%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:33 AM UTC 2026
% Result : Theorem 6.65s 1.33s
% Output : CNFRefutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 29
% Syntax : Number of formulae : 753 ( 386 unt; 0 typ; 0 def)
% Number of atoms : 5957 (2012 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 10817 (2752 ~;1918 |; 127 &;5929 @)
% ( 19 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 18 con; 0-3 aty)
% Number of variables : 1332 ( 0 ^;1308 !; 24 ?;1332 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_sK10_SY64,type,
sK10_SY64: $i > $i > $i > $i ).
thf(tp_sK11_SY66,type,
sK11_SY66: $i > $i > $i > $i ).
thf(tp_sK12_SX0,type,
sK12_SX0: $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i ).
thf(tp_sK14_SX0,type,
sK14_SX0: $i ).
thf(tp_sK15_SX0,type,
sK15_SX0: $i ).
thf(tp_sK16_SX0,type,
sK16_SX0: $i ).
thf(tp_sK17_SX0,type,
sK17_SX0: $i ).
thf(tp_sK18_SY90,type,
sK18_SY90: $i > $i > $i > $i ).
thf(tp_sK19_SY92,type,
sK19_SY92: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY38,type,
sK2_SY38: $i ).
thf(tp_sK3_SY40,type,
sK3_SY40: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $i ).
thf(tp_sK9_SX0,type,
sK9_SX0: $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_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(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(8,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(9,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(11,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(14,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(15,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(17,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(18,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(19,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(24,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(31,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
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 )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(36,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(38,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
thf(39,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[38]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(45,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(46,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(47,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(48,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(49,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(50,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(53,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(57,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(62,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[31]) ).
thf(64,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(65,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(66,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(69,plain,
( ( ! [SY38: $i,SY39: $i] :
( ( ( relation @ SY39 )
& ( function @ SY39 ) )
=> ( ( in @ SY38 @ ( relation_dom @ ( relation_dom_restriction @ SY39 @ sK1_A ) ) )
<=> ( ( in @ SY38 @ ( relation_dom @ SY39 ) )
& ( in @ SY38 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(70,plain,
( ( ! [SY40: $i] :
( ( ( relation @ SY40 )
& ( function @ SY40 ) )
=> ( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ SY40 @ sK1_A ) ) )
<=> ( ( in @ sK2_SY38 @ ( relation_dom @ SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(71,plain,
( ( ( ( relation @ sK3_SY40 )
& ( function @ sK3_SY40 ) )
=> ( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
<=> ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(72,plain,
( ( relation @ sK3_SY40 )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(73,plain,
( ( function @ sK3_SY40 )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(74,plain,
( ( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
<=> ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(75,plain,
( ( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
=> ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[74]) ).
thf(76,plain,
( ( ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) )
=> ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[74]) ).
thf(77,plain,
( ( ~ ( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
=> ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(78,plain,
( ( ~ ( ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) )
=> ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[76]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(80,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(81,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(83,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(84,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(85,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(86,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(87,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(89,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(90,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(94,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(97,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(98,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(99,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(100,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(101,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(102,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(107,plain,
( ( function @ sK3_SY40 )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(108,plain,
( ( relation @ sK3_SY40 )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(109,plain,
( ( ~ ( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
=> ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(113,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(115,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(116,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(118,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ! [SX2: $i] :
( ~ ~ ( ~ ( relation @ SX2 )
| ~ ( function @ SX2 ) )
| ~ ( ~ ( ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ~ ( ( ( relation_dom @ SX1 )
!= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX1 ) )
| ( ( apply @ SX1 @ SX3 )
= ( apply @ SX2 @ SX3 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SX1 )
!= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX1 ) )
| ( ( apply @ SX1 @ SX3 )
= ( apply @ SX2 @ SX3 ) ) ) )
| ( SX1
= ( relation_dom_restriction @ SX2 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(120,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(121,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(122,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(123,plain,
( ( ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
| ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(124,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(125,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(126,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(128,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) )
| ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(130,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(133,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(134,plain,
! [SV1: $i] :
( ( ! [SY41: $i] :
( ~ ( relation @ SV1 )
| ( relation @ ( relation_dom_restriction @ SV1 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(135,plain,
! [SV2: $i] :
( ( ! [SY42: $i,SY43: $i] :
~ ( ~ ( ( SY43
!= ( set_intersection2 @ SV2 @ SY42 ) )
| ! [SY44: $i] :
~ ( ~ ( ~ ( in @ SY44 @ SY43 )
| ~ ( ~ ( in @ SY44 @ SV2 )
| ~ ( in @ SY44 @ SY42 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY44 @ SV2 )
| ~ ( in @ SY44 @ SY42 ) )
| ( in @ SY44 @ SY43 ) ) ) )
| ~ ( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SY43 )
| ~ ( ~ ( in @ SY45 @ SV2 )
| ~ ( in @ SY45 @ SY42 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY45 @ SV2 )
| ~ ( in @ SY45 @ SY42 ) )
| ( in @ SY45 @ SY43 ) ) )
| ( SY43
= ( set_intersection2 @ SV2 @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(136,plain,
! [SV3: $i] :
( ( ! [SY46: $i] :
( ~ ~ ( ~ ( relation @ SV3 )
| ~ ( relation @ SY46 ) )
| ( relation @ ( set_intersection2 @ SV3 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(137,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) )
| ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(138,plain,
! [SV5: $i] :
( ( ! [SY47: $i] :
( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SY47 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(139,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(140,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(141,plain,
! [SV6: $i] :
( ( ! [SY48: $i] :
( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( relation_empty_yielding @ SV6 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SY48 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(142,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(143,plain,
! [SV7: $i] :
( ( ! [SY49: $i] :
( ~ ~ ( ~ ( relation @ SY49 )
| ~ ( function @ SY49 ) )
| ! [SY50: $i] :
( ~ ~ ( ~ ( relation @ SY50 )
| ~ ( function @ SY50 ) )
| ~ ( ~ ( ( SY49
!= ( relation_dom_restriction @ SY50 @ SV7 ) )
| ~ ( ( ( relation_dom @ SY49 )
!= ( set_intersection2 @ ( relation_dom @ SY50 ) @ SV7 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY49 ) )
| ( ( apply @ SY49 @ SX3 )
= ( apply @ SY50 @ SX3 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SY49 )
!= ( set_intersection2 @ ( relation_dom @ SY50 ) @ SV7 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY49 ) )
| ( ( apply @ SY49 @ SX3 )
= ( apply @ SY50 @ SX3 ) ) ) )
| ( SY49
= ( relation_dom_restriction @ SY50 @ SV7 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(144,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(145,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(146,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(147,plain,
( ( ~ ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
| ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(148,plain,
! [SV8: $i] :
( ( ~ ( empty @ SV8 )
| ( relation @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(149,plain,
! [SV9: $i] :
( ( ~ ( empty @ SV9 )
| ~ ( ~ ( empty @ ( relation_dom @ SV9 ) )
| ~ ( relation @ ( relation_dom @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(150,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(151,plain,
! [SV10: $i] :
( ( ! [SY53: $i] :
( ~ ( in @ SV10 @ SY53 )
| ~ ( in @ SY53 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(152,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( empty @ SV11 ) )
| ~ ( function @ SV11 ) )
| ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(153,plain,
! [SV12: $i] :
( ( ! [SY54: $i] :
~ ~ ( ~ ( in @ SV12 @ SY54 )
| ~ ( empty @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(154,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(155,plain,
! [SV13: $i] :
( ( ! [SY55: $i] :
( ~ ( in @ SV13 @ SY55 )
| ( element @ SV13 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(156,plain,
! [SV14: $i] :
( ( ! [SY56: $i] :
( ~ ( element @ SV14 @ SY56 )
| ( empty @ SY56 )
| ( in @ SV14 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(157,plain,
! [SV15: $i] :
( ( ~ ( empty @ SV15 )
| ( function @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(158,plain,
! [SV16: $i,SV1: $i] :
( ( ~ ( relation @ SV1 )
| ( relation @ ( relation_dom_restriction @ SV1 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(159,plain,
! [SV17: $i,SV2: $i] :
( ( ! [SY57: $i] :
~ ( ~ ( ( SY57
!= ( set_intersection2 @ SV2 @ SV17 ) )
| ! [SY58: $i] :
~ ( ~ ( ~ ( in @ SY58 @ SY57 )
| ~ ( ~ ( in @ SY58 @ SV2 )
| ~ ( in @ SY58 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY58 @ SV2 )
| ~ ( in @ SY58 @ SV17 ) )
| ( in @ SY58 @ SY57 ) ) ) )
| ~ ( ~ ! [SY59: $i] :
~ ( ~ ( ~ ( in @ SY59 @ SY57 )
| ~ ( ~ ( in @ SY59 @ SV2 )
| ~ ( in @ SY59 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY59 @ SV2 )
| ~ ( in @ SY59 @ SV17 ) )
| ( in @ SY59 @ SY57 ) ) )
| ( SY57
= ( set_intersection2 @ SV2 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(160,plain,
! [SV18: $i,SV3: $i] :
( ( ~ ~ ( ~ ( relation @ SV3 )
| ~ ( relation @ SV18 ) )
| ( relation @ ( set_intersection2 @ SV3 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(161,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(162,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(163,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[139]) ).
thf(164,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[140]) ).
thf(165,plain,
! [SV20: $i,SV6: $i] :
( ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( relation_empty_yielding @ SV6 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(166,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(167,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(168,plain,
! [SV7: $i,SV21: $i] :
( ( ~ ~ ( ~ ( relation @ SV21 )
| ~ ( function @ SV21 ) )
| ! [SY60: $i] :
( ~ ~ ( ~ ( relation @ SY60 )
| ~ ( function @ SY60 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SY60 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY61 )
= ( apply @ SY60 @ SY61 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY62 )
= ( apply @ SY60 @ SY62 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SY60 @ SV7 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(169,plain,
( ( ~ ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[144]) ).
thf(170,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[145]) ).
thf(171,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(172,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(173,plain,
( ( ~ ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(174,plain,
( ( ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(175,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(176,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV9 ) )
| ~ ( relation @ ( relation_dom @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(177,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(178,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV22 )
| ~ ( in @ SV22 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(179,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( empty @ SV11 ) )
| ~ ( function @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(180,plain,
! [SV23: $i,SV12: $i] :
( ( ~ ~ ( ~ ( in @ SV12 @ SV23 )
| ~ ( empty @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(181,plain,
( ( ~ ~ ( ~ ( relation @ sK9_SX0 )
| ~ ( relation_empty_yielding @ sK9_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[154]) ).
thf(182,plain,
! [SV24: $i,SV13: $i] :
( ( ~ ( in @ SV13 @ SV24 )
| ( element @ SV13 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(183,plain,
! [SV25: $i,SV14: $i] :
( ( ~ ( element @ SV14 @ SV25 )
| ( empty @ SV25 )
| ( in @ SV14 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(184,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( function @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(185,plain,
! [SV16: $i,SV1: $i] :
( ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV1 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(186,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ~ ( ~ ( ( SV26
!= ( set_intersection2 @ SV2 @ SV17 ) )
| ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SV26 )
| ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) )
| ( in @ SY63 @ SV26 ) ) ) )
| ~ ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV26 )
| ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) )
| ( in @ SY64 @ SV26 ) ) )
| ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(187,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV3 )
| ~ ( relation @ SV18 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(188,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(189,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(190,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(191,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(192,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( relation_empty_yielding @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(193,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(194,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(195,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV21 )
| ~ ( function @ SV21 ) ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ~ ( ~ ( relation @ SY60 )
| ~ ( function @ SY60 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SY60 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY61 )
= ( apply @ SY60 @ SY61 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY62 )
= ( apply @ SY60 @ SY62 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SY60 @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(196,plain,
( ( ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(197,plain,
( ( ~ ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(198,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(199,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(200,plain,
( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(201,plain,
( ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(202,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(203,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV9 ) )
| ~ ( relation @ ( relation_dom @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(204,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(205,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV22 ) )
= $true )
| ( ( ~ ( in @ SV22 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(206,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( empty @ SV11 ) )
| ~ ( function @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(207,plain,
! [SV23: $i,SV12: $i] :
( ( ~ ( ~ ( in @ SV12 @ SV23 )
| ~ ( empty @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(208,plain,
( ( ~ ( ~ ( relation @ sK9_SX0 )
| ~ ( relation_empty_yielding @ sK9_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(209,plain,
! [SV24: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ SV24 ) )
= $true )
| ( ( element @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(210,plain,
! [SV25: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ SV25 ) )
= $true )
| ( ( ( empty @ SV25 )
| ( in @ SV14 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(211,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( function @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(212,plain,
! [SV16: $i,SV1: $i] :
( ( ( relation @ SV1 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV1 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(213,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ~ ( ( SV26
!= ( set_intersection2 @ SV2 @ SV17 ) )
| ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SV26 )
| ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) )
| ( in @ SY63 @ SV26 ) ) ) )
| ~ ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV26 )
| ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) )
| ( in @ SY64 @ SV26 ) ) )
| ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(214,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( ~ ( relation @ SV3 )
| ~ ( relation @ SV18 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(215,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ SV4 )
| ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(216,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(217,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(218,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(219,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ( relation @ SV6 )
| ~ ( relation_empty_yielding @ SV6 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(220,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(221,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( ~ ( relation @ SV21 )
| ~ ( function @ SV21 ) ) )
= $false )
| ( ( ! [SY60: $i] :
( ~ ~ ( ~ ( relation @ SY60 )
| ~ ( function @ SY60 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SY60 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY61 )
= ( apply @ SY60 @ SY61 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY62 )
= ( apply @ SY60 @ SY62 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SY60 @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(222,plain,
( ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(223,plain,
( ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(224,plain,
( ( ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) ) )
= $true )
| ( ( ~ ( in @ sK2_SY38 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(225,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV9 ) )
| ~ ( relation @ ( relation_dom @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(226,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(227,plain,
! [SV22: $i,SV10: $i] :
( ( ( in @ SV10 @ SV22 )
= $false )
| ( ( ~ ( in @ SV22 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(228,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( empty @ SV11 ) )
| ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(229,plain,
! [SV23: $i,SV12: $i] :
( ( ~ ( in @ SV12 @ SV23 )
| ~ ( empty @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(230,plain,
( ( ~ ( relation @ sK9_SX0 )
| ~ ( relation_empty_yielding @ sK9_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(231,plain,
! [SV24: $i,SV13: $i] :
( ( ( in @ SV13 @ SV24 )
= $false )
| ( ( element @ SV13 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(232,plain,
! [SV25: $i,SV14: $i] :
( ( ( element @ SV14 @ SV25 )
= $false )
| ( ( ( empty @ SV25 )
| ( in @ SV14 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(233,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ~ ( ( SV26
!= ( set_intersection2 @ SV2 @ SV17 ) )
| ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SV26 )
| ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) )
| ( in @ SY63 @ SV26 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(234,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ~ ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV26 )
| ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) )
| ( in @ SY64 @ SV26 ) ) )
| ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(235,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( relation @ SV3 )
| ~ ( relation @ SV18 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(236,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ SV4 ) )
= $true )
| ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(237,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(238,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(239,plain,
( ( ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(240,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(241,plain,
( ( ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(242,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ SV6 )
| ~ ( relation_empty_yielding @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(243,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(244,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(245,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( relation @ SV21 )
| ~ ( function @ SV21 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ~ ( ~ ( relation @ SY60 )
| ~ ( function @ SY60 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SY60 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY61 )
= ( apply @ SY60 @ SY61 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY62 )
= ( apply @ SY60 @ SY62 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SY60 @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(246,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(247,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(248,plain,
( ( ~ ~ ( empty @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(249,plain,
( ( ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(250,plain,
( ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
= $false )
| ( ( ~ ( in @ sK2_SY38 @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(251,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(252,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(253,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(254,plain,
( ( ~ ( one_to_one @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(255,plain,
! [SV10: $i,SV22: $i] :
( ( ( in @ SV22 @ SV10 )
= $false )
| ( ( in @ SV10 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(256,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( empty @ SV11 ) ) )
= $true )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(257,plain,
! [SV23: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV23 ) )
= $true )
| ( ( ~ ( empty @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(258,plain,
( ( ~ ( relation @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(259,plain,
( ( ~ ( relation_empty_yielding @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(260,plain,
! [SV14: $i,SV25: $i] :
( ( ( empty @ SV25 )
= $true )
| ( ( in @ SV14 @ SV25 )
= $true )
| ( ( element @ SV14 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(261,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ( SV26
!= ( set_intersection2 @ SV2 @ SV17 ) )
| ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SV26 )
| ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) )
| ( in @ SY63 @ SV26 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(262,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV26 )
| ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) )
| ( in @ SY64 @ SV26 ) ) )
| ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(263,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(264,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $false )
| ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(265,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(266,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(267,plain,
( ( function @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(268,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(269,plain,
( ( function @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(270,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(271,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(272,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(273,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( function @ SV21 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ~ ( ~ ( relation @ SY60 )
| ~ ( function @ SY60 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SY60 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY61 )
= ( apply @ SY60 @ SY61 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY62 )
= ( apply @ SY60 @ SY62 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SY60 @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(274,plain,
( ( empty @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(275,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(276,plain,
( ( ~ ( empty @ sK7_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(277,plain,
( ( relation @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(278,plain,
( ( ( in @ sK2_SY38 @ sK1_A )
= $false )
| ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(279,plain,
! [SV9: $i] :
( ( ( empty @ ( relation_dom @ SV9 ) )
= $true )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(280,plain,
! [SV9: $i] :
( ( ( relation @ ( relation_dom @ SV9 ) )
= $true )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(281,plain,
( ( ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(282,plain,
( ( one_to_one @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(283,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( relation @ SV11 )
| ~ ( empty @ SV11 ) ) )
= $false )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(284,plain,
! [SV23: $i,SV12: $i] :
( ( ( in @ SV12 @ SV23 )
= $false )
| ( ( ~ ( empty @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(285,plain,
( ( relation @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(286,plain,
( ( relation_empty_yielding @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(287,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ( SV26
!= ( set_intersection2 @ SV2 @ SV17 ) )
= $true )
| ( ( ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SV26 )
| ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) )
| ( in @ SY63 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(288,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ( ~ ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV26 )
| ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) )
| ( in @ SY64 @ SV26 ) ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(289,plain,
! [SV18: $i,SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(290,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(291,plain,
! [SV19: $i,SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(292,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(293,plain,
! [SV20: $i,SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(294,plain,
! [SV7: $i,SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( ~ ( function @ SV21 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ~ ( ~ ( relation @ SY60 )
| ~ ( function @ SY60 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SY60 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY61 )
= ( apply @ SY60 @ SY61 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY62 )
= ( apply @ SY60 @ SY62 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SY60 @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(295,plain,
( ( empty @ sK7_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(296,plain,
( ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(297,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 )
| ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(298,plain,
! [SV12: $i,SV23: $i] :
( ( ( empty @ SV23 )
= $false )
| ( ( in @ SV12 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(299,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false )
| ( ( ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SV26 )
| ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV2 )
| ~ ( in @ SY63 @ SV17 ) )
| ( in @ SY63 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV17: $i,SV2: $i,SV26: $i] :
( ( ( ! [SY64: $i] :
~ ( ~ ( ~ ( in @ SY64 @ SV26 )
| ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY64 @ SV2 )
| ~ ( in @ SY64 @ SV17 ) )
| ( in @ SY64 @ SV26 ) ) ) )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(301,plain,
! [SV3: $i,SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( relation @ SV3 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(302,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( empty @ SV4 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(303,plain,
! [SV19: $i,SV5: $i] :
( ( ( function @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(304,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(305,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(306,plain,
! [SV20: $i,SV6: $i] :
( ( ( relation_empty_yielding @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(307,plain,
! [SV7: $i,SV21: $i] :
( ( ( function @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( ! [SY60: $i] :
( ~ ~ ( ~ ( relation @ SY60 )
| ~ ( function @ SY60 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SY60 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY61: $i] :
( ~ ( in @ SY61 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY61 )
= ( apply @ SY60 @ SY61 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SY60 ) @ SV7 ) )
| ~ ! [SY62: $i] :
( ~ ( in @ SY62 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY62 )
= ( apply @ SY60 @ SY62 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SY60 @ SV7 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(308,plain,
( ( ~ ( relation @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(309,plain,
( ( ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(310,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(311,plain,
! [SV17: $i,SV2: $i,SV26: $i,SV27: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV27 @ SV26 )
| ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) )
| ( in @ SV27 @ SV26 ) ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(312,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
| ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) ) )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[300]) ).
thf(313,plain,
! [SV4: $i] :
( ( ( empty @ ( relation_dom @ SV4 ) )
= $false )
| ( ( empty @ SV4 )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(314,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
| ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(315,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(316,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(317,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( relation_empty_yielding @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(318,plain,
! [SV7: $i,SV21: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV28 )
| ~ ( function @ SV28 ) )
| ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(319,plain,
( ( relation @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(320,plain,
( ( function @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(321,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(322,plain,
! [SV17: $i,SV2: $i,SV26: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ SV26 )
| ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) )
| ( in @ SV27 @ SV26 ) ) )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(323,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
| ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(324,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(325,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(326,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) ) )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( relation_empty_yielding @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(327,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) ) )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( relation_empty_yielding @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(328,plain,
! [SV7: $i,SV21: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV28 )
| ~ ( function @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(329,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(330,plain,
! [SV17: $i,SV2: $i,SV26: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ SV26 )
| ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) ) )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(331,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) )
| ( in @ SV27 @ SV26 ) ) )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(332,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
| ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(333,plain,
! [SV19: $i,SV5: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV5 @ SV19 ) )
= $true )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(334,plain,
! [SV19: $i,SV5: $i] :
( ( ( function @ ( relation_dom_restriction @ SV5 @ SV19 ) )
= $true )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(335,plain,
! [SV20: $i,SV6: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV6 @ SV20 ) )
= $true )
| ( ( relation @ SV6 )
= $false )
| ( ( relation_empty_yielding @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(336,plain,
! [SV20: $i,SV6: $i] :
( ( ( relation_empty_yielding @ ( relation_dom_restriction @ SV6 @ SV20 ) )
= $true )
| ( ( relation @ SV6 )
= $false )
| ( ( relation_empty_yielding @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(337,plain,
! [SV7: $i,SV21: $i,SV28: $i] :
( ( ( ~ ( ~ ( relation @ SV28 )
| ~ ( function @ SV28 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(338,plain,
! [SV11: $i] :
( ( ( function @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( empty @ SV11 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(339,plain,
! [SV17: $i,SV2: $i,SV26: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV26 )
| ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(340,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) )
| ( in @ SV27 @ SV26 ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(341,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
| ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(342,plain,
! [SV7: $i,SV21: $i,SV28: $i] :
( ( ( ~ ( relation @ SV28 )
| ~ ( function @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(343,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( one_to_one @ SV11 ) )
= $false )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(344,plain,
! [SV17: $i,SV2: $i,SV26: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(345,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) )
= $true )
| ( ( in @ SV27 @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(346,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(347,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(348,plain,
! [SV7: $i,SV21: $i,SV28: $i] :
( ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ~ ( function @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(349,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) ) )
= $false )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(350,plain,
! [SV11: $i] :
( ( ( ~ ( one_to_one @ SV11 ) )
= $false )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(351,plain,
! [SV17: $i,SV2: $i,SV26: $i,SV27: $i] :
( ( ( in @ SV27 @ SV26 )
= $false )
| ( ( ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(352,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) ) )
= $false )
| ( ( in @ SV27 @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(353,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(354,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(355,plain,
! [SV7: $i,SV21: $i,SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( ~ ( function @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(356,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) ) )
= $true )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(357,plain,
! [SV11: $i] :
( ( ( one_to_one @ SV11 )
= $true )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(358,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) )
= $false )
| ( ( in @ SV27 @ SV26 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(359,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV2 )
| ~ ( in @ SV27 @ SV17 ) )
= $true )
| ( ( in @ SV27 @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(360,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(361,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 ) )
= $true )
| ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(362,plain,
! [SV7: $i,SV21: $i,SV28: $i] :
( ( ( function @ SV28 )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( ~ ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(363,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
= $false )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(364,plain,
! [SV17: $i,SV26: $i,SV2: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV2 ) )
= $false )
| ( ( in @ SV27 @ SV26 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(365,plain,
! [SV2: $i,SV26: $i,SV17: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV17 ) )
= $false )
| ( ( in @ SV27 @ SV26 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(366,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ SV2 ) )
= $true )
| ( ( ~ ( in @ SV27 @ SV17 ) )
= $true )
| ( ( in @ SV27 @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(367,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(368,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(369,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(370,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(371,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $false )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(372,plain,
! [SV11: $i] :
( ( ( ~ ( function @ SV11 ) )
= $false )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(373,plain,
! [SV17: $i,SV26: $i,SV2: $i,SV27: $i] :
( ( ( in @ SV27 @ SV2 )
= $true )
| ( ( in @ SV27 @ SV26 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(374,plain,
! [SV2: $i,SV26: $i,SV17: $i,SV27: $i] :
( ( ( in @ SV27 @ SV17 )
= $true )
| ( ( in @ SV27 @ SV26 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(375,plain,
! [SV26: $i,SV17: $i,SV2: $i,SV27: $i] :
( ( ( in @ SV27 @ SV2 )
= $false )
| ( ( ~ ( in @ SV27 @ SV17 ) )
= $true )
| ( ( in @ SV27 @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(376,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
= $true )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(377,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) ) )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(378,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ~ ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(379,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(380,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $true )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(381,plain,
! [SV11: $i] :
( ( ( function @ SV11 )
= $true )
| ( ( empty @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(382,plain,
! [SV26: $i,SV2: $i,SV17: $i,SV27: $i] :
( ( ( in @ SV27 @ SV17 )
= $false )
| ( ( in @ SV27 @ SV2 )
= $false )
| ( ( in @ SV27 @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(383,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(384,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
| ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(385,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
| ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(386,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
| ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(387,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(388,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(389,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(390,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(391,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( SV21
!= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(392,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(393,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $true )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(394,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $true )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(395,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) ) )
= $true )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(396,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(397,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ~ ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(398,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
| ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(399,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(400,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
| ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(401,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(402,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 ) )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(403,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(404,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ~ ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(405,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ( relation_dom @ SV21 )
!= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $true )
| ( ( ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(406,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $true )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(407,plain,
! [SV26: $i,SV2: $i,SV17: $i] :
( ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $true )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV2 )
= $false )
| ( ( in @ ( sK10_SY64 @ SV17 @ SV2 @ SV26 ) @ SV17 )
= $false )
| ( ( SV26
= ( set_intersection2 @ SV2 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(408,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ( relation_dom @ SV21 )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(409,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ! [SY65: $i] :
( ~ ( in @ SY65 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY65 )
= ( apply @ SV28 @ SY65 ) ) ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(410,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ( relation_dom @ SV21 )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $false )
| ( ( ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(411,plain,
! [SV7: $i,SV28: $i,SV21: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SV29 )
= ( apply @ SV28 @ SV29 ) ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(412,plain,
! [SV7: $i,SV28: $i,SV21: $i] :
( ( ( ! [SY66: $i] :
( ~ ( in @ SY66 @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ SY66 )
= ( apply @ SV28 @ SY66 ) ) ) )
= $false )
| ( ( ( relation_dom @ SV21 )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(413,plain,
! [SV7: $i,SV28: $i,SV21: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ ( relation_dom @ SV21 ) ) )
= $true )
| ( ( ( apply @ SV21 @ SV29 )
= ( apply @ SV28 @ SV29 ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(414,plain,
! [SV21: $i,SV28: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK11_SY66 @ SV7 @ SV28 @ SV21 ) @ ( relation_dom @ SV21 ) )
| ( ( apply @ SV21 @ ( sK11_SY66 @ SV7 @ SV28 @ SV21 ) )
= ( apply @ SV28 @ ( sK11_SY66 @ SV7 @ SV28 @ SV21 ) ) ) )
= $false )
| ( ( ( relation_dom @ SV21 )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[412]) ).
thf(415,plain,
! [SV7: $i,SV28: $i,SV21: $i,SV29: $i] :
( ( ( in @ SV29 @ ( relation_dom @ SV21 ) )
= $false )
| ( ( ( apply @ SV21 @ SV29 )
= ( apply @ SV28 @ SV29 ) )
= $true )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $false )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(416,plain,
! [SV21: $i,SV28: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK11_SY66 @ SV7 @ SV28 @ SV21 ) @ ( relation_dom @ SV21 ) ) )
= $false )
| ( ( ( relation_dom @ SV21 )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(417,plain,
! [SV28: $i,SV7: $i,SV21: $i] :
( ( ( ( apply @ SV21 @ ( sK11_SY66 @ SV7 @ SV28 @ SV21 ) )
= ( apply @ SV28 @ ( sK11_SY66 @ SV7 @ SV28 @ SV21 ) ) )
= $false )
| ( ( ( relation_dom @ SV21 )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(418,plain,
! [SV21: $i,SV28: $i,SV7: $i] :
( ( ( in @ ( sK11_SY66 @ SV7 @ SV28 @ SV21 ) @ ( relation_dom @ SV21 ) )
= $true )
| ( ( ( relation_dom @ SV21 )
= ( set_intersection2 @ ( relation_dom @ SV28 ) @ SV7 ) )
= $false )
| ( ( SV21
= ( relation_dom_restriction @ SV28 @ SV7 ) )
= $true )
| ( ( relation @ SV28 )
= $false )
| ( ( function @ SV28 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( function @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(419,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[84,418,417,415,408,407,406,394,393,390,382,381,380,374,373,368,357,336,335,334,333,320,319,316,315,313,301,298,295,286,285,282,280,279,278,277,275,274,272,271,269,268,267,260,255,231,212,211,202,200,199,198,194,108,107,89,87,86,85]) ).
thf(420,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(421,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(422,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(423,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(424,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(425,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(426,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(427,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(428,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(430,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(431,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(435,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(436,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(437,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(438,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(439,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(440,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(441,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(442,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(443,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(446,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(448,plain,
( ( function @ sK3_SY40 )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(449,plain,
( ( relation @ sK3_SY40 )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(450,plain,
( ( ~ ( ( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
& ( in @ sK2_SY38 @ sK1_A ) )
=> ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(451,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(452,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(453,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(454,plain,
( ( ~ ( ~ ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) )
| ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(455,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(456,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(457,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(458,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(459,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) )
| ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(460,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(461,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(462,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(463,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(464,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(465,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(466,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(467,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ! [SX2: $i] :
( ~ ~ ( ~ ( relation @ SX2 )
| ~ ( function @ SX2 ) )
| ~ ( ~ ( ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ~ ( ( ( relation_dom @ SX1 )
!= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX1 ) )
| ( ( apply @ SX1 @ SX3 )
= ( apply @ SX2 @ SX3 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SX1 )
!= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX1 ) )
| ( ( apply @ SX1 @ SX3 )
= ( apply @ SX2 @ SX3 ) ) ) )
| ( SX1
= ( relation_dom_restriction @ SX2 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(468,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(469,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(470,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(471,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(472,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(473,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(474,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(475,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(476,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(477,plain,
! [SV30: $i] :
( ( ! [SY67: $i] :
( ~ ( element @ SV30 @ SY67 )
| ( empty @ SY67 )
| ( in @ SV30 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(478,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) )
| ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(479,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(480,plain,
! [SV31: $i] :
( ( ~ ( empty @ SV31 )
| ( relation @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(481,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV32 )
| ~ ( relation @ SV32 ) )
| ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(482,plain,
! [SV33: $i] :
( ( ! [SY68: $i,SY69: $i] :
~ ( ~ ( ( SY69
!= ( set_intersection2 @ SV33 @ SY68 ) )
| ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ( ~ ( in @ SY70 @ SV33 )
| ~ ( in @ SY70 @ SY68 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY70 @ SV33 )
| ~ ( in @ SY70 @ SY68 ) )
| ( in @ SY70 @ SY69 ) ) ) )
| ~ ( ~ ! [SY71: $i] :
~ ( ~ ( ~ ( in @ SY71 @ SY69 )
| ~ ( ~ ( in @ SY71 @ SV33 )
| ~ ( in @ SY71 @ SY68 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY71 @ SV33 )
| ~ ( in @ SY71 @ SY68 ) )
| ( in @ SY71 @ SY69 ) ) )
| ( SY69
= ( set_intersection2 @ SV33 @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(483,plain,
! [SV34: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( empty @ SV34 ) )
| ~ ( function @ SV34 ) )
| ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(484,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(485,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(486,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(487,plain,
! [SV35: $i] :
( ( ! [SY72: $i] :
( ~ ( in @ SV35 @ SY72 )
| ( element @ SV35 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(488,plain,
! [SV36: $i] :
( ( ! [SY73: $i] :
~ ~ ( ~ ( in @ SV36 @ SY73 )
| ~ ( empty @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(489,plain,
! [SV37: $i] :
( ( ! [SY74: $i] :
( ~ ( in @ SV37 @ SY74 )
| ~ ( in @ SY74 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(490,plain,
! [SV38: $i] :
( ( ~ ( empty @ SV38 )
| ( function @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(491,plain,
! [SV39: $i] :
( ( ! [SY75: $i] :
( ~ ~ ( ~ ( relation @ SY75 )
| ~ ( function @ SY75 ) )
| ! [SY76: $i] :
( ~ ~ ( ~ ( relation @ SY76 )
| ~ ( function @ SY76 ) )
| ~ ( ~ ( ( SY75
!= ( relation_dom_restriction @ SY76 @ SV39 ) )
| ~ ( ( ( relation_dom @ SY75 )
!= ( set_intersection2 @ ( relation_dom @ SY76 ) @ SV39 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY75 ) )
| ( ( apply @ SY75 @ SX3 )
= ( apply @ SY76 @ SX3 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SY75 )
!= ( set_intersection2 @ ( relation_dom @ SY76 ) @ SV39 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY75 ) )
| ( ( apply @ SY75 @ SX3 )
= ( apply @ SY76 @ SX3 ) ) ) )
| ( SY75
= ( relation_dom_restriction @ SY76 @ SV39 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(492,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(493,plain,
! [SV40: $i] :
( ( ! [SY79: $i] :
( ~ ~ ( ~ ( relation @ SV40 )
| ~ ( relation_empty_yielding @ SV40 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SY79 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(494,plain,
! [SV41: $i] :
( ( ! [SY80: $i] :
( ~ ~ ( ~ ( relation @ SV41 )
| ~ ( function @ SV41 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SY80 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(495,plain,
! [SV42: $i] :
( ( ! [SY81: $i] :
( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( relation @ SY81 ) )
| ( relation @ ( set_intersection2 @ SV42 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(496,plain,
! [SV43: $i] :
( ( ~ ( empty @ SV43 )
| ~ ( ~ ( empty @ ( relation_dom @ SV43 ) )
| ~ ( relation @ ( relation_dom @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(497,plain,
! [SV44: $i] :
( ( ! [SY82: $i] :
( ~ ( relation @ SV44 )
| ( relation @ ( relation_dom_restriction @ SV44 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(498,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(499,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
| ~ ( one_to_one @ sK12_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[475]) ).
thf(500,plain,
( ( ~ ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( function @ sK13_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[476]) ).
thf(501,plain,
! [SV45: $i,SV30: $i] :
( ( ~ ( element @ SV30 @ SV45 )
| ( empty @ SV45 )
| ( in @ SV30 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(502,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(503,plain,
( ( in @ sK2_SY38 @ ( relation_dom @ ( relation_dom_restriction @ sK3_SY40 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(504,plain,
( ( ~ ~ ( ~ ( relation @ sK14_SX0 )
| ~ ( relation_empty_yielding @ sK14_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[479]) ).
thf(505,plain,
! [SV31: $i] :
( ( ( ~ ( empty @ SV31 ) )
= $true )
| ( ( relation @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(506,plain,
! [SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV32 )
| ~ ( relation @ SV32 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(507,plain,
! [SV46: $i,SV33: $i] :
( ( ! [SY83: $i] :
~ ( ~ ( ( SY83
!= ( set_intersection2 @ SV33 @ SV46 ) )
| ! [SY84: $i] :
~ ( ~ ( ~ ( in @ SY84 @ SY83 )
| ~ ( ~ ( in @ SY84 @ SV33 )
| ~ ( in @ SY84 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY84 @ SV33 )
| ~ ( in @ SY84 @ SV46 ) )
| ( in @ SY84 @ SY83 ) ) ) )
| ~ ( ~ ! [SY85: $i] :
~ ( ~ ( ~ ( in @ SY85 @ SY83 )
| ~ ( ~ ( in @ SY85 @ SV33 )
| ~ ( in @ SY85 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY85 @ SV33 )
| ~ ( in @ SY85 @ SV46 ) )
| ( in @ SY85 @ SY83 ) ) )
| ( SY83
= ( set_intersection2 @ SV33 @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(508,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( empty @ SV34 ) )
| ~ ( function @ SV34 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(509,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK15_SX0 )
| ~ ( empty @ sK15_SX0 ) )
| ~ ( function @ sK15_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[484]) ).
thf(510,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(511,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(512,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(513,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(514,plain,
! [SV47: $i,SV35: $i] :
( ( ~ ( in @ SV35 @ SV47 )
| ( element @ SV35 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(515,plain,
! [SV48: $i,SV36: $i] :
( ( ~ ~ ( ~ ( in @ SV36 @ SV48 )
| ~ ( empty @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(516,plain,
! [SV49: $i,SV37: $i] :
( ( ~ ( in @ SV37 @ SV49 )
| ~ ( in @ SV49 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(517,plain,
! [SV38: $i] :
( ( ( ~ ( empty @ SV38 ) )
= $true )
| ( ( function @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(518,plain,
! [SV39: $i,SV50: $i] :
( ( ~ ~ ( ~ ( relation @ SV50 )
| ~ ( function @ SV50 ) )
| ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SY86 )
| ~ ( function @ SY86 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SY86 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY87 )
= ( apply @ SY86 @ SY87 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY88 )
= ( apply @ SY86 @ SY88 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SY86 @ SV39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(519,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK16_SX0 )
| ~ ( relation @ sK16_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[492]) ).
thf(520,plain,
! [SV51: $i,SV40: $i] :
( ( ~ ~ ( ~ ( relation @ SV40 )
| ~ ( relation_empty_yielding @ SV40 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(521,plain,
! [SV52: $i,SV41: $i] :
( ( ~ ~ ( ~ ( relation @ SV41 )
| ~ ( function @ SV41 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(522,plain,
! [SV53: $i,SV42: $i] :
( ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( relation @ SV53 ) )
| ( relation @ ( set_intersection2 @ SV42 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(523,plain,
! [SV43: $i] :
( ( ( ~ ( empty @ SV43 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV43 ) )
| ~ ( relation @ ( relation_dom @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(524,plain,
! [SV54: $i,SV44: $i] :
( ( ~ ( relation @ SV44 )
| ( relation @ ( relation_dom_restriction @ SV44 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(525,plain,
( ( ~ ~ ( ~ ( empty @ sK17_SX0 )
| ~ ( relation @ sK17_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[498]) ).
thf(526,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
| ~ ( one_to_one @ sK12_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(527,plain,
( ( ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( function @ sK13_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(528,plain,
! [SV45: $i,SV30: $i] :
( ( ( ~ ( element @ SV30 @ SV45 ) )
= $true )
| ( ( ( empty @ SV45 )
| ( in @ SV30 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(529,plain,
( ( ~ ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(530,plain,
( ( ~ ( ~ ( relation @ sK14_SX0 )
| ~ ( relation_empty_yielding @ sK14_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(531,plain,
! [SV31: $i] :
( ( ( empty @ SV31 )
= $false )
| ( ( relation @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(532,plain,
! [SV32: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV32 )
| ~ ( relation @ SV32 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(533,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ~ ( ~ ( ( SV55
!= ( set_intersection2 @ SV33 @ SV46 ) )
| ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV55 )
| ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) )
| ( in @ SY89 @ SV55 ) ) ) )
| ~ ( ~ ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV55 )
| ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) )
| ( in @ SY90 @ SV55 ) ) )
| ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(534,plain,
! [SV34: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( empty @ SV34 ) )
| ~ ( function @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(535,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK15_SX0 )
| ~ ( empty @ sK15_SX0 ) )
| ~ ( function @ sK15_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(536,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(537,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(538,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(539,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(540,plain,
! [SV47: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ SV47 ) )
= $true )
| ( ( element @ SV35 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(541,plain,
! [SV48: $i,SV36: $i] :
( ( ~ ( ~ ( in @ SV36 @ SV48 )
| ~ ( empty @ SV48 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(542,plain,
! [SV49: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ SV49 ) )
= $true )
| ( ( ~ ( in @ SV49 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(543,plain,
! [SV38: $i] :
( ( ( empty @ SV38 )
= $false )
| ( ( function @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(544,plain,
! [SV39: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV50 )
| ~ ( function @ SV50 ) ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SY86 )
| ~ ( function @ SY86 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SY86 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY87 )
= ( apply @ SY86 @ SY87 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY88 )
= ( apply @ SY86 @ SY88 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SY86 @ SV39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(545,plain,
( ( ~ ( ~ ~ ( empty @ sK16_SX0 )
| ~ ( relation @ sK16_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(546,plain,
! [SV51: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV40 )
| ~ ( relation_empty_yielding @ SV40 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(547,plain,
! [SV52: $i,SV41: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV41 )
| ~ ( function @ SV41 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(548,plain,
! [SV53: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( relation @ SV53 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV42 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(549,plain,
! [SV43: $i] :
( ( ( empty @ SV43 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV43 ) )
| ~ ( relation @ ( relation_dom @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(550,plain,
! [SV54: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV44 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(551,plain,
( ( ~ ( ~ ( empty @ sK17_SX0 )
| ~ ( relation @ sK17_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(552,plain,
( ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
| ~ ( one_to_one @ sK12_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(553,plain,
( ( ~ ( relation @ sK13_SX0 )
| ~ ( function @ sK13_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(554,plain,
! [SV45: $i,SV30: $i] :
( ( ( element @ SV30 @ SV45 )
= $false )
| ( ( ( empty @ SV45 )
| ( in @ SV30 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(555,plain,
( ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
| ~ ( in @ sK2_SY38 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(556,plain,
( ( ~ ( relation @ sK14_SX0 )
| ~ ( relation_empty_yielding @ sK14_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(557,plain,
! [SV32: $i] :
( ( ( ~ ~ ( empty @ SV32 )
| ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(558,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ~ ( ( SV55
!= ( set_intersection2 @ SV33 @ SV46 ) )
| ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV55 )
| ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) )
| ( in @ SY89 @ SV55 ) ) ) )
| ~ ( ~ ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV55 )
| ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) )
| ( in @ SY90 @ SV55 ) ) )
| ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(559,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( empty @ SV34 ) )
| ~ ( function @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(560,plain,
( ( ~ ~ ( ~ ( relation @ sK15_SX0 )
| ~ ( empty @ sK15_SX0 ) )
| ~ ( function @ sK15_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(561,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(562,plain,
! [SV47: $i,SV35: $i] :
( ( ( in @ SV35 @ SV47 )
= $false )
| ( ( element @ SV35 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(563,plain,
! [SV48: $i,SV36: $i] :
( ( ~ ( in @ SV36 @ SV48 )
| ~ ( empty @ SV48 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(564,plain,
! [SV49: $i,SV37: $i] :
( ( ( in @ SV37 @ SV49 )
= $false )
| ( ( ~ ( in @ SV49 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(565,plain,
! [SV39: $i,SV50: $i] :
( ( ( ~ ( ~ ( relation @ SV50 )
| ~ ( function @ SV50 ) ) )
= $false )
| ( ( ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SY86 )
| ~ ( function @ SY86 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SY86 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY87 )
= ( apply @ SY86 @ SY87 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY88 )
= ( apply @ SY86 @ SY88 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SY86 @ SV39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(566,plain,
( ( ~ ~ ( empty @ sK16_SX0 )
| ~ ( relation @ sK16_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(567,plain,
! [SV51: $i,SV40: $i] :
( ( ( ~ ( ~ ( relation @ SV40 )
| ~ ( relation_empty_yielding @ SV40 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(568,plain,
! [SV52: $i,SV41: $i] :
( ( ( ~ ( ~ ( relation @ SV41 )
| ~ ( function @ SV41 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(569,plain,
! [SV53: $i,SV42: $i] :
( ( ( ~ ( ~ ( relation @ SV42 )
| ~ ( relation @ SV53 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV42 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(570,plain,
! [SV43: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV43 ) )
| ~ ( relation @ ( relation_dom @ SV43 ) ) )
= $false )
| ( ( empty @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(571,plain,
! [SV54: $i,SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV44 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(572,plain,
( ( ~ ( empty @ sK17_SX0 )
| ~ ( relation @ sK17_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(573,plain,
( ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(574,plain,
( ( ~ ( one_to_one @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(575,plain,
( ( ~ ( relation @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(576,plain,
( ( ~ ( function @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(577,plain,
! [SV30: $i,SV45: $i] :
( ( ( empty @ SV45 )
= $true )
| ( ( in @ SV30 @ SV45 )
= $true )
| ( ( element @ SV30 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(578,plain,
( ( ~ ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(579,plain,
( ( ~ ( in @ sK2_SY38 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(580,plain,
( ( ~ ( relation @ sK14_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(581,plain,
( ( ~ ( relation_empty_yielding @ sK14_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(582,plain,
! [SV32: $i] :
( ( ( ~ ~ ( empty @ SV32 ) )
= $true )
| ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(583,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ~ ( ( SV55
!= ( set_intersection2 @ SV33 @ SV46 ) )
| ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV55 )
| ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) )
| ( in @ SY89 @ SV55 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(584,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ~ ( ~ ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV55 )
| ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) )
| ( in @ SY90 @ SV55 ) ) )
| ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(585,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( empty @ SV34 ) ) )
= $true )
| ( ( ~ ( function @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(586,plain,
( ( ~ ~ ( ~ ( relation @ sK15_SX0 )
| ~ ( empty @ sK15_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(587,plain,
( ( ~ ( function @ sK15_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(588,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(589,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(590,plain,
! [SV48: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ SV48 ) )
= $true )
| ( ( ~ ( empty @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(591,plain,
! [SV37: $i,SV49: $i] :
( ( ( in @ SV49 @ SV37 )
= $false )
| ( ( in @ SV37 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(592,plain,
! [SV39: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 )
| ~ ( function @ SV50 ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SY86 )
| ~ ( function @ SY86 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SY86 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY87 )
= ( apply @ SY86 @ SY87 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY88 )
= ( apply @ SY86 @ SY88 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SY86 @ SV39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(593,plain,
( ( ~ ~ ( empty @ sK16_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(594,plain,
( ( ~ ( relation @ sK16_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(595,plain,
! [SV51: $i,SV40: $i] :
( ( ( ~ ( relation @ SV40 )
| ~ ( relation_empty_yielding @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(596,plain,
! [SV52: $i,SV41: $i] :
( ( ( ~ ( relation @ SV41 )
| ~ ( function @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(597,plain,
! [SV53: $i,SV42: $i] :
( ( ( ~ ( relation @ SV42 )
| ~ ( relation @ SV53 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV42 @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(598,plain,
! [SV43: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV43 ) ) )
= $false )
| ( ( empty @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(599,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV43 ) ) )
= $false )
| ( ( empty @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(600,plain,
( ( ~ ( empty @ sK17_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(601,plain,
( ( ~ ( relation @ sK17_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(602,plain,
( ( ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(603,plain,
( ( one_to_one @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(604,plain,
( ( relation @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(605,plain,
( ( function @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(606,plain,
( ( in @ sK2_SY38 @ ( relation_dom @ sK3_SY40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(607,plain,
( ( in @ sK2_SY38 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(608,plain,
( ( relation @ sK14_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(609,plain,
( ( relation_empty_yielding @ sK14_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(610,plain,
! [SV32: $i] :
( ( ( ~ ( empty @ SV32 ) )
= $false )
| ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(611,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ( SV55
!= ( set_intersection2 @ SV33 @ SV46 ) )
| ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV55 )
| ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) )
| ( in @ SY89 @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(612,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ~ ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV55 )
| ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) )
| ( in @ SY90 @ SV55 ) ) )
| ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(613,plain,
! [SV34: $i] :
( ( ( ~ ( ~ ( relation @ SV34 )
| ~ ( empty @ SV34 ) ) )
= $false )
| ( ( ~ ( function @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(614,plain,
( ( ~ ( ~ ( relation @ sK15_SX0 )
| ~ ( empty @ sK15_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(615,plain,
( ( function @ sK15_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(616,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(617,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(618,plain,
! [SV48: $i,SV36: $i] :
( ( ( in @ SV36 @ SV48 )
= $false )
| ( ( ~ ( empty @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(619,plain,
! [SV39: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( ~ ( function @ SV50 ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SY86 )
| ~ ( function @ SY86 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SY86 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY87 )
= ( apply @ SY86 @ SY87 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY88 )
= ( apply @ SY86 @ SY88 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SY86 @ SV39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(620,plain,
( ( ~ ( empty @ sK16_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(621,plain,
( ( relation @ sK16_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(622,plain,
! [SV51: $i,SV40: $i] :
( ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(623,plain,
! [SV52: $i,SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ~ ( function @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(624,plain,
! [SV53: $i,SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV42 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(625,plain,
! [SV43: $i] :
( ( ( empty @ ( relation_dom @ SV43 ) )
= $true )
| ( ( empty @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(626,plain,
! [SV43: $i] :
( ( ( relation @ ( relation_dom @ SV43 ) )
= $true )
| ( ( empty @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(627,plain,
( ( empty @ sK17_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(628,plain,
( ( relation @ sK17_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(629,plain,
( ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(630,plain,
! [SV32: $i] :
( ( ( empty @ SV32 )
= $true )
| ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(631,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ( SV55
!= ( set_intersection2 @ SV33 @ SV46 ) )
= $true )
| ( ( ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV55 )
| ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) )
| ( in @ SY89 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(632,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ( ~ ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV55 )
| ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) )
| ( in @ SY90 @ SV55 ) ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(633,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 )
| ~ ( empty @ SV34 ) )
= $true )
| ( ( ~ ( function @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(634,plain,
( ( ~ ( relation @ sK15_SX0 )
| ~ ( empty @ sK15_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(635,plain,
! [SV36: $i,SV48: $i] :
( ( ( empty @ SV48 )
= $false )
| ( ( in @ SV36 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(636,plain,
! [SV39: $i,SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( ~ ( function @ SV50 ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SY86 )
| ~ ( function @ SY86 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SY86 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY87 )
= ( apply @ SY86 @ SY87 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY88 )
= ( apply @ SY86 @ SY88 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SY86 @ SV39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(637,plain,
( ( empty @ sK16_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(638,plain,
! [SV51: $i,SV40: $i] :
( ( ( relation @ SV40 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(639,plain,
! [SV52: $i,SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ~ ( function @ SV41 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(640,plain,
! [SV53: $i,SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV42 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(641,plain,
( ( ~ ( relation @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(642,plain,
( ( ~ ( function @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(643,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( empty @ SV32 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(644,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false )
| ( ( ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV55 )
| ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY89 @ SV33 )
| ~ ( in @ SY89 @ SV46 ) )
| ( in @ SY89 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(645,plain,
! [SV46: $i,SV33: $i,SV55: $i] :
( ( ( ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV55 )
| ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV33 )
| ~ ( in @ SY90 @ SV46 ) )
| ( in @ SY90 @ SV55 ) ) ) )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(646,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true )
| ( ( ~ ( function @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(647,plain,
( ( ~ ( relation @ sK15_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(648,plain,
( ( ~ ( empty @ sK15_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(649,plain,
! [SV39: $i,SV50: $i] :
( ( ( function @ SV50 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SY86 )
| ~ ( function @ SY86 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SY86 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY87: $i] :
( ~ ( in @ SY87 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY87 )
= ( apply @ SY86 @ SY87 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SY86 ) @ SV39 ) )
| ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY88 )
= ( apply @ SY86 @ SY88 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SY86 @ SV39 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(650,plain,
! [SV51: $i,SV40: $i] :
( ( ( relation_empty_yielding @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(651,plain,
! [SV52: $i,SV41: $i] :
( ( ( function @ SV41 )
= $false )
| ( ( relation @ SV41 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(652,plain,
! [SV42: $i,SV53: $i] :
( ( ( relation @ SV53 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV42 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(653,plain,
( ( relation @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(654,plain,
( ( function @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(655,plain,
! [SV32: $i] :
( ( ( empty @ ( relation_dom @ SV32 ) )
= $false )
| ( ( empty @ SV32 )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(656,plain,
! [SV46: $i,SV33: $i,SV55: $i,SV56: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV56 @ SV55 )
| ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) )
| ( in @ SV56 @ SV55 ) ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(657,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
| ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) ) )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[645]) ).
thf(658,plain,
! [SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ~ ( empty @ SV34 ) )
= $true )
| ( ( ~ ( function @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(659,plain,
( ( relation @ sK15_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(660,plain,
( ( empty @ sK15_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(661,plain,
! [SV39: $i,SV50: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV57 )
| ~ ( function @ SV57 ) )
| ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(662,plain,
! [SV51: $i,SV40: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( relation_empty_yielding @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(663,plain,
! [SV52: $i,SV41: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) )
= $false )
| ( ( relation @ SV41 )
= $false )
| ( ( function @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(664,plain,
! [SV46: $i,SV33: $i,SV55: $i,SV56: $i] :
( ( ( ~ ( ~ ( in @ SV56 @ SV55 )
| ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) )
| ( in @ SV56 @ SV55 ) ) )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(665,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
| ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(666,plain,
! [SV34: $i] :
( ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( ~ ( function @ SV34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(667,plain,
! [SV39: $i,SV50: $i,SV57: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV57 )
| ~ ( function @ SV57 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(668,plain,
! [SV51: $i,SV40: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) ) )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( relation_empty_yielding @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(669,plain,
! [SV51: $i,SV40: $i] :
( ( ( ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) ) )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( relation_empty_yielding @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(670,plain,
! [SV52: $i,SV41: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) ) )
= $false )
| ( ( relation @ SV41 )
= $false )
| ( ( function @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(671,plain,
! [SV52: $i,SV41: $i] :
( ( ( ~ ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) ) )
= $false )
| ( ( relation @ SV41 )
= $false )
| ( ( function @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(672,plain,
! [SV46: $i,SV33: $i,SV55: $i,SV56: $i] :
( ( ( ~ ( ~ ( in @ SV56 @ SV55 )
| ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) ) )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(673,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) )
| ( in @ SV56 @ SV55 ) ) )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[664]) ).
thf(674,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
| ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(675,plain,
! [SV34: $i] :
( ( ( function @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(676,plain,
! [SV39: $i,SV50: $i,SV57: $i] :
( ( ( ~ ( ~ ( relation @ SV57 )
| ~ ( function @ SV57 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(677,plain,
! [SV51: $i,SV40: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV40 @ SV51 ) )
= $true )
| ( ( relation @ SV40 )
= $false )
| ( ( relation_empty_yielding @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(678,plain,
! [SV51: $i,SV40: $i] :
( ( ( relation_empty_yielding @ ( relation_dom_restriction @ SV40 @ SV51 ) )
= $true )
| ( ( relation @ SV40 )
= $false )
| ( ( relation_empty_yielding @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(679,plain,
! [SV52: $i,SV41: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV41 @ SV52 ) )
= $true )
| ( ( relation @ SV41 )
= $false )
| ( ( function @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(680,plain,
! [SV52: $i,SV41: $i] :
( ( ( function @ ( relation_dom_restriction @ SV41 @ SV52 ) )
= $true )
| ( ( relation @ SV41 )
= $false )
| ( ( function @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(681,plain,
! [SV46: $i,SV33: $i,SV55: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV55 )
| ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(682,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) )
| ( in @ SV56 @ SV55 ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(683,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
| ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(684,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
| ~ ( one_to_one @ SV34 ) )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(685,plain,
! [SV39: $i,SV50: $i,SV57: $i] :
( ( ( ~ ( relation @ SV57 )
| ~ ( function @ SV57 ) )
= $true )
| ( ( ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(686,plain,
! [SV46: $i,SV33: $i,SV55: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(687,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) )
= $true )
| ( ( in @ SV56 @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(688,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(689,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(690,plain,
! [SV34: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) ) )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(691,plain,
! [SV34: $i] :
( ( ( ~ ( one_to_one @ SV34 ) )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(692,plain,
! [SV39: $i,SV50: $i,SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ~ ( function @ SV57 ) )
= $true )
| ( ( ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(693,plain,
! [SV46: $i,SV33: $i,SV55: $i,SV56: $i] :
( ( ( in @ SV56 @ SV55 )
= $false )
| ( ( ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(694,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) ) )
= $false )
| ( ( in @ SV56 @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(695,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(696,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(697,plain,
! [SV34: $i] :
( ( ( ~ ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) ) )
= $true )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(698,plain,
! [SV34: $i] :
( ( ( one_to_one @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(699,plain,
! [SV39: $i,SV50: $i,SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( ~ ( function @ SV57 ) )
= $true )
| ( ( ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(700,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) )
= $false )
| ( ( in @ SV56 @ SV55 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(701,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV33 )
| ~ ( in @ SV56 @ SV46 ) )
= $true )
| ( ( in @ SV56 @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(702,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(703,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 ) )
= $true )
| ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(704,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 )
| ~ ( function @ SV34 ) )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(705,plain,
! [SV39: $i,SV50: $i,SV57: $i] :
( ( ( function @ SV57 )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( ~ ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(706,plain,
! [SV46: $i,SV55: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV33 ) )
= $false )
| ( ( in @ SV56 @ SV55 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(707,plain,
! [SV33: $i,SV55: $i,SV46: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV46 ) )
= $false )
| ( ( in @ SV56 @ SV55 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(708,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV56 @ SV46 ) )
= $true )
| ( ( in @ SV56 @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(709,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(710,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(711,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(712,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(713,plain,
! [SV34: $i] :
( ( ( ~ ( function @ SV34 ) )
= $false )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(714,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
| ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(715,plain,
! [SV46: $i,SV55: $i,SV33: $i,SV56: $i] :
( ( ( in @ SV56 @ SV33 )
= $true )
| ( ( in @ SV56 @ SV55 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(716,plain,
! [SV33: $i,SV55: $i,SV46: $i,SV56: $i] :
( ( ( in @ SV56 @ SV46 )
= $true )
| ( ( in @ SV56 @ SV55 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(717,plain,
! [SV55: $i,SV46: $i,SV33: $i,SV56: $i] :
( ( ( in @ SV56 @ SV33 )
= $false )
| ( ( ~ ( in @ SV56 @ SV46 ) )
= $true )
| ( ( in @ SV56 @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(718,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
= $true )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(719,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) ) )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(720,plain,
! [SV34: $i] :
( ( ( relation @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(721,plain,
! [SV34: $i] :
( ( ( function @ SV34 )
= $true )
| ( ( empty @ SV34 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( function @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(722,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(723,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(724,plain,
! [SV55: $i,SV33: $i,SV46: $i,SV56: $i] :
( ( ( in @ SV56 @ SV46 )
= $false )
| ( ( in @ SV56 @ SV33 )
= $false )
| ( ( in @ SV56 @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(725,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(726,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
| ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(727,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
| ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(728,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
| ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(729,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(730,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(731,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(732,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(733,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( SV50
!= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(734,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ~ ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(735,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $true )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(736,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $true )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(737,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) ) )
= $true )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(738,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(739,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ~ ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(740,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
| ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(741,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(742,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
| ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(743,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(744,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 ) )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(745,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(746,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ~ ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[741]) ).
thf(747,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ( relation_dom @ SV50 )
!= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $true )
| ( ( ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(748,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $true )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(749,plain,
! [SV55: $i,SV33: $i,SV46: $i] :
( ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $true )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV33 )
= $false )
| ( ( in @ ( sK18_SY90 @ SV46 @ SV33 @ SV55 ) @ SV46 )
= $false )
| ( ( SV55
= ( set_intersection2 @ SV33 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(750,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ( relation_dom @ SV50 )
= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(751,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ! [SY91: $i] :
( ~ ( in @ SY91 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY91 )
= ( apply @ SV57 @ SY91 ) ) ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(752,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ( relation_dom @ SV50 )
= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(753,plain,
! [SV39: $i,SV57: $i,SV50: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SV58 )
= ( apply @ SV57 @ SV58 ) ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(754,plain,
! [SV39: $i,SV57: $i,SV50: $i] :
( ( ( ! [SY92: $i] :
( ~ ( in @ SY92 @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ SY92 )
= ( apply @ SV57 @ SY92 ) ) ) )
= $false )
| ( ( ( relation_dom @ SV50 )
= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(755,plain,
! [SV39: $i,SV57: $i,SV50: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ ( relation_dom @ SV50 ) ) )
= $true )
| ( ( ( apply @ SV50 @ SV58 )
= ( apply @ SV57 @ SV58 ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(756,plain,
! [SV50: $i,SV57: $i,SV39: $i] :
( ( ( ~ ( in @ ( sK19_SY92 @ SV39 @ SV57 @ SV50 ) @ ( relation_dom @ SV50 ) )
| ( ( apply @ SV50 @ ( sK19_SY92 @ SV39 @ SV57 @ SV50 ) )
= ( apply @ SV57 @ ( sK19_SY92 @ SV39 @ SV57 @ SV50 ) ) ) )
= $false )
| ( ( ( relation_dom @ SV50 )
= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[754]) ).
thf(757,plain,
! [SV39: $i,SV57: $i,SV50: $i,SV58: $i] :
( ( ( in @ SV58 @ ( relation_dom @ SV50 ) )
= $false )
| ( ( ( apply @ SV50 @ SV58 )
= ( apply @ SV57 @ SV58 ) )
= $true )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $false )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(758,plain,
! [SV50: $i,SV57: $i,SV39: $i] :
( ( ( ~ ( in @ ( sK19_SY92 @ SV39 @ SV57 @ SV50 ) @ ( relation_dom @ SV50 ) ) )
= $false )
| ( ( ( relation_dom @ SV50 )
= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(759,plain,
! [SV57: $i,SV39: $i,SV50: $i] :
( ( ( ( apply @ SV50 @ ( sK19_SY92 @ SV39 @ SV57 @ SV50 ) )
= ( apply @ SV57 @ ( sK19_SY92 @ SV39 @ SV57 @ SV50 ) ) )
= $false )
| ( ( ( relation_dom @ SV50 )
= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(760,plain,
! [SV50: $i,SV57: $i,SV39: $i] :
( ( ( in @ ( sK19_SY92 @ SV39 @ SV57 @ SV50 ) @ ( relation_dom @ SV50 ) )
= $true )
| ( ( ( relation_dom @ SV50 )
= ( set_intersection2 @ ( relation_dom @ SV57 ) @ SV39 ) )
= $false )
| ( ( SV50
= ( relation_dom_restriction @ SV57 @ SV39 ) )
= $true )
| ( ( relation @ SV57 )
= $false )
| ( ( function @ SV57 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( function @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(761,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[425,760,759,757,750,749,748,736,735,732,724,721,720,716,715,710,698,680,679,678,677,660,659,655,654,653,652,637,635,628,627,626,625,621,617,616,615,609,608,607,606,605,604,603,591,577,571,562,543,539,537,536,531,503,449,448,430,428,427,426]) ).
thf(762,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[761,419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 15:07:39 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.65/1.33
% 6.65/1.33 No.of.Axioms: 28
% 6.65/1.33
% 6.65/1.33 Length.of.Defs: 0
% 6.65/1.33
% 6.65/1.33 Contains.Choice.Funs: false
% 6.65/1.33 ...................
% 6.65/1.33
% 6.65/1.33 ********************************
% 6.65/1.33 * All subproblems solved! *
% 6.65/1.33 ********************************
% 6.65/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:30,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:761,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.65/1.33
% 6.65/1.33 %**** Beginning of derivation protocol ****
% 6.65/1.33 % SZS output start CNFRefutation
% See solution above
% 6.65/1.33
% 6.65/1.33 %**** End of derivation protocol ****
% 6.65/1.33 %**** no. of clauses in derivation: 753 ****
% 6.65/1.33 %**** clause counter: 761 ****
% 6.65/1.33
% 6.65/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:30,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:761,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------