%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU277+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 : n011.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 10:43:46 AM UTC 2026
% Result : Theorem 85.18s 14.59s
% Output : CNFRefutation 85.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 11
% Syntax : Number of formulae : 628 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 11354 (4661 equ; 0 cnn)
% Maximal formula atoms : 15 ( 18 avg)
% Number of connectives : 31234 (7747 ~;4334 |; 75 &;19045 @)
% ( 12 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 8 con; 0-4 aty)
% Number of variables : 3784 ( 0 ^;3724 !; 60 ?;3784 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
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_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_sK10_SY102,type,
sK10_SY102: $i > $i ).
thf(tp_sK11_SY111,type,
sK11_SY111: $i > $i > $i > $i ).
thf(tp_sK12_SY116,type,
sK12_SY116: $i > $i ).
thf(tp_sK13_SY92,type,
sK13_SY92: $i > $i > $i > $i ).
thf(tp_sK14_SY119,type,
sK14_SY119: $i > $i > $i > $i ).
thf(tp_sK15_SY92,type,
sK15_SY92: $i > $i > $i > $i ).
thf(tp_sK16_SY134,type,
sK16_SY134: $i > $i > $i > $i ).
thf(tp_sK17_SY128,type,
sK17_SY128: $i > $i > $i > $i > $i ).
thf(tp_sK18_SY102,type,
sK18_SY102: $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_sK20_SY112,type,
sK20_SY112: $i > $i > $i > $i ).
thf(tp_sK21_SY152,type,
sK21_SY152: $i > $i > $i > $i ).
thf(tp_sK22_SY160,type,
sK22_SY160: $i > $i > $i > $i ).
thf(tp_sK23_SY92,type,
sK23_SY92: $i > $i > $i > $i ).
thf(tp_sK24_SY92,type,
sK24_SY92: $i > $i > $i > $i ).
thf(tp_sK25_SY129,type,
sK25_SY129: $i > $i > $i > $i > $i ).
thf(tp_sK26_SY142,type,
sK26_SY142: $i > $i > $i > $i > $i ).
thf(tp_sK27_SY193,type,
sK27_SY193: $i > $i > $i > $i > $i ).
thf(tp_sK28_SY161,type,
sK28_SY161: $i > $i > $i > $i > $i ).
thf(tp_sK29_SY92,type,
sK29_SY92: $i > $i > $i > $i ).
thf(tp_sK2_SY30,type,
sK2_SY30: $i ).
thf(tp_sK30_SY92,type,
sK30_SY92: $i > $i > $i > $i ).
thf(tp_sK31_SY143,type,
sK31_SY143: $i > $i > $i > $i > $i ).
thf(tp_sK32_SY181,type,
sK32_SY181: $i > $i > $i > $i > $i ).
thf(tp_sK33_SY187,type,
sK33_SY187: $i > $i > $i > $i > $i ).
thf(tp_sK34_SY162,type,
sK34_SY162: $i > $i > $i > $i > $i ).
thf(tp_sK35_SY229,type,
sK35_SY229: $i > $i > $i > $i > $i ).
thf(tp_sK36_SY238,type,
sK36_SY238: $i > $i > $i > $i > $i ).
thf(tp_sK37_SY217,type,
sK37_SY217: $i > $i > $i > $i > $i ).
thf(tp_sK38_SY223,type,
sK38_SY223: $i > $i > $i > $i > $i ).
thf(tp_sK39_SY182,type,
sK39_SY182: $i > $i > $i > $i > $i ).
thf(tp_sK3_SY36,type,
sK3_SY36: $i ).
thf(tp_sK40_SY188,type,
sK40_SY188: $i > $i > $i > $i > $i ).
thf(tp_sK41_SY248,type,
sK41_SY248: $i > $i > $i > $i > $i ).
thf(tp_sK42_SY249,type,
sK42_SY249: $i > $i > $i > $i > $i ).
thf(tp_sK43_SY218,type,
sK43_SY218: $i > $i > $i > $i > $i ).
thf(tp_sK44_SY224,type,
sK44_SY224: $i > $i > $i > $i > $i ).
thf(tp_sK45_SY253,type,
sK45_SY253: $i > $i > $i > $i > $i ).
thf(tp_sK46_SY254,type,
sK46_SY254: $i > $i > $i > $i > $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_SY80,type,
sK7_SY80: $i > $i ).
thf(tp_sK8_SY85,type,
sK8_SY85: $i > $i > $i > $i ).
thf(tp_sK9_SY105,type,
sK9_SY105: $i > $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) )
& ( D = F )
& ? [I: $i,J: $i] :
( ( F
= ( ordered_pair @ I @ J ) )
& ( in @ ( ordered_pair @ ( apply @ C @ I ) @ ( apply @ C @ J ) ) @ B ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ A ) )
& ( F = E )
& ? [K: $i,L: $i] :
( ( E
= ( ordered_pair @ K @ L ) )
& ( in @ ( ordered_pair @ ( apply @ C @ K ) @ ( apply @ C @ L ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(3,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(13,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(19,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(20,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ A @ A ) )
& ? [F: $i,G: $i] :
( ( E
= ( ordered_pair @ F @ G ) )
& ( in @ ( ordered_pair @ ( apply @ C @ F ) @ ( apply @ C @ G ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
thf(21,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ A @ A ) )
& ? [F: $i,G: $i] :
( ( E
= ( ordered_pair @ F @ G ) )
& ( in @ ( ordered_pair @ ( apply @ C @ F ) @ ( apply @ C @ G ) ) @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ A @ A ) )
& ? [F: $i,G: $i] :
( ( E
= ( ordered_pair @ F @ G ) )
& ( in @ ( ordered_pair @ ( apply @ C @ F ) @ ( apply @ C @ G ) ) @ B ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) )
& ( D = F )
& ? [I: $i,J: $i] :
( ( F
= ( ordered_pair @ I @ J ) )
& ( in @ ( ordered_pair @ ( apply @ C @ I ) @ ( apply @ C @ J ) ) @ B ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ A ) )
& ( F = E )
& ? [K: $i,L: $i] :
( ( E
= ( ordered_pair @ K @ L ) )
& ( in @ ( ordered_pair @ ( apply @ C @ K ) @ ( apply @ C @ L ) ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(28,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(32,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(33,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( ( relation @ SY30 )
& ( relation @ SY31 )
& ( function @ SY31 ) )
=> ? [SY32: $i] :
! [SY33: $i] :
( ( in @ SY33 @ SY32 )
<=> ( ( in @ SY33 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
& ? [F: $i,G: $i] :
( ( SY33
= ( ordered_pair @ F @ G ) )
& ( in @ ( ordered_pair @ ( apply @ SY31 @ F ) @ ( apply @ SY31 @ G ) ) @ SY30 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(34,plain,
( ( ! [SY36: $i] :
( ( ( relation @ sK2_SY30 )
& ( relation @ SY36 )
& ( function @ SY36 ) )
=> ? [SY37: $i] :
! [SY38: $i] :
( ( in @ SY38 @ SY37 )
<=> ( ( in @ SY38 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
& ? [SY39: $i,SY40: $i] :
( ( SY38
= ( ordered_pair @ SY39 @ SY40 ) )
& ( in @ ( ordered_pair @ ( apply @ SY36 @ SY39 ) @ ( apply @ SY36 @ SY40 ) ) @ sK2_SY30 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(35,plain,
( ( ( ( relation @ sK2_SY30 )
& ( relation @ sK3_SY36 )
& ( function @ sK3_SY36 ) )
=> ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
& ? [SY43: $i,SY44: $i] :
( ( SY42
= ( ordered_pair @ SY43 @ SY44 ) )
& ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY43 ) @ ( apply @ sK3_SY36 @ SY44 ) ) @ sK2_SY30 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(36,plain,
( ( relation @ sK2_SY30 )
= $true ),
inference(standard_cnf,[status(thm)],[35]) ).
thf(37,plain,
( ( relation @ sK3_SY36 )
= $true ),
inference(standard_cnf,[status(thm)],[35]) ).
thf(38,plain,
( ( function @ sK3_SY36 )
= $true ),
inference(standard_cnf,[status(thm)],[35]) ).
thf(39,plain,
( ( ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
& ? [SY43: $i,SY44: $i] :
( ( SY42
= ( ordered_pair @ SY43 @ SY44 ) )
& ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY43 ) @ ( apply @ sK3_SY36 @ SY44 ) ) @ sK2_SY30 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
& ? [SY43: $i,SY44: $i] :
( ( SY42
= ( ordered_pair @ SY43 @ SY44 ) )
& ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY43 ) @ ( apply @ sK3_SY36 @ SY44 ) ) @ sK2_SY30 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(41,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
$true = $true,
inference(copy,[status(thm)],[28]) ).
thf(46,plain,
$true = $true,
inference(copy,[status(thm)],[27]) ).
thf(47,plain,
$true = $true,
inference(copy,[status(thm)],[26]) ).
thf(48,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(50,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ B )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( E
= ( ordered_pair @ G @ H ) )
& ( in @ ( ordered_pair @ ( apply @ C @ G ) @ ( apply @ C @ H ) ) @ B ) )
& ( D = F )
& ? [I: $i,J: $i] :
( ( F
= ( ordered_pair @ I @ J ) )
& ( in @ ( ordered_pair @ ( apply @ C @ I ) @ ( apply @ C @ J ) ) @ B ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ A ) )
& ( F = E )
& ? [K: $i,L: $i] :
( ( E
= ( ordered_pair @ K @ L ) )
& ( in @ ( ordered_pair @ ( apply @ C @ K ) @ ( apply @ C @ L ) ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(51,plain,
( ( function @ sK3_SY36 )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(52,plain,
( ( relation @ sK3_SY36 )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(53,plain,
( ( relation @ sK2_SY30 )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(54,plain,
( ( ~ ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
& ? [SY43: $i,SY44: $i] :
( ( SY42
= ( ordered_pair @ SY43 @ SY44 ) )
& ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY43 ) @ ( apply @ sK3_SY36 @ SY44 ) ) @ sK2_SY30 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(55,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(56,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(57,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(59,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(60,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( relation @ SX2 ) )
| ~ ( function @ SX2 ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX3 != SX4 )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SX4
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ SX6 ) @ ( apply @ SX2 @ SX7 ) ) @ SX1 ) ) )
| ( SX3 != SX5 ) )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SX5
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ SX6 ) @ ( apply @ SX2 @ SX7 ) ) @ SX1 ) ) )
| ( SX4 = SX5 ) )
| ~ ! [SX3: $i] :
~ ! [SX4: $i] :
~ ( ~ ( ~ ( in @ SX4 @ SX3 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ ( cartesian_product2 @ SX0 @ SX0 ) )
| ( SX5 != SX4 ) )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SX4
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ SX6 ) @ ( apply @ SX2 @ SX7 ) ) @ SX1 ) ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ ( cartesian_product2 @ SX0 @ SX0 ) )
| ( SX5 != SX4 ) )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SX4
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ SX6 ) @ ( apply @ SX2 @ SX7 ) ) @ SX1 ) ) )
| ( in @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(62,plain,
! [SV1: $i] :
( ( ! [SY45: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(63,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(65,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV3: $i] :
( ( ! [SY46: $i] :
( ~ ( in @ SV3 @ SY46 )
| ~ ( in @ SY46 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(67,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(68,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV4: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SY47 )
| ~ ( relation @ SY48 ) )
| ~ ( function @ SY48 ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX3 != SX4 )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SX4
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY48 @ SX6 ) @ ( apply @ SY48 @ SX7 ) ) @ SY47 ) ) )
| ( SX3 != SX5 ) )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SX5
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY48 @ SX6 ) @ ( apply @ SY48 @ SX7 ) ) @ SY47 ) ) )
| ( SX4 = SX5 ) )
| ~ ! [SY56: $i] :
~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SY56 )
| ~ ! [SY58: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY58 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY58 != SY57 ) )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SY57
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY48 @ SX6 ) @ ( apply @ SY48 @ SX7 ) ) @ SY47 ) ) ) )
| ~ ( ~ ~ ! [SY61: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY61 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY61 != SY57 ) )
| ~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ( ( SY57
!= ( ordered_pair @ SX6 @ SX7 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY48 @ SX6 ) @ ( apply @ SY48 @ SX7 ) ) @ SY47 ) ) )
| ( in @ SY57 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(71,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(73,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
| ~ ( one_to_one @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(74,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV6 )
| ~ ( in @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SX1
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(76,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(77,plain,
! [SV4: $i,SV7: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SY64 ) )
| ~ ( function @ SY64 ) )
| ~ ! [SY65: $i,SY66: $i,SY67: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY65 != SY66 )
| ~ ~ ! [SY68: $i] :
~ ~ ! [SY69: $i] :
~ ~ ( ( SY66
!= ( ordered_pair @ SY68 @ SY69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY64 @ SY68 ) @ ( apply @ SY64 @ SY69 ) ) @ SV7 ) ) )
| ( SY65 != SY67 ) )
| ~ ~ ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ( ( SY67
!= ( ordered_pair @ SY70 @ SY71 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY64 @ SY70 ) @ ( apply @ SY64 @ SY71 ) ) @ SV7 ) ) )
| ( SY66 = SY67 ) )
| ~ ! [SY72: $i] :
~ ! [SY73: $i] :
~ ( ~ ( ~ ( in @ SY73 @ SY72 )
| ~ ! [SY74: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY74 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY74 != SY73 ) )
| ~ ~ ! [SY75: $i] :
~ ~ ! [SY76: $i] :
~ ~ ( ( SY73
!= ( ordered_pair @ SY75 @ SY76 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY64 @ SY75 ) @ ( apply @ SY64 @ SY76 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY77: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY77 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY77 != SY73 ) )
| ~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ~ ( ( SY73
!= ( ordered_pair @ SY78 @ SY79 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY64 @ SY78 ) @ ( apply @ SY64 @ SY79 ) ) @ SV7 ) ) )
| ( in @ SY73 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV5: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
| ~ ( one_to_one @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV8: $i] :
( ( ~ ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV8 )
| ~ ( ~ ( in @ SY80 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY80 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) )
| ( in @ SY80 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(84,plain,
( ( ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(85,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV9 ) )
| ~ ( function @ SV9 ) )
| ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(86,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
| ~ ( one_to_one @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ SV3 @ SV6 )
= $false )
| ( ( ~ ( in @ SV6 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV8: $i] :
( ( ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV8 )
| ~ ( ~ ( in @ SY80 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY80 @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ( SY80
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SX2 ) @ ( apply @ sK3_SY36 @ SX3 ) ) @ sK2_SY30 ) ) )
| ( in @ SY80 @ SV8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(90,plain,
( ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV9 ) )
| ~ ( function @ SV9 ) ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(92,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(93,plain,
( ( ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(94,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(95,plain,
( ( ~ ( one_to_one @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(96,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ SV3 )
= $false )
| ( ( in @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV8: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
| ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(98,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(99,plain,
( ( ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(100,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV9 ) )
| ~ ( function @ SV9 ) ) )
= $false )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(101,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(102,plain,
( ( function @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(103,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(104,plain,
( ( one_to_one @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(105,plain,
! [SV8: $i] :
( ( ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
| ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(106,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(107,plain,
( ( function @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(108,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV9 ) )
| ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(109,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(110,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
| ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV9 ) ) )
= $true )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(113,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(114,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(115,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(116,plain,
( ( ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(117,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
| ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(118,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV9 ) ) )
= $false )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(119,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(120,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(121,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(122,plain,
( ( function @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(123,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(124,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(125,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( relation @ SV7 )
| ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(126,plain,
! [SV8: $i] :
( ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(127,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(128,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) ) )
= $true )
| ( ( ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(133,plain,
! [SV8: $i] :
( ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(134,plain,
! [SV8: $i] :
( ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(137,plain,
! [SV8: $i] :
( ( ( ~ ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(138,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( function @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) )
| ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV8: $i] :
( ( ( ! [SY100: $i] :
~ ~ ! [SY101: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY100 @ SY101 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY100 ) @ ( apply @ sK3_SY36 @ SY101 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(141,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(143,plain,
! [SV8: $i] :
( ( ( ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(144,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ~ ! [SY104: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SV10 @ SY104 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SY104 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY85 != SY86 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY86
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( SY85 != SY87 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY87
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY86 = SY87 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV8: $i] :
( ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(147,plain,
! [SV8: $i] :
( ( ( ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(148,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ! [SY104: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SV10 @ SY104 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SY104 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(149,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= SY105 )
| ~ ~ ! [SY88: $i] :
~ ~ ! [SY89: $i] :
~ ~ ( ( SY105
!= ( ordered_pair @ SY88 @ SY89 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY88 ) @ ( apply @ SV9 @ SY89 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= SY106 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY106
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( SY105 = SY106 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[145]) ).
thf(150,plain,
! [SV8: $i] :
( ( ( ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(151,plain,
! [SV10: $i,SV8: $i] :
( ( ( ! [SY104: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SV10 @ SY104 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SY104 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(152,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY111: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= SY111 ) )
| ~ ~ ! [SY90: $i] :
~ ~ ! [SY91: $i] :
~ ~ ( ( SY111
!= ( ordered_pair @ SY90 @ SY91 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY90 ) @ ( apply @ SV9 @ SY91 ) ) @ SV7 ) ) )
| ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= SY111 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[149]) ).
thf(153,plain,
! [SV8: $i] :
( ( ( ~ ~ ! [SY116: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ SY116 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ SY116 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(154,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SV10 @ SV11 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(155,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) )
| ~ ~ ! [SY119: $i] :
~ ~ ! [SY120: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY119 @ SY120 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY119 ) @ ( apply @ SV9 @ SY120 ) ) @ SV7 ) ) )
| ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[152]) ).
thf(156,plain,
! [SV8: $i] :
( ( ( ~ ! [SY116: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ SY116 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ SY116 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(157,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SV10 @ SV11 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) )
| ~ ~ ! [SY119: $i] :
~ ~ ! [SY120: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY119 @ SY120 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY119 ) @ ( apply @ SV9 @ SY120 ) ) @ SV7 ) ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(159,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(160,plain,
! [SV8: $i] :
( ( ( ! [SY116: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ SY116 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ SY116 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(161,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SV10 @ SV11 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(162,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) )
| ~ ~ ! [SY119: $i] :
~ ~ ! [SY120: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY119 @ SY120 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY119 ) @ ( apply @ SV9 @ SY120 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV7: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ ( sK12_SY116 @ SV8 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK12_SY116 @ SV8 ) ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[160]) ).
thf(165,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SV10 @ SV11 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) )
| ~ ~ ! [SY119: $i] :
~ ~ ! [SY120: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY119 @ SY120 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY119 ) @ ( apply @ SV9 @ SY120 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY121 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY121
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY121 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY121
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY121 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[163]) ).
thf(168,plain,
! [SV8: $i] :
( ( ( ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ ( sK12_SY116 @ SV8 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK12_SY116 @ SV8 ) ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(169,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(170,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(171,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ~ ! [SY119: $i] :
~ ~ ! [SY120: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY119 @ SY120 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY119 ) @ ( apply @ SV9 @ SY120 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(172,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY121 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY121
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY121 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY121
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY121 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(173,plain,
! [SV8: $i] :
( ( ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ ( sK12_SY116 @ SV8 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK12_SY116 @ SV8 ) ) ) @ sK2_SY30 ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(174,plain,
! [SV8: $i,SV11: $i,SV10: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(175,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(176,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ! [SY119: $i] :
~ ~ ! [SY120: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY119 @ SY120 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY119 ) @ ( apply @ SV9 @ SY120 ) ) @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(177,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV12: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY128: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY128 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY128 != SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY131 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY131 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
| ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV8: $i] :
( ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ ( sK12_SY116 @ SV8 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(179,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK12_SY116 @ SV8 ) ) ) @ sK2_SY30 ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(180,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
| ( in @ ( sK7_SY80 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(181,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
| ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(182,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ! [SY119: $i] :
~ ~ ! [SY120: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY119 @ SY120 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY119 ) @ ( apply @ SV9 @ SY120 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(183,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY128: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY128 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY128 != SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY131 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY131 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
| ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(184,plain,
! [SV8: $i] :
( ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ ( sK10_SY102 @ SV8 ) @ ( sK12_SY116 @ SV8 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(185,plain,
! [SV8: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK10_SY102 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK12_SY116 @ SV8 ) ) ) @ sK2_SY30 )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(186,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(187,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( in @ ( sK7_SY80 @ SV8 ) @ SV8 )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(188,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(189,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(190,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ~ ! [SY134: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ SY134 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ SY134 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[182]) ).
thf(191,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY128: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY128 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY128 != SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(192,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY131 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY131 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
| ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(193,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(194,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(195,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(196,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ! [SY134: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ SY134 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ SY134 ) ) @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(197,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY128: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY128 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY128 != SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(198,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY131 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY131 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
| ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(199,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
| ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
| ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV7: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ! [SY134: $i] :
~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ SY134 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ SY134 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY128 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY128 != SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(204,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ! [SY131: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY131 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY131 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(206,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(207,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
!= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(208,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(209,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY135 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY135
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY135 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY135
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY135 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[201]) ).
thf(210,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[202]) ).
thf(211,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV12: $i] :
( ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY128 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY128 != SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i] :
( ( ( ~ ! [SY131: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY131 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY131 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(214,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ~ ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(215,plain,
! [SV9: $i,SV7: $i,SV4: $i] :
( ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(216,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(217,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY135 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY135
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY135 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY135
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY135 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(218,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(219,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY128 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY128 != SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY131: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY131 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY131 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(221,plain,
! [SV11: $i,SV10: $i,SV8: $i] :
( ( ( ! [SY102: $i] :
~ ~ ! [SY103: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ SY102 @ SY103 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SY102 ) @ ( apply @ sK3_SY36 @ SY103 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(222,plain,
! [SV7: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(223,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ SY112 @ SY113 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY112 ) @ ( apply @ SV9 @ SY113 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(224,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY142: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY142 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY142 != SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY145: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY145 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY145 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
| ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(226,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
!= SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[219]) ).
thf(227,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV14 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(228,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ~ ~ ! [SY152: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ SY152 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ SY152 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[221]) ).
thf(229,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY153: $i] :
~ ( ~ ( ~ ( in @ SY153 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY153 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY153
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY153 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY153
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY153 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[222]) ).
thf(230,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ~ ! [SY160: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ SY160 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ SY160 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[223]) ).
thf(231,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY142: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY142 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY142 != SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY145: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY145 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY145 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
| ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(232,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(233,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(234,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
!= SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(235,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV14 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(236,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ~ ! [SY152: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ SY152 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ SY152 ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(237,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY153: $i] :
~ ( ~ ( ~ ( in @ SY153 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY153 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY153
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY153 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY153
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY153 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(238,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ! [SY160: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ SY160 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ SY160 ) ) @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(239,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY142: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY142 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY142 != SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY145: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY145 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY145 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
| ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(241,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(242,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(243,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
!= SV12 ) )
| ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV14 != SV12 ) )
| ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(245,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ! [SY152: $i] :
~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ SY152 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ SY152 ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(246,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY161 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY161 != SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY164 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY164 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
| ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(247,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ! [SY160: $i] :
~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ SY160 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ SY160 ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(248,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY142: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY142 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY142 != SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(249,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i] :
( ( ( ~ ~ ! [SY145: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY145 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY145 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
| ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(250,plain,
! [SV7: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(251,plain,
! [SV7: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(252,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
!= SV12 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(253,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV12: $i] :
( ( ( ~ ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(254,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV14 != SV12 ) ) )
= $true )
| ( ( ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(255,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ~ ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) ) @ sK2_SY30 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[245]) ).
thf(256,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY161 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY161 != SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY164 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY164 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
| ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(257,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[247]) ).
thf(258,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY142: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY142 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY142 != SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(259,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i] :
( ( ( ~ ~ ! [SY145: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY145 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY145 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(260,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY167 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY167
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY167 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY167
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY167 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[250]) ).
thf(261,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY174: $i] :
~ ( ~ ( ~ ( in @ SY174 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY174 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY174
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY174 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY174
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY174 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[251]) ).
thf(262,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
!= SV12 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(263,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV12: $i] :
( ( ( ~ ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(264,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV14 != SV12 ) ) )
= $false )
| ( ( ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(265,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ~ ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) ) @ sK2_SY30 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(266,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY161 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY161 != SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(267,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY164 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY164 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
| ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(268,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(269,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV13: $i] :
( ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ~ ! [SY142: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY142 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY142 != SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i] :
( ( ( ~ ! [SY145: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY145 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY145 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY167: $i] :
~ ( ~ ( ~ ( in @ SY167 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY167 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY167
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY167 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY167
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY167 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(272,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY174: $i] :
~ ( ~ ( ~ ( in @ SY174 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY174 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY174
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY174 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY174
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY174 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(273,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
!= SV12 ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(274,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV12: $i] :
( ( ( ! [SY129: $i] :
~ ~ ! [SY130: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY129 @ SY130 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY129 ) @ ( apply @ SV9 @ SY130 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(275,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV14 != SV12 ) )
= $true )
| ( ( ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(276,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) ) @ sK2_SY30 ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY161: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY161 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY161 != SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(278,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i] :
( ( ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY164 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY164 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
| ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(279,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(280,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i] :
( ( ( ! [SY142: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY142 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY142 != SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(281,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i] :
( ( ( ! [SY145: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY145 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY145 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(282,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY181: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY181 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY181 != SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY184 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY184 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
| ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(283,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY187 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY187 != SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY190 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
| ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(284,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(285,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
!= SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(286,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( ~ ~ ! [SY193: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ SY193 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ SY193 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[274]) ).
thf(287,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $true )
| ( ( SV14 != SV12 )
= $true )
| ( ( ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(288,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ( sK7_SY80 @ SV8 )
!= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(289,plain,
! [SV8: $i,SV10: $i,SV11: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) ) @ sK2_SY30 ) )
= $false )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(290,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY161: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY161 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY161 != SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(291,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i] :
( ( ( ~ ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY164 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY164 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(292,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
!= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(293,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 ) )
= $false )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(294,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
!= SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[280]) ).
thf(295,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV18 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(296,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY181: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY181 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY181 != SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY184: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY184 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY184 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
| ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(297,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY187 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY187 != SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY190 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
| ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(298,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(299,plain,
! [SV4: $i,SV12: $i,SV9: $i,SV7: $i] :
( ( ( ( sK17_SY128 @ SV7 @ SV9 @ SV12 @ SV4 )
= SV12 )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(300,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( ~ ! [SY193: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ SY193 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ SY193 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(301,plain,
! [SV7: $i,SV9: $i,SV12: $i,SV4: $i,SV14: $i] :
( ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 != SV12 )
= $true )
| ( ( ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(302,plain,
! [SV10: $i,SV11: $i,SV8: $i] :
( ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(303,plain,
! [SV8: $i,SV10: $i,SV11: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ ( sK18_SY102 @ SV11 @ SV10 @ SV8 ) ) @ ( apply @ sK3_SY36 @ ( sK21_SY152 @ SV10 @ SV11 @ SV8 ) ) ) @ sK2_SY30 )
= $true )
| ( ( in @ ( sK7_SY80 @ SV8 ) @ ( cartesian_product2 @ sK1_A @ sK1_A ) )
= $false )
| ( ( ( sK7_SY80 @ SV8 )
= ( ordered_pair @ SV10 @ SV11 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ sK3_SY36 @ SV10 ) @ ( apply @ sK3_SY36 @ SV11 ) ) @ sK2_SY30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(304,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV15: $i] :
( ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ~ ! [SY161: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY161 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY161 != SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(305,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i] :
( ( ( ~ ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY164 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY164 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(306,plain,
! [SV4: $i,SV7: $i,SV9: $i] :
( ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(307,plain,
! [SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( ~ ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(308,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
!= SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(309,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV18 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(310,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY181: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY181 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY181 != SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(311,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY184: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY184 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY184 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
| ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(312,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY187 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY187 != SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(313,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY190 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
| ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(314,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( ! [SY193: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ SY193 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ SY193 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(315,plain,
! [SV7: $i,SV9: $i,SV4: $i,SV12: $i,SV14: $i] :
( ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( ~ ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(316,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i] :
( ( ( ! [SY161: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY161 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY161 != SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(317,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i] :
( ( ( ! [SY164: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY164 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY164 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(318,plain,
! [SV7: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(319,plain,
! [SV7: $i,SV9: $i,SV4: $i] :
( ( ( ! [SY92: $i] :
~ ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY93 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY93 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY93
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY93 @ SY92 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(320,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
!= SV13 ) )
| ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(321,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV18 != SV13 ) )
| ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(322,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY181: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY181 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY181 != SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(323,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i] :
( ( ( ~ ~ ! [SY184: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY184 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY184 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
| ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(324,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY187 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY187 != SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(325,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i] :
( ( ( ~ ~ ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY190 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
| ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(326,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12
!= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[314]) ).
thf(327,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV12: $i] :
( ( ( ~ ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(328,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
!= SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[316]) ).
thf(329,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV19 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(330,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY202: $i] :
~ ( ~ ( ~ ( in @ SY202 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY202 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY202
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY202 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY202
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY202 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[318]) ).
thf(331,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ~ ! [SY209: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY209 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY209
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY209 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY209
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY209 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[319]) ).
thf(332,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
!= SV13 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(333,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV13: $i] :
( ( ( ~ ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(334,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV18 != SV13 ) ) )
= $true )
| ( ( ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(335,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY181: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY181 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY181 != SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(336,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i] :
( ( ( ~ ~ ! [SY184: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY184 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY184 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(337,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY187 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY187 != SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(338,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i] :
( ( ( ~ ~ ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY190 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(339,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( ( SV12
!= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(340,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV12: $i] :
( ( ( ! [SY132: $i] :
~ ~ ! [SY133: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SY132 @ SY133 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY132 ) @ ( apply @ SV9 @ SY133 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(341,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
!= SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(342,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV19 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(343,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY202: $i] :
~ ( ~ ( ~ ( in @ SY202 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY202 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY202
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY202 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY202
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY202 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(344,plain,
! [SV4: $i,SV9: $i,SV7: $i] :
( ( ( ! [SY209: $i] :
~ ( ~ ( ~ ( in @ SY209 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY94: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY94 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY94 != SY209 ) )
| ~ ~ ! [SY95: $i] :
~ ~ ! [SY96: $i] :
~ ~ ( ( SY209
!= ( ordered_pair @ SY95 @ SY96 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY95 ) @ ( apply @ SV9 @ SY96 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY97 != SY209 ) )
| ~ ~ ! [SY98: $i] :
~ ~ ! [SY99: $i] :
~ ~ ( ( SY209
!= ( ordered_pair @ SY98 @ SY99 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY98 ) @ ( apply @ SV9 @ SY99 ) ) @ SV7 ) ) )
| ( in @ SY209 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(345,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
!= SV13 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(346,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV13: $i] :
( ( ( ~ ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(347,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV18 != SV13 ) ) )
= $false )
| ( ( ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(348,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV16: $i] :
( ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ~ ! [SY181: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY181 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY181 != SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(349,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i] :
( ( ( ~ ! [SY184: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY184 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY184 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(350,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV17: $i] :
( ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY187 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY187 != SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(351,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i] :
( ( ( ~ ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY190 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(352,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( ( SV12
!= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(353,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV20: $i,SV12: $i] :
( ( ( ~ ~ ! [SY216: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SV20 @ SY216 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SY216 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(354,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
!= SV15 ) )
| ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(355,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV19 != SV15 ) )
| ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(356,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY217: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY217 != SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY220 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
| ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(357,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY223: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY223 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY223 != SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY226 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY226 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
| ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(358,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
!= SV13 ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(359,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV13: $i] :
( ( ( ! [SY143: $i] :
~ ~ ! [SY144: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY143 @ SY144 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY143 ) @ ( apply @ SV9 @ SY144 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(360,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV18 != SV13 ) )
= $true )
| ( ( ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(361,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i] :
( ( ( ! [SY181: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY181 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY181 != SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(362,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i] :
( ( ( ! [SY184: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY184 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY184 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(363,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i] :
( ( ( ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY187 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY187 != SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i] :
( ( ( ! [SY190: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY190 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(365,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( SV12
!= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(366,plain,
! [SV12: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(367,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV20: $i,SV12: $i] :
( ( ( ~ ! [SY216: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SV20 @ SY216 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SY216 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(368,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
!= SV15 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(369,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV15: $i] :
( ( ( ~ ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(370,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV19 != SV15 ) ) )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(371,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY217: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY217 != SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY220 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
| ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(372,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY223: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY223 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY223 != SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
| ~ ( ~ ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY226 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY226 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
| ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(373,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(374,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
!= SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(375,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ~ ~ ! [SY229: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ SY229 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ SY229 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[359]) ).
thf(376,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $true )
| ( ( SV18 != SV13 )
= $true )
| ( ( ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(377,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
!= SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[361]) ).
thf(378,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV23 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(379,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
!= SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[363]) ).
thf(380,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV24 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(381,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV12: $i] :
( ( ( SV12
= ( ordered_pair @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(382,plain,
! [SV12: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK25_SY129 @ SV4 @ SV7 @ SV9 @ SV12 ) ) @ ( apply @ SV9 @ ( sK27_SY193 @ SV9 @ SV7 @ SV4 @ SV12 ) ) ) @ SV7 )
= $true )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(383,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV20: $i,SV12: $i] :
( ( ( ! [SY216: $i] :
~ ~ ( ( SV12
!= ( ordered_pair @ SV20 @ SY216 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SY216 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(384,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
!= SV15 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(385,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV15: $i] :
( ( ( ~ ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(386,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV19 != SV15 ) ) )
= $false )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(387,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY217: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY217 != SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(388,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY220 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
| ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(389,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY223: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY223 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY223 != SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(390,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY226 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY226 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
| ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(391,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(392,plain,
! [SV4: $i,SV13: $i,SV9: $i,SV7: $i] :
( ( ( ( sK26_SY142 @ SV7 @ SV9 @ SV13 @ SV4 )
= SV13 )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(393,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ~ ! [SY229: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ SY229 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ SY229 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(394,plain,
! [SV7: $i,SV9: $i,SV13: $i,SV4: $i,SV18: $i] :
( ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 != SV13 )
= $true )
| ( ( ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(395,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
!= SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(396,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV23 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(397,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
!= SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(398,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV24 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(399,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ( ~ ~ ( ( SV12
!= ( ordered_pair @ SV20 @ SV25 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SV25 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(400,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
!= SV15 ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(401,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV15: $i] :
( ( ( ! [SY162: $i] :
~ ~ ! [SY163: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY162 @ SY163 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY162 ) @ ( apply @ SV9 @ SY163 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(402,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV19 != SV15 ) )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(403,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY217: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY217 != SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(404,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i] :
( ( ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY220 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
| ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(405,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
| ~ ! [SY223: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY223 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY223 != SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(406,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i] :
( ( ( ~ ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY226 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY226 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
| ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(407,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ! [SY229: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ SY229 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ SY229 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(408,plain,
! [SV7: $i,SV9: $i,SV4: $i,SV13: $i,SV18: $i] :
( ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( ~ ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(409,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
!= SV16 ) )
| ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(410,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV23 != SV16 ) )
| ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(411,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
!= SV17 ) )
| ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(412,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV24 != SV17 ) )
| ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(413,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( ( SV12
!= ( ordered_pair @ SV20 @ SV25 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SV25 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(414,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(415,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
!= SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(416,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( ~ ~ ! [SY238: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ SY238 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ SY238 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[401]) ).
thf(417,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $true )
| ( ( SV19 != SV15 )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(418,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY217: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY217 != SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(419,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i] :
( ( ( ~ ~ ! [SY220: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY220 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(420,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) ) )
= $true )
| ( ( ~ ! [SY223: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY223 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY223 != SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(421,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i] :
( ( ( ~ ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY226 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY226 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(422,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ~ ~ ( ( SV13
!= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[407]) ).
thf(423,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV13: $i] :
( ( ( ~ ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(424,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
!= SV16 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(425,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV16: $i] :
( ( ( ~ ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(426,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV23 != SV16 ) ) )
= $true )
| ( ( ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(427,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
!= SV17 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(428,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV17: $i] :
( ( ( ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(429,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV24 != SV17 ) ) )
= $true )
| ( ( ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(430,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ( ( SV12
!= ( ordered_pair @ SV20 @ SV25 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SV25 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(431,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(432,plain,
! [SV4: $i,SV15: $i,SV9: $i,SV7: $i] :
( ( ( ( sK28_SY161 @ SV7 @ SV9 @ SV15 @ SV4 )
= SV15 )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(433,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( ~ ! [SY238: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ SY238 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ SY238 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(434,plain,
! [SV7: $i,SV9: $i,SV15: $i,SV4: $i,SV19: $i] :
( ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 != SV15 )
= $true )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(435,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV21: $i] :
( ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ~ ! [SY217: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY217 != SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(436,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i] :
( ( ( ~ ! [SY220: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY220 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(437,plain,
! [SV4: $i,SV9: $i,SV7: $i,SV22: $i] :
( ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ~ ! [SY223: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY223 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY223 != SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(438,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i] :
( ( ( ~ ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY226 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY226 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(439,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(440,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV13: $i] :
( ( ( ! [SY146: $i] :
~ ~ ! [SY147: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SY146 @ SY147 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY146 ) @ ( apply @ SV9 @ SY147 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(441,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
!= SV16 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(442,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV16: $i] :
( ( ( ~ ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(443,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV23 != SV16 ) ) )
= $false )
| ( ( ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(444,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
!= SV17 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(445,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV17: $i] :
( ( ( ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(446,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV24 != SV17 ) ) )
= $false )
| ( ( ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(447,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ( SV12
!= ( ordered_pair @ SV20 @ SV25 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SV25 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(448,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( ! [SY238: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ SY238 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ SY238 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(449,plain,
! [SV7: $i,SV9: $i,SV4: $i,SV15: $i,SV19: $i] :
( ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( ~ ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(450,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i] :
( ( ( ! [SY217: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY217 != SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(451,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i] :
( ( ( ! [SY220: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY220 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY220 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(452,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i] :
( ( ( ! [SY223: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY223 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY223 != SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(453,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i] :
( ( ( ! [SY226: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY226 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SY226 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(454,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ( SV13
!= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(455,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV26: $i,SV13: $i] :
( ( ( ~ ~ ! [SY239: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SV26 @ SY239 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SY239 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(456,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
!= SV16 ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(457,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV16: $i] :
( ( ( ! [SY182: $i] :
~ ~ ! [SY183: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY182 @ SY183 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY182 ) @ ( apply @ SV9 @ SY183 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(458,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV23 != SV16 ) )
= $true )
| ( ( ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(459,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
!= SV17 ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(460,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV17: $i] :
( ( ( ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY188 @ SY189 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY188 ) @ ( apply @ SV9 @ SY189 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(461,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV24 != SV17 ) )
= $true )
| ( ( ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(462,plain,
! [SV4: $i,SV14: $i,SV7: $i,SV9: $i,SV25: $i,SV20: $i,SV12: $i] :
( ( ( SV12
= ( ordered_pair @ SV20 @ SV25 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SV25 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(463,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( ~ ~ ( ( SV15
!= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[448]) ).
thf(464,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV15: $i] :
( ( ( ~ ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(465,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
!= SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[450]) ).
thf(466,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV27 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(467,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
!= SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[452]) ).
thf(468,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV28 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(469,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( SV13
!= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(470,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(471,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV26: $i,SV13: $i] :
( ( ( ~ ! [SY239: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SV26 @ SY239 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SY239 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(472,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(473,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
!= SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(474,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ~ ~ ! [SY248: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ SY248 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ SY248 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[457]) ).
thf(475,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $true )
| ( ( SV23 != SV16 )
= $true )
| ( ( ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(476,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(477,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
!= SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(478,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( ~ ~ ! [SY249: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ SY249 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ SY249 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[460]) ).
thf(479,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $true )
| ( ( SV24 != SV17 )
= $true )
| ( ( ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(480,plain,
! [SV4: $i,SV14: $i,SV12: $i,SV7: $i,SV25: $i,SV20: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ SV20 ) @ ( apply @ SV9 @ SV25 ) ) @ SV7 )
= $false )
| ( ( SV12
= ( ordered_pair @ SV20 @ SV25 ) )
= $false )
| ( ( in @ SV14 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV14 = SV12 )
= $false )
| ( ( in @ SV12 @ ( sK13_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(481,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(482,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV15: $i] :
( ( ( ! [SY165: $i] :
~ ~ ! [SY166: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SY165 @ SY166 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY165 ) @ ( apply @ SV9 @ SY166 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(483,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
!= SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(484,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV27 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(485,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
!= SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(486,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV28 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(487,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( SV13
= ( ordered_pair @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(488,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK31_SY143 @ SV4 @ SV7 @ SV9 @ SV13 ) ) @ ( apply @ SV9 @ ( sK35_SY229 @ SV9 @ SV7 @ SV4 @ SV13 ) ) ) @ SV7 )
= $true )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(489,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV26: $i,SV13: $i] :
( ( ( ! [SY239: $i] :
~ ~ ( ( SV13
!= ( ordered_pair @ SV26 @ SY239 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SY239 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(490,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(491,plain,
! [SV4: $i,SV16: $i,SV9: $i,SV7: $i] :
( ( ( ( sK32_SY181 @ SV7 @ SV9 @ SV16 @ SV4 )
= SV16 )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(492,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ~ ! [SY248: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ SY248 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ SY248 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(493,plain,
! [SV7: $i,SV9: $i,SV16: $i,SV4: $i,SV23: $i] :
( ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 != SV16 )
= $true )
| ( ( ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(494,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(495,plain,
! [SV4: $i,SV17: $i,SV9: $i,SV7: $i] :
( ( ( ( sK33_SY187 @ SV7 @ SV9 @ SV17 @ SV4 )
= SV17 )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(496,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( ~ ! [SY249: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ SY249 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ SY249 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(497,plain,
! [SV7: $i,SV9: $i,SV17: $i,SV4: $i,SV24: $i] :
( ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 != SV17 )
= $true )
| ( ( ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(498,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( ( SV15
!= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(499,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ! [SY250: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SV29 @ SY250 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SY250 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(500,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
!= SV21 ) )
| ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(501,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV27 != SV21 ) )
| ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(502,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
!= SV22 ) )
| ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(503,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV28 != SV22 ) )
| ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(504,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV30: $i,SV26: $i,SV13: $i] :
( ( ( ~ ~ ( ( SV13
!= ( ordered_pair @ SV26 @ SV30 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SV30 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(505,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ! [SY248: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ SY248 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ SY248 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(506,plain,
! [SV7: $i,SV9: $i,SV4: $i,SV16: $i,SV23: $i] :
( ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( ~ ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(507,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( ! [SY249: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ SY249 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ SY249 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(508,plain,
! [SV7: $i,SV9: $i,SV4: $i,SV17: $i,SV24: $i] :
( ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( ~ ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(509,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( SV15
!= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(510,plain,
! [SV15: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(511,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV29: $i,SV15: $i] :
( ( ( ~ ! [SY250: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SV29 @ SY250 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SY250 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(512,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
!= SV21 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(513,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV21: $i] :
( ( ( ~ ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(514,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV27 != SV21 ) ) )
= $true )
| ( ( ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(515,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
!= SV22 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(516,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV22: $i] :
( ( ( ~ ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(517,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV28 != SV22 ) ) )
= $true )
| ( ( ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(518,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV30: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( ordered_pair @ SV26 @ SV30 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SV30 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(519,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ~ ~ ( ( SV16
!= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[505]) ).
thf(520,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV16: $i] :
( ( ( ~ ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(521,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( ~ ~ ( ( SV17
!= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[507]) ).
thf(522,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV17: $i] :
( ( ( ~ ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(523,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV15: $i] :
( ( ( SV15
= ( ordered_pair @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(524,plain,
! [SV15: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK34_SY162 @ SV4 @ SV7 @ SV9 @ SV15 ) ) @ ( apply @ SV9 @ ( sK36_SY238 @ SV9 @ SV7 @ SV4 @ SV15 ) ) ) @ SV7 )
= $true )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(525,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV29: $i,SV15: $i] :
( ( ( ! [SY250: $i] :
~ ~ ( ( SV15
!= ( ordered_pair @ SV29 @ SY250 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SY250 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(526,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
!= SV21 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(527,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV21: $i] :
( ( ( ~ ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(528,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV27 != SV21 ) ) )
= $false )
| ( ( ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(529,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
!= SV22 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(530,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV22: $i] :
( ( ( ~ ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(531,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( ~ ( ~ ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV28 != SV22 ) ) )
= $false )
| ( ( ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(532,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV30: $i,SV26: $i,SV13: $i] :
( ( ( ( SV13
!= ( ordered_pair @ SV26 @ SV30 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SV30 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(533,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( ( SV16
!= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(534,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV16: $i] :
( ( ( ! [SY185: $i] :
~ ~ ! [SY186: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SY185 @ SY186 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY185 ) @ ( apply @ SV9 @ SY186 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(535,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(536,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV17: $i] :
( ( ( ! [SY191: $i] :
~ ~ ! [SY192: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SY191 @ SY192 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY191 ) @ ( apply @ SV9 @ SY192 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(537,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV31: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ( SV15
!= ( ordered_pair @ SV29 @ SV31 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SV31 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(538,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
!= SV21 ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(539,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV21: $i] :
( ( ( ! [SY218: $i] :
~ ~ ! [SY219: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY218 @ SY219 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY218 ) @ ( apply @ SV9 @ SY219 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(540,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV27 != SV21 ) )
= $true )
| ( ( ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(541,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
!= SV22 ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(542,plain,
! [SV4: $i,SV7: $i,SV9: $i,SV22: $i] :
( ( ( ! [SY224: $i] :
~ ~ ! [SY225: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY224 @ SY225 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY224 ) @ ( apply @ SV9 @ SY225 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(543,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
| ( SV28 != SV22 ) )
= $true )
| ( ( ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(544,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV30: $i,SV26: $i,SV13: $i] :
( ( ( SV13
!= ( ordered_pair @ SV26 @ SV30 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SV30 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(545,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( ( SV16
!= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(546,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV32: $i,SV16: $i] :
( ( ( ~ ~ ! [SY251: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SV32 @ SY251 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SY251 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(547,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( ( SV17
!= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(548,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV33: $i,SV17: $i] :
( ( ( ~ ~ ! [SY252: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SV33 @ SY252 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SY252 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(549,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV31: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( ordered_pair @ SV29 @ SV31 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SV31 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(550,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(551,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
!= SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(552,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ SY253 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ SY253 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[539]) ).
thf(553,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $true )
| ( ( SV27 != SV21 )
= $true )
| ( ( ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(554,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(555,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
!= SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(556,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( ~ ~ ! [SY254: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ SY254 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ SY254 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[542]) ).
thf(557,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) ) )
= $true )
| ( ( SV28 != SV22 )
= $true )
| ( ( ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(558,plain,
! [SV4: $i,SV18: $i,SV7: $i,SV9: $i,SV30: $i,SV26: $i,SV13: $i] :
( ( ( SV13
= ( ordered_pair @ SV26 @ SV30 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SV30 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(559,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( SV16
!= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(560,plain,
! [SV16: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(561,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV32: $i,SV16: $i] :
( ( ( ~ ! [SY251: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SV32 @ SY251 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SY251 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(562,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( SV17
!= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(563,plain,
! [SV17: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(564,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV33: $i,SV17: $i] :
( ( ( ~ ! [SY252: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SV33 @ SY252 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SY252 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(565,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV31: $i,SV29: $i,SV15: $i] :
( ( ( ( SV15
!= ( ordered_pair @ SV29 @ SV31 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SV31 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(566,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(567,plain,
! [SV4: $i,SV21: $i,SV9: $i,SV7: $i] :
( ( ( ( sK37_SY217 @ SV7 @ SV9 @ SV21 @ SV4 )
= SV21 )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(568,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( ~ ! [SY253: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ SY253 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ SY253 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(569,plain,
! [SV7: $i,SV9: $i,SV21: $i,SV4: $i,SV27: $i] :
( ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 != SV21 )
= $true )
| ( ( ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(570,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( in @ ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 ) @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(571,plain,
! [SV4: $i,SV22: $i,SV9: $i,SV7: $i] :
( ( ( ( sK38_SY223 @ SV7 @ SV9 @ SV22 @ SV4 )
= SV22 )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(572,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( ~ ! [SY254: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ SY254 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ SY254 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(573,plain,
! [SV7: $i,SV9: $i,SV22: $i,SV4: $i,SV28: $i] :
( ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 != SV22 )
= $true )
| ( ( ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(574,plain,
! [SV4: $i,SV18: $i,SV13: $i,SV7: $i,SV30: $i,SV26: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ SV26 ) @ ( apply @ SV9 @ SV30 ) ) @ SV7 )
= $false )
| ( ( SV13
= ( ordered_pair @ SV26 @ SV30 ) )
= $false )
| ( ( in @ SV18 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV18 = SV13 )
= $false )
| ( ( in @ SV13 @ ( sK15_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK11_SY111 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(575,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV16: $i] :
( ( ( SV16
= ( ordered_pair @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(576,plain,
! [SV16: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK39_SY182 @ SV4 @ SV7 @ SV9 @ SV16 ) ) @ ( apply @ SV9 @ ( sK41_SY248 @ SV9 @ SV7 @ SV4 @ SV16 ) ) ) @ SV7 )
= $true )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(577,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV32: $i,SV16: $i] :
( ( ( ! [SY251: $i] :
~ ~ ( ( SV16
!= ( ordered_pair @ SV32 @ SY251 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SY251 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(578,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV17: $i] :
( ( ( SV17
= ( ordered_pair @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(579,plain,
! [SV17: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK40_SY188 @ SV4 @ SV7 @ SV9 @ SV17 ) ) @ ( apply @ SV9 @ ( sK42_SY249 @ SV9 @ SV7 @ SV4 @ SV17 ) ) ) @ SV7 )
= $true )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(580,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV33: $i,SV17: $i] :
( ( ( ! [SY252: $i] :
~ ~ ( ( SV17
!= ( ordered_pair @ SV33 @ SY252 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SY252 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(581,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV31: $i,SV29: $i,SV15: $i] :
( ( ( SV15
!= ( ordered_pair @ SV29 @ SV31 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SV31 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(582,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( ! [SY253: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ SY253 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ SY253 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(583,plain,
! [SV7: $i,SV9: $i,SV4: $i,SV21: $i,SV27: $i] :
( ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( ~ ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(584,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( ! [SY254: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ SY254 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ SY254 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(585,plain,
! [SV7: $i,SV9: $i,SV4: $i,SV22: $i,SV28: $i] :
( ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( ~ ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(586,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV34: $i,SV32: $i,SV16: $i] :
( ( ( ~ ~ ( ( SV16
!= ( ordered_pair @ SV32 @ SV34 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SV34 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(587,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV35: $i,SV33: $i,SV17: $i] :
( ( ( ~ ~ ( ( SV17
!= ( ordered_pair @ SV33 @ SV35 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SV35 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(588,plain,
! [SV4: $i,SV19: $i,SV7: $i,SV9: $i,SV31: $i,SV29: $i,SV15: $i] :
( ( ( SV15
= ( ordered_pair @ SV29 @ SV31 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SV31 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(589,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( ~ ~ ( ( SV21
!= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[582]) ).
thf(590,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV21: $i] :
( ( ( ~ ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(591,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( ~ ~ ( ( SV22
!= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[584]) ).
thf(592,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV22: $i] :
( ( ( ~ ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(593,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV34: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( ( SV16
!= ( ordered_pair @ SV32 @ SV34 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SV34 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(594,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV35: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( ordered_pair @ SV33 @ SV35 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SV35 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(595,plain,
! [SV4: $i,SV19: $i,SV15: $i,SV7: $i,SV31: $i,SV29: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ SV29 ) @ ( apply @ SV9 @ SV31 ) ) @ SV7 )
= $false )
| ( ( SV15
= ( ordered_pair @ SV29 @ SV31 ) )
= $false )
| ( ( in @ SV19 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV19 = SV15 )
= $false )
| ( ( in @ SV15 @ ( sK19_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK8_SY85 @ SV4 @ SV7 @ SV9 )
= ( sK9_SY105 @ SV9 @ SV7 @ SV4 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(596,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( ~ ( ( SV21
!= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(597,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV21: $i] :
( ( ( ! [SY221: $i] :
~ ~ ! [SY222: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SY221 @ SY222 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY221 ) @ ( apply @ SV9 @ SY222 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(598,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( ~ ( ( SV22
!= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(599,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV22: $i] :
( ( ( ! [SY227: $i] :
~ ~ ! [SY228: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SY227 @ SY228 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SY227 ) @ ( apply @ SV9 @ SY228 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(600,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV34: $i,SV32: $i,SV16: $i] :
( ( ( ( SV16
!= ( ordered_pair @ SV32 @ SV34 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SV34 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(601,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV35: $i,SV33: $i,SV17: $i] :
( ( ( ( SV17
!= ( ordered_pair @ SV33 @ SV35 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SV35 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(602,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( ( SV21
!= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(603,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV36: $i,SV21: $i] :
( ( ( ~ ~ ! [SY255: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SV36 @ SY255 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SY255 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(604,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( ( SV22
!= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(605,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV37: $i,SV22: $i] :
( ( ( ~ ~ ! [SY256: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SV37 @ SY256 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SY256 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(606,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV34: $i,SV32: $i,SV16: $i] :
( ( ( SV16
!= ( ordered_pair @ SV32 @ SV34 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SV34 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(607,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV35: $i,SV33: $i,SV17: $i] :
( ( ( SV17
!= ( ordered_pair @ SV33 @ SV35 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SV35 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(608,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( SV21
!= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(609,plain,
! [SV21: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(610,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV36: $i,SV21: $i] :
( ( ( ~ ! [SY255: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SV36 @ SY255 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SY255 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(611,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( SV22
!= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(612,plain,
! [SV22: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) ) @ SV7 ) )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[604]) ).
thf(613,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV37: $i,SV22: $i] :
( ( ( ~ ! [SY256: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SV37 @ SY256 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SY256 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(614,plain,
! [SV4: $i,SV23: $i,SV7: $i,SV9: $i,SV34: $i,SV32: $i,SV16: $i] :
( ( ( SV16
= ( ordered_pair @ SV32 @ SV34 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SV34 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(615,plain,
! [SV4: $i,SV24: $i,SV7: $i,SV9: $i,SV35: $i,SV33: $i,SV17: $i] :
( ( ( SV17
= ( ordered_pair @ SV33 @ SV35 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SV35 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(616,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV21: $i] :
( ( ( SV21
= ( ordered_pair @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(617,plain,
! [SV21: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK43_SY218 @ SV4 @ SV7 @ SV9 @ SV21 ) ) @ ( apply @ SV9 @ ( sK45_SY253 @ SV9 @ SV7 @ SV4 @ SV21 ) ) ) @ SV7 )
= $true )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(618,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV36: $i,SV21: $i] :
( ( ( ! [SY255: $i] :
~ ~ ( ( SV21
!= ( ordered_pair @ SV36 @ SY255 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SY255 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(619,plain,
! [SV9: $i,SV7: $i,SV4: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(620,plain,
! [SV22: $i,SV7: $i,SV4: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK44_SY224 @ SV4 @ SV7 @ SV9 @ SV22 ) ) @ ( apply @ SV9 @ ( sK46_SY254 @ SV9 @ SV7 @ SV4 @ SV22 ) ) ) @ SV7 )
= $true )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(621,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV37: $i,SV22: $i] :
( ( ( ! [SY256: $i] :
~ ~ ( ( SV22
!= ( ordered_pair @ SV37 @ SY256 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SY256 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(622,plain,
! [SV4: $i,SV23: $i,SV16: $i,SV7: $i,SV34: $i,SV32: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ SV32 ) @ ( apply @ SV9 @ SV34 ) ) @ SV7 )
= $false )
| ( ( SV16
= ( ordered_pair @ SV32 @ SV34 ) )
= $false )
| ( ( in @ SV23 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV23 = SV16 )
= $false )
| ( ( in @ SV16 @ ( sK23_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK11_SY111 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(623,plain,
! [SV4: $i,SV24: $i,SV17: $i,SV7: $i,SV35: $i,SV33: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ SV33 ) @ ( apply @ SV9 @ SV35 ) ) @ SV7 )
= $false )
| ( ( SV17
= ( ordered_pair @ SV33 @ SV35 ) )
= $false )
| ( ( in @ SV24 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV24 = SV17 )
= $false )
| ( ( in @ SV17 @ ( sK24_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK14_SY119 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK16_SY134 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(624,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV38: $i,SV36: $i,SV21: $i] :
( ( ( ~ ~ ( ( SV21
!= ( ordered_pair @ SV36 @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SV38 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(625,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV39: $i,SV37: $i,SV22: $i] :
( ( ( ~ ~ ( ( SV22
!= ( ordered_pair @ SV37 @ SV39 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SV39 ) ) @ SV7 ) ) )
= $true )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(626,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV38: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( ( SV21
!= ( ordered_pair @ SV36 @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SV38 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(627,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV39: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( ( SV22
!= ( ordered_pair @ SV37 @ SV39 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SV39 ) ) @ SV7 ) ) )
= $false )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(628,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV38: $i,SV36: $i,SV21: $i] :
( ( ( ( SV21
!= ( ordered_pair @ SV36 @ SV38 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SV38 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(629,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV39: $i,SV37: $i,SV22: $i] :
( ( ( ( SV22
!= ( ordered_pair @ SV37 @ SV39 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SV39 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(630,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV38: $i,SV36: $i,SV21: $i] :
( ( ( SV21
!= ( ordered_pair @ SV36 @ SV38 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SV38 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(631,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV39: $i,SV37: $i,SV22: $i] :
( ( ( SV22
!= ( ordered_pair @ SV37 @ SV39 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SV39 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(632,plain,
! [SV4: $i,SV27: $i,SV7: $i,SV9: $i,SV38: $i,SV36: $i,SV21: $i] :
( ( ( SV21
= ( ordered_pair @ SV36 @ SV38 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SV38 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(633,plain,
! [SV4: $i,SV28: $i,SV7: $i,SV9: $i,SV39: $i,SV37: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ SV37 @ SV39 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SV39 ) ) @ SV7 ) )
= $true )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(634,plain,
! [SV4: $i,SV27: $i,SV21: $i,SV7: $i,SV38: $i,SV36: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ SV36 ) @ ( apply @ SV9 @ SV38 ) ) @ SV7 )
= $false )
| ( ( SV21
= ( ordered_pair @ SV36 @ SV38 ) )
= $false )
| ( ( in @ SV27 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV27 = SV21 )
= $false )
| ( ( in @ SV21 @ ( sK29_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( ( sK9_SY105 @ SV9 @ SV7 @ SV4 )
= ( ordered_pair @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(635,plain,
! [SV4: $i,SV28: $i,SV22: $i,SV7: $i,SV39: $i,SV37: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV9 @ SV37 ) @ ( apply @ SV9 @ SV39 ) ) @ SV7 )
= $false )
| ( ( SV22
= ( ordered_pair @ SV37 @ SV39 ) )
= $false )
| ( ( in @ SV28 @ ( cartesian_product2 @ SV4 @ SV4 ) )
= $false )
| ( ( SV28 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK30_SY92 @ SV7 @ SV9 @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV9 @ ( sK20_SY112 @ SV4 @ SV7 @ SV9 ) ) @ ( apply @ SV9 @ ( sK22_SY160 @ SV4 @ SV7 @ SV9 ) ) ) @ SV7 )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(636,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,635,634,623,622,620,619,617,616,595,579,578,576,575,574,571,570,567,566,524,523,495,494,491,490,488,487,480,432,431,392,391,382,381,303,302,299,298,213,187,185,184,146,133,122,121,120,119,107,106,104,102,96,80,78,53,52,51,47,46]) ).
thf(637,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU277+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
% 0.10/0.19 % Computer : n011.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 15:10:36 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 85.18/14.59
% 85.18/14.59 No.of.Axioms: 10
% 85.18/14.59
% 85.18/14.59 Length.of.Defs: 0
% 85.18/14.59
% 85.18/14.59 Contains.Choice.Funs: false
% 85.18/14.59 .........................
% 85.18/14.59
% 85.18/14.59 ********************************
% 85.18/14.59 * All subproblems solved! *
% 85.18/14.59 ********************************
% 85.18/14.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:636,loop_count:0,foatp_calls:1,translation:fof_full)
% 85.18/14.59
% 85.18/14.59 %**** Beginning of derivation protocol ****
% 85.18/14.59 % SZS output start CNFRefutation
% See solution above
% 85.18/14.60
% 85.18/14.60 %**** End of derivation protocol ****
% 85.18/14.60 %**** no. of clauses in derivation: 628 ****
% 85.18/14.60 %**** clause counter: 636 ****
% 85.18/14.60
% 85.18/14.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:636,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------