487,plain,
( ( function @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(488,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(489,plain,
( ( ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(490,plain,
( ( function @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(491,plain,
! [SV64: $i,SV45: $i] :
( ( ( in @ SV45 @ SV64 )
= $false )
| ( ( ~ ( in @ SV64 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(492,plain,
! [SV73: $i,SV53: $i] :
( ( ( empty @ ( set_union2 @ SV53 @ SV73 ) )
= $false )
| ( ( empty @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(493,plain,
! [SV54: $i,SV74: $i] :
( ( ( empty @ ( set_union2 @ SV74 @ SV54 ) )
= $false )
| ( ( empty @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(494,plain,
! [SV69: $i,SV57: $i] :
( ( ( in @ SV57 @ SV69 )
= $false )
| ( ( element @ SV57 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(495,plain,
! [SV70: $i,SV58: $i] :
( ( ( element @ SV58 @ SV70 )
= $false )
| ( ( ( empty @ SV70 )
| ( in @ SV58 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(496,plain,
! [SV60: $i,SV71: $i] :
( ( ( empty @ SV71 )
= $false )
| ( ( ~ ( in @ SV60 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(497,plain,
! [SV72: $i,SV61: $i] :
( ( ( SV61 = SV72 )
= $true )
| ( ( ~ ( empty @ SV61 ) )
= $true )
| ( ( ~ ( empty @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(498,plain,
( ( ~ ( function @ sK5_A )
| ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(499,plain,
! [SV62: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ( relation @ SY98 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY97 ) @ SY98 )
| ( in @ SV62 @ ( relation_field @ SY98 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(500,plain,
! [SV62: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( relation @ SY100 )
| ~ ( in @ ( ordered_pair @ SV62 @ SY99 ) @ SY100 )
| ( in @ SY99 @ ( relation_field @ SY100 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(501,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(502,plain,
! [SV75: $i] :
( ( ~ ( empty @ SV75 )
| ~ ( relation @ SV75 )
| ~ ( function @ SV75 )
| ( one_to_one @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(503,plain,
! [SV76: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( in @ ( ordered_pair @ SV76 @ SY106 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SY106 @ SY107 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV76 @ SY107 ) @ sK1_A ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(504,plain,
( ( transitive @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(505,plain,
! [SV77: $i] :
( ( ~ ( relation @ SV77 )
| ~ ( is_transitive_in @ SV77 @ ( relation_field @ SV77 ) )
| ( transitive @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(506,plain,
! [SV78: $i] :
( ( ~ ( relation @ SV78 )
| ~ ( transitive @ SV78 )
| ( is_transitive_in @ SV78 @ ( relation_field @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(507,plain,
! [SV63: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY101 @ SV63 ) @ SY101 )
| ~ ( in @ ( sK12_SY55 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( sK13_SY57 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK12_SY55 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ( is_transitive_in @ SV63 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( is_transitive_in @ SV63 @ SY102 )
| ! [SY103: $i,SY104: $i,SY105: $i] :
( ~ ( in @ SY103 @ SY102 )
| ~ ( in @ SY104 @ SY102 )
| ~ ( in @ SY105 @ SY102 )
| ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY104 @ SY105 ) @ SV63 )
| ( in @ ( ordered_pair @ SY103 @ SY105 ) @ SV63 ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(508,plain,
( ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(509,plain,
! [SV45: $i,SV64: $i] :
( ( ( in @ SV64 @ SV45 )
= $false )
| ( ( in @ SV45 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(510,plain,
! [SV58: $i,SV70: $i] :
( ( ( empty @ SV70 )
= $true )
| ( ( in @ SV58 @ SV70 )
= $true )
| ( ( element @ SV58 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(511,plain,
! [SV71: $i,SV60: $i] :
( ( ( in @ SV60 @ SV71 )
= $false )
| ( ( empty @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(512,plain,
! [SV72: $i,SV61: $i] :
( ( ( empty @ SV61 )
= $false )
| ( ( SV61 = SV72 )
= $true )
| ( ( ~ ( empty @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(513,plain,
( ( ~ ( function @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(514,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(515,plain,
! [SV79: $i,SV62: $i] :
( ( ! [SY108: $i] :
( ~ ( relation @ SY108 )
| ~ ( in @ ( ordered_pair @ SV62 @ SV79 ) @ SY108 )
| ( in @ SV62 @ ( relation_field @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(516,plain,
! [SV80: $i,SV62: $i] :
( ( ! [SY109: $i] :
( ~ ( relation @ SY109 )
| ~ ( in @ ( ordered_pair @ SV62 @ SV80 ) @ SY109 )
| ( in @ SV80 @ ( relation_field @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(517,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(518,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(519,plain,
! [SV75: $i] :
( ( ( ~ ( empty @ SV75 )
| ~ ( relation @ SV75 )
| ~ ( function @ SV75 ) )
= $true )
| ( ( one_to_one @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(520,plain,
! [SV81: $i,SV76: $i] :
( ( ! [SY110: $i] :
( ~ ( in @ ( ordered_pair @ SV76 @ SV81 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV81 @ SY110 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV76 @ SY110 ) @ sK1_A ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(521,plain,
! [SV77: $i] :
( ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV77 @ ( relation_field @ SV77 ) )
| ( transitive @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(522,plain,
! [SV78: $i] :
( ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( transitive @ SV78 )
| ( is_transitive_in @ SV78 @ ( relation_field @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(523,plain,
! [SV63: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY101 @ SV63 ) @ SY101 )
| ~ ( in @ ( sK12_SY55 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( sK13_SY57 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK12_SY55 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ( is_transitive_in @ SV63 @ SY101 ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(524,plain,
! [SV63: $i] :
( ( ( ~ ! [SY102: $i] :
( ~ ( is_transitive_in @ SV63 @ SY102 )
| ! [SY103: $i,SY104: $i,SY105: $i] :
( ~ ( in @ SY103 @ SY102 )
| ~ ( in @ SY104 @ SY102 )
| ~ ( in @ SY105 @ SY102 )
| ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY104 @ SY105 ) @ SV63 )
| ( in @ ( ordered_pair @ SY103 @ SY105 ) @ SV63 ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(525,plain,
( ( ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(526,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(527,plain,
! [SV61: $i,SV72: $i] :
( ( ( empty @ SV72 )
= $false )
| ( ( SV61 = SV72 )
= $true )
| ( ( empty @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(528,plain,
( ( function @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(529,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(530,plain,
! [SV79: $i,SV62: $i,SV82: $i] :
( ( ~ ( relation @ SV82 )
| ~ ( in @ ( ordered_pair @ SV62 @ SV79 ) @ SV82 )
| ( in @ SV62 @ ( relation_field @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(531,plain,
! [SV80: $i,SV62: $i,SV83: $i] :
( ( ~ ( relation @ SV83 )
| ~ ( in @ ( ordered_pair @ SV62 @ SV80 ) @ SV83 )
| ( in @ SV80 @ ( relation_field @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(532,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(533,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(534,plain,
! [SV75: $i] :
( ( ( ~ ( empty @ SV75 )
| ~ ( relation @ SV75 ) )
= $true )
| ( ( ~ ( function @ SV75 ) )
= $true )
| ( ( one_to_one @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(535,plain,
! [SV84: $i,SV81: $i,SV76: $i] :
( ( ~ ( in @ ( ordered_pair @ SV76 @ SV81 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV81 @ SV84 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV76 @ SV84 ) @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(536,plain,
! [SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( ~ ( is_transitive_in @ SV77 @ ( relation_field @ SV77 ) )
| ( transitive @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(537,plain,
! [SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( ~ ( transitive @ SV78 )
| ( is_transitive_in @ SV78 @ ( relation_field @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(538,plain,
! [SV63: $i] :
( ( ( ! [SY101: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SY101 @ SV63 ) @ SY101 )
| ~ ( in @ ( sK12_SY55 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( sK13_SY57 @ SY101 @ SV63 ) @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK12_SY55 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SY101 @ SV63 ) @ ( sK13_SY57 @ SY101 @ SV63 ) ) @ SV63 ) )
| ( is_transitive_in @ SV63 @ SY101 ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(539,plain,
! [SV63: $i] :
( ( ( ! [SY102: $i] :
( ~ ( is_transitive_in @ SV63 @ SY102 )
| ! [SY103: $i,SY104: $i,SY105: $i] :
( ~ ( in @ SY103 @ SY102 )
| ~ ( in @ SY104 @ SY102 )
| ~ ( in @ SY105 @ SY102 )
| ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY104 @ SY105 ) @ SV63 )
| ( in @ ( ordered_pair @ SY103 @ SY105 ) @ SV63 ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(540,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(541,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(542,plain,
! [SV79: $i,SV62: $i,SV82: $i] :
( ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV62 @ SV79 ) @ SV82 )
| ( in @ SV62 @ ( relation_field @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(543,plain,
! [SV80: $i,SV62: $i,SV83: $i] :
( ( ( ~ ( relation @ SV83 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV62 @ SV80 ) @ SV83 )
| ( in @ SV80 @ ( relation_field @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(544,plain,
! [SV85: $i] :
( ( ~ ( empty @ SV85 )
| ~ ( relation @ SV85 )
| ~ ( function @ SV85 )
| ( function @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(545,plain,
! [SV86: $i] :
( ( ~ ( empty @ SV86 )
| ~ ( relation @ SV86 )
| ~ ( function @ SV86 )
| ( relation @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(546,plain,
! [SV75: $i] :
( ( ( ~ ( empty @ SV75 ) )
= $true )
| ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( ~ ( function @ SV75 ) )
= $true )
| ( ( one_to_one @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(547,plain,
! [SV84: $i,SV81: $i,SV76: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV76 @ SV81 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV81 @ SV84 ) @ sK1_A ) )
= $true )
| ( ( in @ ( ordered_pair @ SV76 @ SV84 ) @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(548,plain,
! [SV77: $i] :
( ( ( ~ ( is_transitive_in @ SV77 @ ( relation_field @ SV77 ) ) )
= $true )
| ( ( transitive @ SV77 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(549,plain,
! [SV78: $i] :
( ( ( ~ ( transitive @ SV78 ) )
= $true )
| ( ( is_transitive_in @ SV78 @ ( relation_field @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(550,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
| ( is_transitive_in @ SV63 @ SV87 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(551,plain,
! [SV88: $i,SV63: $i] :
( ( ( ~ ( is_transitive_in @ SV63 @ SV88 )
| ! [SY111: $i,SY112: $i,SY113: $i] :
( ~ ( in @ SY111 @ SV88 )
| ~ ( in @ SY112 @ SV88 )
| ~ ( in @ SY113 @ SV88 )
| ~ ( in @ ( ordered_pair @ SY111 @ SY112 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY112 @ SY113 ) @ SV63 )
| ( in @ ( ordered_pair @ SY111 @ SY113 ) @ SV63 ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(552,plain,
! [SV79: $i,SV62: $i,SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV62 @ SV79 ) @ SV82 )
| ( in @ SV62 @ ( relation_field @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(553,plain,
! [SV80: $i,SV62: $i,SV83: $i] :
( ( ( relation @ SV83 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV62 @ SV80 ) @ SV83 )
| ( in @ SV80 @ ( relation_field @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(554,plain,
! [SV85: $i] :
( ( ( ~ ( empty @ SV85 )
| ~ ( relation @ SV85 )
| ~ ( function @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(555,plain,
! [SV86: $i] :
( ( ( ~ ( empty @ SV86 )
| ~ ( relation @ SV86 )
| ~ ( function @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(556,plain,
! [SV75: $i] :
( ( ( empty @ SV75 )
= $false )
| ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( ~ ( function @ SV75 ) )
= $true )
| ( ( one_to_one @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(557,plain,
! [SV84: $i,SV81: $i,SV76: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV76 @ SV81 ) @ sK1_A ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV81 @ SV84 ) @ sK1_A ) )
= $true )
| ( ( in @ ( ordered_pair @ SV76 @ SV84 ) @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(558,plain,
! [SV77: $i] :
( ( ( is_transitive_in @ SV77 @ ( relation_field @ SV77 ) )
= $false )
| ( ( transitive @ SV77 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(559,plain,
! [SV78: $i] :
( ( ( transitive @ SV78 )
= $false )
| ( ( is_transitive_in @ SV78 @ ( relation_field @ SV78 ) )
= $true )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(560,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(561,plain,
! [SV88: $i,SV63: $i] :
( ( ( ~ ( is_transitive_in @ SV63 @ SV88 ) )
= $true )
| ( ( ! [SY111: $i,SY112: $i,SY113: $i] :
( ~ ( in @ SY111 @ SV88 )
| ~ ( in @ SY112 @ SV88 )
| ~ ( in @ SY113 @ SV88 )
| ~ ( in @ ( ordered_pair @ SY111 @ SY112 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY112 @ SY113 ) @ SV63 )
| ( in @ ( ordered_pair @ SY111 @ SY113 ) @ SV63 ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(562,plain,
! [SV82: $i,SV79: $i,SV62: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV62 @ SV79 ) @ SV82 ) )
= $true )
| ( ( in @ SV62 @ ( relation_field @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(563,plain,
! [SV83: $i,SV80: $i,SV62: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV62 @ SV80 ) @ SV83 ) )
= $true )
| ( ( in @ SV80 @ ( relation_field @ SV83 ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(564,plain,
! [SV85: $i] :
( ( ( ~ ( empty @ SV85 )
| ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( function @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(565,plain,
! [SV86: $i] :
( ( ( ~ ( empty @ SV86 )
| ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(566,plain,
! [SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( empty @ SV75 )
= $false )
| ( ( ~ ( function @ SV75 ) )
= $true )
| ( ( one_to_one @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(567,plain,
! [SV84: $i,SV81: $i,SV76: $i] :
( ( ( in @ ( ordered_pair @ SV76 @ SV81 ) @ sK1_A )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV81 @ SV84 ) @ sK1_A ) )
= $true )
| ( ( in @ ( ordered_pair @ SV76 @ SV84 ) @ sK1_A )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(568,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(569,plain,
! [SV88: $i,SV63: $i] :
( ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( ! [SY111: $i,SY112: $i,SY113: $i] :
( ~ ( in @ SY111 @ SV88 )
| ~ ( in @ SY112 @ SV88 )
| ~ ( in @ SY113 @ SV88 )
| ~ ( in @ ( ordered_pair @ SY111 @ SY112 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY112 @ SY113 ) @ SV63 )
| ( in @ ( ordered_pair @ SY111 @ SY113 ) @ SV63 ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(570,plain,
! [SV82: $i,SV79: $i,SV62: $i] :
( ( ( in @ ( ordered_pair @ SV62 @ SV79 ) @ SV82 )
= $false )
| ( ( in @ SV62 @ ( relation_field @ SV82 ) )
= $true )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(571,plain,
! [SV83: $i,SV80: $i,SV62: $i] :
( ( ( in @ ( ordered_pair @ SV62 @ SV80 ) @ SV83 )
= $false )
| ( ( in @ SV80 @ ( relation_field @ SV83 ) )
= $true )
| ( ( relation @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(572,plain,
! [SV85: $i] :
( ( ( ~ ( empty @ SV85 ) )
= $true )
| ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( function @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(573,plain,
! [SV86: $i] :
( ( ( ~ ( empty @ SV86 ) )
= $true )
| ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(574,plain,
! [SV75: $i] :
( ( ( function @ SV75 )
= $false )
| ( ( empty @ SV75 )
= $false )
| ( ( relation @ SV75 )
= $false )
| ( ( one_to_one @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(575,plain,
! [SV76: $i,SV84: $i,SV81: $i] :
( ( ( in @ ( ordered_pair @ SV81 @ SV84 ) @ sK1_A )
= $false )
| ( ( in @ ( ordered_pair @ SV76 @ SV81 ) @ sK1_A )
= $false )
| ( ( in @ ( ordered_pair @ SV76 @ SV84 ) @ sK1_A )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(576,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(577,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(578,plain,
! [SV63: $i,SV88: $i,SV89: $i] :
( ( ( ! [SY114: $i,SY115: $i] :
( ~ ( in @ SV89 @ SV88 )
| ~ ( in @ SY114 @ SV88 )
| ~ ( in @ SY115 @ SV88 )
| ~ ( in @ ( ordered_pair @ SV89 @ SY114 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SY114 @ SY115 ) @ SV63 )
| ( in @ ( ordered_pair @ SV89 @ SY115 ) @ SV63 ) ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(579,plain,
! [SV85: $i] :
( ( ( empty @ SV85 )
= $false )
| ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( function @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(580,plain,
! [SV86: $i] :
( ( ( empty @ SV86 )
= $false )
| ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(581,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(582,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(583,plain,
! [SV63: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( ! [SY116: $i] :
( ~ ( in @ SV89 @ SV88 )
| ~ ( in @ SV90 @ SV88 )
| ~ ( in @ SY116 @ SV88 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SV90 @ SY116 ) @ SV63 )
| ( in @ ( ordered_pair @ SV89 @ SY116 ) @ SV63 ) ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(584,plain,
! [SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( empty @ SV85 )
= $false )
| ( ( ~ ( function @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(585,plain,
! [SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( empty @ SV86 )
= $false )
| ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( relation @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(586,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(587,plain,
! [SV63: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(588,plain,
! [SV63: $i,SV91: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV88 )
| ~ ( in @ SV90 @ SV88 )
| ~ ( in @ SV91 @ SV88 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 )
| ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(589,plain,
! [SV85: $i] :
( ( ( function @ SV85 )
= $false )
| ( ( empty @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false )
| ( ( function @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(590,plain,
! [SV86: $i] :
( ( ( function @ SV86 )
= $false )
| ( ( empty @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(591,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(592,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(593,plain,
! [SV63: $i,SV91: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV88 )
| ~ ( in @ SV90 @ SV88 )
| ~ ( in @ SV91 @ SV88 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 )
| ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(594,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(595,plain,
! [SV63: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_SY55 @ SV87 @ SV63 ) @ ( sK13_SY57 @ SV87 @ SV63 ) ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(596,plain,
! [SV63: $i,SV91: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV88 )
| ~ ( in @ SV90 @ SV88 )
| ~ ( in @ SV91 @ SV88 )
| ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(597,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(598,plain,
! [SV63: $i,SV91: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV88 )
| ~ ( in @ SV90 @ SV88 )
| ~ ( in @ SV91 @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(599,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(600,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(601,plain,
! [SV63: $i,SV91: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV88 )
| ~ ( in @ SV90 @ SV88 ) )
= $true )
| ( ( ~ ( in @ SV91 @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(602,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(603,plain,
! [SV63: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_C @ SV87 @ SV63 ) @ ( sK12_SY55 @ SV87 @ SV63 ) ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(604,plain,
! [SV63: $i,SV91: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( ~ ( in @ SV89 @ SV88 ) )
= $true )
| ( ( ~ ( in @ SV90 @ SV88 ) )
= $true )
| ( ( ~ ( in @ SV91 @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(605,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
| ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(606,plain,
! [SV63: $i,SV91: $i,SV90: $i,SV88: $i,SV89: $i] :
( ( ( in @ SV89 @ SV88 )
= $false )
| ( ( ~ ( in @ SV90 @ SV88 ) )
= $true )
| ( ( ~ ( in @ SV91 @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(607,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(608,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(609,plain,
! [SV63: $i,SV91: $i,SV89: $i,SV88: $i,SV90: $i] :
( ( ( in @ SV90 @ SV88 )
= $false )
| ( ( in @ SV89 @ SV88 )
= $false )
| ( ( ~ ( in @ SV91 @ SV88 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(610,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) ) )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(611,plain,
! [SV63: $i,SV87: $i] :
( ( ( in @ ( sK13_SY57 @ SV87 @ SV63 ) @ SV87 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(612,plain,
! [SV63: $i,SV90: $i,SV89: $i,SV88: $i,SV91: $i] :
( ( ( in @ SV91 @ SV88 )
= $false )
| ( ( in @ SV89 @ SV88 )
= $false )
| ( ( in @ SV90 @ SV88 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(613,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
| ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(614,plain,
! [SV91: $i,SV88: $i,SV63: $i,SV90: $i,SV89: $i] :
( ( ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 )
= $false )
| ( ( in @ SV90 @ SV88 )
= $false )
| ( ( in @ SV89 @ SV88 )
= $false )
| ( ( in @ SV91 @ SV88 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(615,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(616,plain,
! [SV63: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 ) )
= $false )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(617,plain,
! [SV89: $i,SV88: $i,SV63: $i,SV91: $i,SV90: $i] :
( ( ( in @ ( ordered_pair @ SV90 @ SV91 ) @ SV63 )
= $false )
| ( ( in @ SV91 @ SV88 )
= $false )
| ( ( in @ SV89 @ SV88 )
= $false )
| ( ( in @ SV90 @ SV88 )
= $false )
| ( ( in @ ( ordered_pair @ SV89 @ SV90 ) @ SV63 )
= $false )
| ( ( in @ ( ordered_pair @ SV89 @ SV91 ) @ SV63 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV88 )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(618,plain,
! [SV63: $i,SV87: $i] :
( ( ( in @ ( sK11_C @ SV87 @ SV63 ) @ SV87 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(619,plain,
! [SV63: $i,SV87: $i] :
( ( ( in @ ( sK12_SY55 @ SV87 @ SV63 ) @ SV87 )
= $true )
| ( ( is_transitive_in @ SV63 @ SV87 )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(620,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[374,619,618,617,611,603,595,590,589,587,575,574,571,570,559,558,541,540,529,528,527,511,510,509,504,494,493,492,490,488,487,477,473,468,467,466,441,440,439,423,422,421,417,401,390,384,382,381,380,379,378,377,376,375]) ).
thf(621,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[620,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU240+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 01:11:29 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 36
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.37 .
% 0.14/0.37 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:38,loop_count:0,foatp_calls:0,translation:fof_full)...........................
% 0.60/0.87
% 0.60/0.87 ********************************
% 0.60/0.87 * All subproblems solved! *
% 0.60/0.87 ********************************
% 0.60/0.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:37,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:620,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.83/1.03
% 0.83/1.03 %**** Beginning of derivation protocol ****
% 0.83/1.03 % SZS output start CNFRefutation
% See solution above
% 0.83/1.03
% 0.83/1.03 %**** End of derivation protocol ****
% 0.83/1.03 %**** no. of clauses in derivation: 621 ****
% 0.83/1.03 %**** clause counter: 620 ****
% 0.83/1.03
% 0.83/1.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:37,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:620,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------