TSTP Solution File: SEU281+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:09:30 EDT 2022
% Result : Theorem 26.55s 26.77s
% Output : CNFRefutation 26.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 44
% Syntax : Number of formulae : 634 ( 125 unt; 29 typ; 0 def)
% Number of atoms : 6827 (3334 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 18202 (3546 ~;2732 |; 108 &;11794 @)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 8 con; 0-3 aty)
% Number of variables : 2228 ( 0 ^2186 !; 42 ?;2228 :)
% Comments :
%------------------------------------------------------------------------------
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_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_sK10_C,type,
sK10_C: $i > $i ).
thf(tp_sK11_SY55,type,
sK11_SY55: $i > $i ).
thf(tp_sK12_SY61,type,
sK12_SY61: $i > $i ).
thf(tp_sK13_SY68,type,
sK13_SY68: $i > $i ).
thf(tp_sK14_SY70,type,
sK14_SY70: $i > $i ).
thf(tp_sK15_SY62,type,
sK15_SY62: $i > $i ).
thf(tp_sK16_SY71,type,
sK16_SY71: $i > $i ).
thf(tp_sK17_A,type,
sK17_A: $i ).
thf(tp_sK18_A,type,
sK18_A: $i ).
thf(tp_sK19_A,type,
sK19_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_A,type,
sK20_A: $i ).
thf(tp_sK2_SY32,type,
sK2_SY32: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i > $i ).
thf(tp_sK4_SY43,type,
sK4_SY43: $i > $i ).
thf(tp_sK5_SY45,type,
sK5_SY45: $i > $i ).
thf(tp_sK6_C,type,
sK6_C: $i > $i > $i ).
thf(tp_sK7_J,type,
sK7_J: $i > $i > $i > $i ).
thf(tp_sK8_SY54,type,
sK8_SY54: $i > $i > $i > $i ).
thf(tp_sK9_E,type,
sK9_E: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) )
& ( C = E )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= E )
& ( in @ H @ A )
& ( I
= ( singleton @ H ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( cartesian_product2 @ A @ B ) )
& ( E = D )
& ? [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
= D )
& ( in @ J @ A )
& ( K
= ( singleton @ J ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
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,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(9,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(10,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(11,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(12,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(13,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(14,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(15,conjecture,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
thf(16,negated_conjecture,
( ( ! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) )
& ( C = E )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= E )
& ( in @ H @ A )
& ( I
= ( singleton @ H ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( cartesian_product2 @ A @ B ) )
& ( E = D )
& ? [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
= D )
& ( in @ J @ A )
& ( K
= ( singleton @ J ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
$true = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(32,plain,
( ( ! [SY32: $i] :
? [SY33: $i] :
! [SY34: $i] :
( ( in @ SY34 @ SY33 )
<=> ( ( in @ SY34 @ ( cartesian_product2 @ sK1_A @ SY32 ) )
& ? [SY35: $i,SY36: $i] :
( ( ( ordered_pair @ SY35 @ SY36 )
= SY34 )
& ( in @ SY35 @ sK1_A )
& ( SY36
= ( singleton @ SY35 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(33,plain,
( ( ? [SY37: $i] :
! [SY38: $i] :
( ( in @ SY38 @ SY37 )
<=> ( ( in @ SY38 @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
& ? [SY35: $i,SY36: $i] :
( ( ( ordered_pair @ SY35 @ SY36 )
= SY38 )
& ( in @ SY35 @ sK1_A )
& ( SY36
= ( singleton @ SY35 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(34,plain,
( ( ~ ? [SY37: $i] :
! [SY38: $i] :
( ( in @ SY38 @ SY37 )
<=> ( ( in @ SY38 @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
& ? [SY35: $i,SY36: $i] :
( ( ( ordered_pair @ SY35 @ SY36 )
= SY38 )
& ( in @ SY35 @ sK1_A )
& ( SY36
= ( singleton @ SY35 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [SY37: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( ( ordered_pair @ SY41 @ SY42 )
!= ( sK3_SY38 @ SY37 ) )
| ~ ( in @ SY41 @ sK1_A )
| ( SY42
!= ( singleton @ SY41 ) ) )
| ~ ( in @ ( sK3_SY38 @ SY37 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ~ ( in @ ( sK3_SY38 @ SY37 ) @ SY37 ) )
& ( ( ( ( ordered_pair @ ( sK4_SY43 @ SY37 ) @ ( sK5_SY45 @ SY37 ) )
= ( sK3_SY38 @ SY37 ) )
& ( in @ ( sK4_SY43 @ SY37 ) @ sK1_A )
& ( ( sK5_SY45 @ SY37 )
= ( singleton @ ( sK4_SY43 @ SY37 ) ) ) )
| ( in @ ( sK3_SY38 @ SY37 ) @ SY37 ) )
& ( ( in @ ( sK3_SY38 @ SY37 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SY37 ) @ SY37 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( ( ( sK10_C @ A )
= ( sK11_SY55 @ A ) )
& ( ( ordered_pair @ ( sK15_SY62 @ A ) @ ( sK16_SY71 @ A ) )
= ( sK11_SY55 @ A ) )
& ( in @ ( sK15_SY62 @ A ) @ A )
& ( ( sK16_SY71 @ A )
= ( singleton @ ( sK15_SY62 @ A ) ) )
& ( ( sK10_C @ A )
= ( sK12_SY61 @ A ) )
& ( ( ordered_pair @ ( sK13_SY68 @ A ) @ ( sK14_SY70 @ A ) )
= ( sK12_SY61 @ A ) )
& ( in @ ( sK13_SY68 @ A ) @ A )
& ( ( sK14_SY70 @ A )
= ( singleton @ ( sK13_SY68 @ A ) ) )
& ( ( sK11_SY55 @ A )
!= ( sK12_SY61 @ A ) ) )
| ! [B: $i] :
( ! [SY46: $i] :
( ! [E: $i] :
( ( E != SY46 )
| ~ ( in @ E @ ( cartesian_product2 @ A @ B ) ) )
| ! [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
!= SY46 )
| ~ ( in @ J @ A )
| ( K
!= ( singleton @ J ) ) )
| ( in @ SY46 @ ( sK6_C @ B @ A ) ) )
& ! [SY50: $i] :
( ~ ( in @ SY50 @ ( sK6_C @ B @ A ) )
| ( ( ( sK9_E @ SY50 @ B @ A )
= SY50 )
& ( in @ ( sK9_E @ SY50 @ B @ A ) @ ( cartesian_product2 @ A @ B ) )
& ( ( ordered_pair @ ( sK7_J @ SY50 @ B @ A ) @ ( sK8_SY54 @ SY50 @ B @ A ) )
= SY50 )
& ( in @ ( sK7_J @ SY50 @ B @ A ) @ A )
& ( ( sK8_SY54 @ SY50 @ B @ A )
= ( singleton @ ( sK7_J @ SY50 @ B @ A ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(38,plain,
( ( ~ ( empty @ sK17_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(39,plain,
( ( empty @ sK18_A )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(40,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(41,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(42,plain,
( ( ~ ( empty @ sK19_A )
& ( epsilon_transitive @ sK19_A )
& ( epsilon_connected @ sK19_A )
& ( ordinal @ sK19_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(43,plain,
( ( ( epsilon_connected @ sK20_A )
& ( epsilon_transitive @ sK20_A )
& ( ordinal @ sK20_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(44,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(45,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(46,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(48,plain,
( ( ( epsilon_connected @ sK20_A )
& ( epsilon_transitive @ sK20_A )
& ( ordinal @ sK20_A ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(49,plain,
( ( ~ ( empty @ sK19_A )
& ( epsilon_transitive @ sK19_A )
& ( epsilon_connected @ sK19_A )
& ( ordinal @ sK19_A ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(50,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(51,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(52,plain,
( ( empty @ sK18_A )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(53,plain,
( ( ~ ( empty @ sK17_A ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(55,plain,
$true = $true,
inference(copy,[status(thm)],[22]) ).
thf(56,plain,
$true = $true,
inference(copy,[status(thm)],[21]) ).
thf(57,plain,
$true = $true,
inference(copy,[status(thm)],[20]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( ( ( sK10_C @ A )
= ( sK11_SY55 @ A ) )
& ( ( ordered_pair @ ( sK15_SY62 @ A ) @ ( sK16_SY71 @ A ) )
= ( sK11_SY55 @ A ) )
& ( in @ ( sK15_SY62 @ A ) @ A )
& ( ( sK16_SY71 @ A )
= ( singleton @ ( sK15_SY62 @ A ) ) )
& ( ( sK10_C @ A )
= ( sK12_SY61 @ A ) )
& ( ( ordered_pair @ ( sK13_SY68 @ A ) @ ( sK14_SY70 @ A ) )
= ( sK12_SY61 @ A ) )
& ( in @ ( sK13_SY68 @ A ) @ A )
& ( ( sK14_SY70 @ A )
= ( singleton @ ( sK13_SY68 @ A ) ) )
& ( ( sK11_SY55 @ A )
!= ( sK12_SY61 @ A ) ) )
| ! [B: $i] :
( ! [SY46: $i] :
( ! [E: $i] :
( ( E != SY46 )
| ~ ( in @ E @ ( cartesian_product2 @ A @ B ) ) )
| ! [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
!= SY46 )
| ~ ( in @ J @ A )
| ( K
!= ( singleton @ J ) ) )
| ( in @ SY46 @ ( sK6_C @ B @ A ) ) )
& ! [SY50: $i] :
( ~ ( in @ SY50 @ ( sK6_C @ B @ A ) )
| ( ( ( sK9_E @ SY50 @ B @ A )
= SY50 )
& ( in @ ( sK9_E @ SY50 @ B @ A ) @ ( cartesian_product2 @ A @ B ) )
& ( ( ordered_pair @ ( sK7_J @ SY50 @ B @ A ) @ ( sK8_SY54 @ SY50 @ B @ A ) )
= SY50 )
& ( in @ ( sK7_J @ SY50 @ B @ A ) @ A )
& ( ( sK8_SY54 @ SY50 @ B @ A )
= ( singleton @ ( sK7_J @ SY50 @ B @ A ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(60,plain,
( ( ! [SY37: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( ( ordered_pair @ SY41 @ SY42 )
!= ( sK3_SY38 @ SY37 ) )
| ~ ( in @ SY41 @ sK1_A )
| ( SY42
!= ( singleton @ SY41 ) ) )
| ~ ( in @ ( sK3_SY38 @ SY37 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ~ ( in @ ( sK3_SY38 @ SY37 ) @ SY37 ) )
& ( ( ( ( ordered_pair @ ( sK4_SY43 @ SY37 ) @ ( sK5_SY45 @ SY37 ) )
= ( sK3_SY38 @ SY37 ) )
& ( in @ ( sK4_SY43 @ SY37 ) @ sK1_A )
& ( ( sK5_SY45 @ SY37 )
= ( singleton @ ( sK4_SY43 @ SY37 ) ) ) )
| ( in @ ( sK3_SY38 @ SY37 ) @ SY37 ) )
& ( ( in @ ( sK3_SY38 @ SY37 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SY37 ) @ SY37 ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(61,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(62,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(63,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK20_A )
| ~ ( epsilon_transitive @ sK20_A ) )
| ~ ( ordinal @ sK20_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(64,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SX0 )
!= ( sK11_SY55 @ SX0 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SX0 ) @ ( sK16_SY71 @ SX0 ) )
!= ( sK11_SY55 @ SX0 ) )
| ~ ( in @ ( sK15_SY62 @ SX0 ) @ SX0 ) )
| ( ( sK16_SY71 @ SX0 )
!= ( singleton @ ( sK15_SY62 @ SX0 ) ) ) ) )
| ( ( sK10_C @ SX0 )
!= ( sK12_SY61 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SX0 ) @ ( sK14_SY70 @ SX0 ) )
!= ( sK12_SY61 @ SX0 ) )
| ~ ( in @ ( sK13_SY68 @ SX0 ) @ SX0 ) )
| ( ( sK14_SY70 @ SX0 )
!= ( singleton @ ( sK13_SY68 @ SX0 ) ) ) ) )
| ~ ( ( ( sK11_SY55 @ SX0 )
!= ( sK12_SY61 @ SX0 ) ) ) )
| ! [SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX3 != SX2 )
| ~ ( in @ SX3 @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ! [SX3: $i,SX4: $i] :
( ( ( ordered_pair @ SX3 @ SX4 )
!= SX2 )
| ~ ( in @ SX3 @ SX0 )
| ( SX4
!= ( singleton @ SX3 ) ) )
| ( in @ SX2 @ ( sK6_C @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK6_C @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SX2 @ SX1 @ SX0 )
!= SX2 )
| ~ ( in @ ( sK9_E @ SX2 @ SX1 @ SX0 ) @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY54 @ SX2 @ SX1 @ SX0 ) )
!= SX2 )
| ~ ( in @ ( sK7_J @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ( ( sK8_SY54 @ SX2 @ SX1 @ SX0 )
!= ( singleton @ ( sK7_J @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(65,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ! [SX1: $i,SX2: $i] :
( ( ( ordered_pair @ SX1 @ SX2 )
!= ( sK3_SY38 @ SX0 ) )
| ~ ( in @ SX1 @ sK1_A )
| ( SX2
!= ( singleton @ SX1 ) ) )
| ~ ( in @ ( sK3_SY38 @ SX0 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ~ ( in @ ( sK3_SY38 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SX0 ) @ ( sK5_SY45 @ SX0 ) )
!= ( sK3_SY38 @ SX0 ) )
| ~ ( in @ ( sK4_SY43 @ SX0 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SX0 )
!= ( singleton @ ( sK4_SY43 @ SX0 ) ) ) )
| ( in @ ( sK3_SY38 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK3_SY38 @ SX0 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(66,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) )
| ~ ( epsilon_connected @ sK19_A ) )
| ~ ( ordinal @ sK19_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(67,plain,
! [SV1: $i] :
( ( ~ ( epsilon_connected @ SV1 )
| ~ ( epsilon_transitive @ SV1 )
| ( ordinal @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(68,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(69,plain,
( ( empty @ sK17_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(70,plain,
! [SV3: $i] :
( ( ! [SY72: $i] :
( ~ ( in @ SV3 @ SY72 )
| ~ ( in @ SY72 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(71,plain,
! [SV4: $i] :
( ( ! [SY73: $i] :
~ ( empty @ ( ordered_pair @ SV4 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(72,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(73,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(74,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK20_A )
| ~ ( epsilon_transitive @ sK20_A ) )
| ~ ( ordinal @ sK20_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(75,plain,
! [SV5: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) )
| ~ ( ( ( sK11_SY55 @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) ) )
| ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(76,plain,
! [SV6: $i] :
( ( ~ ( ~ ( ! [SY80: $i,SY81: $i] :
( ( ( ordered_pair @ SY80 @ SY81 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SY80 @ sK1_A )
| ( SY81
!= ( singleton @ SY80 ) ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
| ~ ~ ( ~ ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
| ~ ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(77,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) )
| ~ ( epsilon_connected @ sK19_A ) )
| ~ ( ordinal @ sK19_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(78,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_connected @ SV1 )
| ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(79,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV7 )
| ~ ( in @ SV7 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV4 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(85,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(86,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK20_A )
| ~ ( epsilon_transitive @ sK20_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(87,plain,
( ( ~ ( ordinal @ sK20_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(88,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) )
| ~ ( ( ( sK11_SY55 @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(89,plain,
! [SV6: $i] :
( ( ~ ( ! [SY80: $i,SY81: $i] :
( ( ( ordered_pair @ SY80 @ SY81 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SY80 @ sK1_A )
| ( SY81
!= ( singleton @ SY80 ) ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
| ~ ~ ( ~ ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
| ~ ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(90,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) )
| ~ ( epsilon_connected @ sK19_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(91,plain,
( ( ~ ( ordinal @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(92,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_connected @ SV1 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(94,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(95,plain,
! [SV8: $i,SV4: $i] :
( ( empty @ ( ordered_pair @ SV4 @ SV8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(96,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(97,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(98,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(99,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(100,plain,
( ( ~ ( ~ ( epsilon_connected @ sK20_A )
| ~ ( epsilon_transitive @ sK20_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(101,plain,
( ( ordinal @ sK20_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) )
| ~ ( ( ( sK11_SY55 @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV6: $i] :
( ( ~ ( ! [SY80: $i,SY81: $i] :
( ( ( ordered_pair @ SY80 @ SY81 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SY80 @ sK1_A )
| ( SY81
!= ( singleton @ SY80 ) ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(104,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
| ~ ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(105,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) )
| ~ ( epsilon_connected @ sK19_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(106,plain,
( ( ordinal @ sK19_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(107,plain,
! [SV1: $i] :
( ( ( epsilon_connected @ SV1 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV7: $i,SV3: $i] :
( ( ( in @ SV3 @ SV7 )
= $false )
| ( ( ~ ( in @ SV7 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(109,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV9: $i] :
( ( ~ ( empty @ SV9 )
| ( ordinal @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV10: $i] :
( ( ~ ( ordinal @ SV10 )
| ( epsilon_connected @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV11: $i] :
( ( ~ ( ordinal @ SV11 )
| ( epsilon_transitive @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(113,plain,
( ( ~ ( epsilon_connected @ sK20_A )
| ~ ( epsilon_transitive @ sK20_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(115,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( sK11_SY55 @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(116,plain,
! [SV6: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ( ( ordered_pair @ SY80 @ SY81 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SY80 @ sK1_A )
| ( SY81
!= ( singleton @ SY80 ) ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(117,plain,
! [SV6: $i] :
( ( ~ ( ~ ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
| ~ ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(118,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) )
| ~ ( epsilon_connected @ sK19_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV1: $i] :
( ( ( epsilon_transitive @ SV1 )
= $false )
| ( ( epsilon_connected @ SV1 )
= $false )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ SV7 @ SV3 )
= $false )
| ( ( in @ SV3 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(121,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(122,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(123,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( ordinal @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV10: $i] :
( ( ( ~ ( ordinal @ SV10 ) )
= $true )
| ( ( epsilon_connected @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV11: $i] :
( ( ( ~ ( ordinal @ SV11 ) )
= $true )
| ( ( epsilon_transitive @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(126,plain,
( ( ~ ( epsilon_connected @ sK20_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(127,plain,
( ( ~ ( epsilon_transitive @ sK20_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(128,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(129,plain,
! [SV5: $i] :
( ( ( ( ( sK11_SY55 @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(130,plain,
! [SV6: $i] :
( ( ( ! [SY80: $i,SY81: $i] :
( ( ( ordered_pair @ SY80 @ SY81 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SY80 @ sK1_A )
| ( SY81
!= ( singleton @ SY80 ) ) )
| ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV6: $i] :
( ( ~ ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
| ~ ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(132,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(133,plain,
( ( ~ ( epsilon_connected @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(134,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(135,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(136,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( ordinal @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(137,plain,
! [SV10: $i] :
( ( ( ordinal @ SV10 )
= $false )
| ( ( epsilon_connected @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(138,plain,
! [SV11: $i] :
( ( ( ordinal @ SV11 )
= $false )
| ( ( epsilon_transitive @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(139,plain,
( ( epsilon_connected @ sK20_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(140,plain,
( ( epsilon_transitive @ sK20_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(141,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(142,plain,
! [SV5: $i] :
( ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(143,plain,
! [SV6: $i] :
( ( ( ! [SY80: $i,SY81: $i] :
( ( ( ordered_pair @ SY80 @ SY81 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SY80 @ sK1_A )
| ( SY81
!= ( singleton @ SY80 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(144,plain,
! [SV6: $i] :
( ( ~ ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(145,plain,
! [SV6: $i] :
( ( ~ ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(146,plain,
( ( ~ ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(147,plain,
( ( epsilon_connected @ sK19_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(148,plain,
! [SV12: $i] :
( ( ~ ( empty @ SV12 )
| ( epsilon_connected @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV13: $i] :
( ( ~ ( empty @ SV13 )
| ( epsilon_transitive @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(151,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(152,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY82: $i] :
( ! [SY83: $i] :
( ( SY83 != SY82 )
| ~ ( in @ SY83 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY82 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY82 @ ( sK6_C @ SV14 @ SV5 ) ) )
| ~ ! [SY86: $i] :
( ~ ( in @ SY86 @ ( sK6_C @ SV14 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY86 @ SV14 @ SV5 )
!= SY86 )
| ~ ( in @ ( sK9_E @ SY86 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SY86 @ SV14 @ SV5 ) )
!= SY86 )
| ~ ( in @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY86 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SY86 @ SV14 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV6: $i,SV15: $i] :
( ( ( ! [SY87: $i] :
( ( ( ordered_pair @ SV15 @ SY87 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SV15 @ sK1_A )
| ( SY87
!= ( singleton @ SV15 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV6: $i] :
( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(155,plain,
! [SV6: $i] :
( ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
| ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(156,plain,
( ( ~ ~ ( empty @ sK19_A )
| ~ ( epsilon_transitive @ sK19_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $true )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(158,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $true )
| ( ( epsilon_transitive @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(159,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(160,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(161,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ! [SY82: $i] :
( ! [SY83: $i] :
( ( SY83 != SY82 )
| ~ ( in @ SY83 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY82 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY82 @ ( sK6_C @ SV14 @ SV5 ) ) )
| ~ ! [SY86: $i] :
( ~ ( in @ SY86 @ ( sK6_C @ SV14 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY86 @ SV14 @ SV5 )
!= SY86 )
| ~ ( in @ ( sK9_E @ SY86 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SY86 @ SV14 @ SV5 ) )
!= SY86 )
| ~ ( in @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY86 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SY86 @ SV14 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV6: $i,SV16: $i,SV15: $i] :
( ( ( ( ( ordered_pair @ SV15 @ SV16 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SV15 @ sK1_A )
| ( SV16
!= ( singleton @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) ) )
= $true )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV6: $i] :
( ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
= $true )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,plain,
( ( ~ ~ ( empty @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(166,plain,
( ( ~ ( epsilon_transitive @ sK19_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(167,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $false )
| ( ( epsilon_connected @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( epsilon_transitive @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
| ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
| ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ! [SY82: $i] :
( ! [SY83: $i] :
( ( SY83 != SY82 )
| ~ ( in @ SY83 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY82 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY82 @ ( sK6_C @ SV14 @ SV5 ) ) ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(172,plain,
! [SV5: $i,SV14: $i] :
( ( ( ~ ! [SY86: $i] :
( ~ ( in @ SY86 @ ( sK6_C @ SV14 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY86 @ SV14 @ SV5 )
!= SY86 )
| ~ ( in @ ( sK9_E @ SY86 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SY86 @ SV14 @ SV5 ) )
!= SY86 )
| ~ ( in @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY86 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SY86 @ SV14 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(173,plain,
! [SV6: $i,SV16: $i,SV15: $i] :
( ( ( ( ( ordered_pair @ SV15 @ SV16 )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ SV15 @ sK1_A ) )
= $true )
| ( ( ( SV16
!= ( singleton @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(174,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
| ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(175,plain,
( ( ~ ( empty @ sK19_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(176,plain,
( ( epsilon_transitive @ sK19_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(177,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(178,plain,
! [SV5: $i] :
( ( ( ( ( sK10_C @ SV5 )
!= ( sK12_SY61 @ SV5 ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(179,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(180,plain,
! [SV5: $i] :
( ( ( ( ( sK14_SY70 @ SV5 )
!= ( singleton @ ( sK13_SY68 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(181,plain,
! [SV14: $i,SV5: $i] :
( ( ( ! [SY82: $i] :
( ! [SY83: $i] :
( ( SY83 != SY82 )
| ~ ( in @ SY83 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY82 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY82 @ ( sK6_C @ SV14 @ SV5 ) ) ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(182,plain,
! [SV5: $i,SV14: $i] :
( ( ( ! [SY86: $i] :
( ~ ( in @ SY86 @ ( sK6_C @ SV14 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY86 @ SV14 @ SV5 )
!= SY86 )
| ~ ( in @ ( sK9_E @ SY86 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SY86 @ SV14 @ SV5 ) )
!= SY86 )
| ~ ( in @ ( sK7_J @ SY86 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY86 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SY86 @ SV14 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV6: $i,SV16: $i,SV15: $i] :
( ( ( ( ( ordered_pair @ SV15 @ SV16 )
!= ( sK3_SY38 @ SV6 ) ) )
= $true )
| ( ( ~ ( in @ SV15 @ sK1_A ) )
= $true )
| ( ( ( SV16
!= ( singleton @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(185,plain,
! [SV6: $i] :
( ( ( ( ( sK5_SY45 @ SV6 )
!= ( singleton @ ( sK4_SY43 @ SV6 ) ) ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(186,plain,
( ( empty @ sK19_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(188,plain,
! [SV5: $i] :
( ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(189,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(190,plain,
! [SV5: $i] :
( ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(191,plain,
! [SV14: $i,SV5: $i,SV17: $i] :
( ( ( ! [SY88: $i] :
( ( SY88 != SV17 )
| ~ ( in @ SY88 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ! [SY89: $i,SY90: $i] :
( ( ( ordered_pair @ SY89 @ SY90 )
!= SV17 )
| ~ ( in @ SY89 @ SV5 )
| ( SY90
!= ( singleton @ SY89 ) ) )
| ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(192,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 )
| ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(193,plain,
! [SV6: $i,SV16: $i,SV15: $i] :
( ( ( ( ordered_pair @ SV15 @ SV16 )
= ( sK3_SY38 @ SV6 ) )
= $false )
| ( ( ~ ( in @ SV15 @ sK1_A ) )
= $true )
| ( ( ( SV16
!= ( singleton @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(194,plain,
! [SV6: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) ) )
= $true )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(195,plain,
! [SV6: $i] :
( ( ( ( sK5_SY45 @ SV6 )
= ( singleton @ ( sK4_SY43 @ SV6 ) ) )
= $true )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(196,plain,
! [SV5: $i] :
( ( ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(197,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
( ( SY92 != SY91 )
| ~ ( in @ SY92 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY91 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY91 @ ( sK6_C @ SV19 @ SV5 ) ) )
| ~ ! [SY95: $i] :
( ~ ( in @ SY95 @ ( sK6_C @ SV19 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY95 @ SV19 @ SV5 )
!= SY95 )
| ~ ( in @ ( sK9_E @ SY95 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SY95 @ SV19 @ SV5 ) )
!= SY95 )
| ~ ( in @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY95 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SY95 @ SV19 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(198,plain,
! [SV5: $i] :
( ( ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) )
| ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(199,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY96: $i] :
( ! [SY97: $i] :
( ( SY97 != SY96 )
| ~ ( in @ SY97 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY96 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY96 @ ( sK6_C @ SV20 @ SV5 ) ) )
| ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ ( sK6_C @ SV20 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY100 @ SV20 @ SV5 )
!= SY100 )
| ~ ( in @ ( sK9_E @ SY100 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SY100 @ SV20 @ SV5 ) )
!= SY100 )
| ~ ( in @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY100 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SY100 @ SV20 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(200,plain,
! [SV14: $i,SV5: $i,SV17: $i] :
( ( ( ! [SY88: $i] :
( ( SY88 != SV17 )
| ~ ( in @ SY88 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ! [SY89: $i,SY90: $i] :
( ( ( ordered_pair @ SY89 @ SY90 )
!= SV17 )
| ~ ( in @ SY89 @ SV5 )
| ( SY90
!= ( singleton @ SY89 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(201,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 )
| ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(202,plain,
! [SV6: $i,SV16: $i,SV15: $i] :
( ( ( in @ SV15 @ sK1_A )
= $false )
| ( ( ( ordered_pair @ SV15 @ SV16 )
= ( sK3_SY38 @ SV6 ) )
= $false )
| ( ( ( SV16
!= ( singleton @ SV15 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV6: $i] :
( ( ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) )
| ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV5: $i] :
( ( ( ( ( sK10_C @ SV5 )
!= ( sK11_SY55 @ SV5 ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(205,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(206,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
( ( SY92 != SY91 )
| ~ ( in @ SY92 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY91 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY91 @ ( sK6_C @ SV19 @ SV5 ) ) )
| ~ ! [SY95: $i] :
( ~ ( in @ SY95 @ ( sK6_C @ SV19 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY95 @ SV19 @ SV5 )
!= SY95 )
| ~ ( in @ ( sK9_E @ SY95 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SY95 @ SV19 @ SV5 ) )
!= SY95 )
| ~ ( in @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY95 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SY95 @ SV19 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV5: $i] :
( ( ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
!= ( sK12_SY61 @ SV5 ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(208,plain,
! [SV5: $i] :
( ( ( ~ ( in @ ( sK13_SY68 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(209,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ! [SY96: $i] :
( ! [SY97: $i] :
( ( SY97 != SY96 )
| ~ ( in @ SY97 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY96 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY96 @ ( sK6_C @ SV20 @ SV5 ) ) )
| ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ ( sK6_C @ SV20 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY100 @ SV20 @ SV5 )
!= SY100 )
| ~ ( in @ ( sK9_E @ SY100 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SY100 @ SV20 @ SV5 ) )
!= SY100 )
| ~ ( in @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY100 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SY100 @ SV20 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(210,plain,
! [SV14: $i,SV5: $i,SV17: $i] :
( ( ( ! [SY88: $i] :
( ( SY88 != SV17 )
| ~ ( in @ SY88 @ ( cartesian_product2 @ SV5 @ SV14 ) ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ( ( ordered_pair @ SY89 @ SY90 )
!= SV17 )
| ~ ( in @ SY89 @ SV5 )
| ( SY90
!= ( singleton @ SY89 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(211,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 )
| ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV6: $i,SV15: $i,SV16: $i] :
( ( ( SV16
= ( singleton @ SV15 ) )
= $false )
| ( ( ( ordered_pair @ SV15 @ SV16 )
= ( sK3_SY38 @ SV6 ) )
= $false )
| ( ( in @ SV15 @ sK1_A )
= $false )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(213,plain,
! [SV6: $i] :
( ( ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
!= ( sK3_SY38 @ SV6 ) ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(214,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(215,plain,
! [SV5: $i] :
( ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(216,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(217,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
( ( SY92 != SY91 )
| ~ ( in @ SY92 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY91 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY91 @ ( sK6_C @ SV19 @ SV5 ) ) ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(218,plain,
! [SV5: $i,SV19: $i] :
( ( ( ~ ! [SY95: $i] :
( ~ ( in @ SY95 @ ( sK6_C @ SV19 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY95 @ SV19 @ SV5 )
!= SY95 )
| ~ ( in @ ( sK9_E @ SY95 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SY95 @ SV19 @ SV5 ) )
!= SY95 )
| ~ ( in @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY95 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SY95 @ SV19 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(219,plain,
! [SV5: $i] :
( ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(220,plain,
! [SV5: $i] :
( ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(221,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ! [SY96: $i] :
( ! [SY97: $i] :
( ( SY97 != SY96 )
| ~ ( in @ SY97 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY96 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY96 @ ( sK6_C @ SV20 @ SV5 ) ) ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(222,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ ( sK6_C @ SV20 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY100 @ SV20 @ SV5 )
!= SY100 )
| ~ ( in @ ( sK9_E @ SY100 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SY100 @ SV20 @ SV5 ) )
!= SY100 )
| ~ ( in @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY100 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SY100 @ SV20 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(223,plain,
! [SV14: $i,SV5: $i,SV17: $i,SV21: $i] :
( ( ( ( SV21 != SV17 )
| ~ ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ( ( ordered_pair @ SY89 @ SY90 )
!= SV17 )
| ~ ( in @ SY89 @ SV5 )
| ( SY90
!= ( singleton @ SY89 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(224,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 )
| ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(225,plain,
! [SV16: $i,SV15: $i,SV6: $i] :
( ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
= $false )
| ( ( in @ SV15 @ sK1_A )
= $false )
| ( ( ( ordered_pair @ SV15 @ SV16 )
= ( sK3_SY38 @ SV6 ) )
= $false )
| ( ( SV16
= ( singleton @ SV15 ) )
= $false )
| ( ( ~ ( in @ ( sK3_SY38 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(226,plain,
! [SV6: $i] :
( ( ( ( ordered_pair @ ( sK4_SY43 @ SV6 ) @ ( sK5_SY45 @ SV6 ) )
= ( sK3_SY38 @ SV6 ) )
= $true )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(227,plain,
! [SV6: $i] :
( ( ( in @ ( sK4_SY43 @ SV6 ) @ sK1_A )
= $true )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(228,plain,
! [SV22: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY101: $i] :
( ! [SY102: $i] :
( ( SY102 != SY101 )
| ~ ( in @ SY102 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY101 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY101 @ ( sK6_C @ SV22 @ SV5 ) ) )
| ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ ( sK6_C @ SV22 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY105 @ SV22 @ SV5 )
!= SY105 )
| ~ ( in @ ( sK9_E @ SY105 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SY105 @ SV22 @ SV5 ) )
!= SY105 )
| ~ ( in @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY105 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SY105 @ SV22 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(229,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
| ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(230,plain,
! [SV19: $i,SV5: $i] :
( ( ( ! [SY91: $i] :
( ! [SY92: $i] :
( ( SY92 != SY91 )
| ~ ( in @ SY92 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY91 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY91 @ ( sK6_C @ SV19 @ SV5 ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(231,plain,
! [SV5: $i,SV19: $i] :
( ( ( ! [SY95: $i] :
( ~ ( in @ SY95 @ ( sK6_C @ SV19 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY95 @ SV19 @ SV5 )
!= SY95 )
| ~ ( in @ ( sK9_E @ SY95 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SY95 @ SV19 @ SV5 ) )
!= SY95 )
| ~ ( in @ ( sK7_J @ SY95 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY95 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SY95 @ SV19 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(232,plain,
! [SV23: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( SY107 != SY106 )
| ~ ( in @ SY107 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY106 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY106 @ ( sK6_C @ SV23 @ SV5 ) ) )
| ~ ! [SY110: $i] :
( ~ ( in @ SY110 @ ( sK6_C @ SV23 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY110 @ SV23 @ SV5 )
!= SY110 )
| ~ ( in @ ( sK9_E @ SY110 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SY110 @ SV23 @ SV5 ) )
!= SY110 )
| ~ ( in @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY110 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SY110 @ SV23 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(233,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY111: $i] :
( ! [SY112: $i] :
( ( SY112 != SY111 )
| ~ ( in @ SY112 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY111 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY111 @ ( sK6_C @ SV24 @ SV5 ) ) )
| ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( sK6_C @ SV24 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY115 @ SV24 @ SV5 )
!= SY115 )
| ~ ( in @ ( sK9_E @ SY115 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SY115 @ SV24 @ SV5 ) )
!= SY115 )
| ~ ( in @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY115 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SY115 @ SV24 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(234,plain,
! [SV20: $i,SV5: $i] :
( ( ( ! [SY96: $i] :
( ! [SY97: $i] :
( ( SY97 != SY96 )
| ~ ( in @ SY97 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY96 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY96 @ ( sK6_C @ SV20 @ SV5 ) ) ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(235,plain,
! [SV5: $i,SV20: $i] :
( ( ( ! [SY100: $i] :
( ~ ( in @ SY100 @ ( sK6_C @ SV20 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY100 @ SV20 @ SV5 )
!= SY100 )
| ~ ( in @ ( sK9_E @ SY100 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SY100 @ SV20 @ SV5 ) )
!= SY100 )
| ~ ( in @ ( sK7_J @ SY100 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY100 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SY100 @ SV20 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(236,plain,
! [SV14: $i,SV5: $i,SV17: $i,SV21: $i] :
( ( ( ( SV21 != SV17 ) )
= $true )
| ( ( ~ ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ( ( ordered_pair @ SY89 @ SY90 )
!= SV17 )
| ~ ( in @ SY89 @ SV5 )
| ( SY90
!= ( singleton @ SY89 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(237,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 )
| ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(238,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(239,plain,
! [SV15: $i,SV16: $i,SV6: $i] :
( ( ( in @ ( sK3_SY38 @ SV6 ) @ SV6 )
= $false )
| ( ( SV16
= ( singleton @ SV15 ) )
= $false )
| ( ( ( ordered_pair @ SV15 @ SV16 )
= ( sK3_SY38 @ SV6 ) )
= $false )
| ( ( in @ SV15 @ sK1_A )
= $false )
| ( ( in @ ( sK3_SY38 @ SV6 ) @ ( cartesian_product2 @ sK1_A @ sK2_SY32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV22: $i,SV5: $i] :
( ( ( ~ ! [SY101: $i] :
( ! [SY102: $i] :
( ( SY102 != SY101 )
| ~ ( in @ SY102 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY101 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY101 @ ( sK6_C @ SV22 @ SV5 ) ) )
| ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ ( sK6_C @ SV22 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY105 @ SV22 @ SV5 )
!= SY105 )
| ~ ( in @ ( sK9_E @ SY105 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SY105 @ SV22 @ SV5 ) )
!= SY105 )
| ~ ( in @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY105 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SY105 @ SV22 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(241,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(242,plain,
! [SV5: $i] :
( ( ( ( ( sK16_SY71 @ SV5 )
!= ( singleton @ ( sK15_SY62 @ SV5 ) ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(243,plain,
! [SV19: $i,SV5: $i,SV25: $i] :
( ( ( ! [SY116: $i] :
( ( SY116 != SV25 )
| ~ ( in @ SY116 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ! [SY117: $i,SY118: $i] :
( ( ( ordered_pair @ SY117 @ SY118 )
!= SV25 )
| ~ ( in @ SY117 @ SV5 )
| ( SY118
!= ( singleton @ SY117 ) ) )
| ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(244,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 )
| ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(245,plain,
! [SV23: $i,SV5: $i] :
( ( ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( SY107 != SY106 )
| ~ ( in @ SY107 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY106 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY106 @ ( sK6_C @ SV23 @ SV5 ) ) )
| ~ ! [SY110: $i] :
( ~ ( in @ SY110 @ ( sK6_C @ SV23 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY110 @ SV23 @ SV5 )
!= SY110 )
| ~ ( in @ ( sK9_E @ SY110 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SY110 @ SV23 @ SV5 ) )
!= SY110 )
| ~ ( in @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY110 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SY110 @ SV23 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(246,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ! [SY111: $i] :
( ! [SY112: $i] :
( ( SY112 != SY111 )
| ~ ( in @ SY112 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY111 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY111 @ ( sK6_C @ SV24 @ SV5 ) ) )
| ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( sK6_C @ SV24 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY115 @ SV24 @ SV5 )
!= SY115 )
| ~ ( in @ ( sK9_E @ SY115 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SY115 @ SV24 @ SV5 ) )
!= SY115 )
| ~ ( in @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY115 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SY115 @ SV24 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(247,plain,
! [SV20: $i,SV5: $i,SV27: $i] :
( ( ( ! [SY119: $i] :
( ( SY119 != SV27 )
| ~ ( in @ SY119 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ! [SY120: $i,SY121: $i] :
( ( ( ordered_pair @ SY120 @ SY121 )
!= SV27 )
| ~ ( in @ SY120 @ SV5 )
| ( SY121
!= ( singleton @ SY120 ) ) )
| ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(248,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 )
| ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(249,plain,
! [SV14: $i,SV5: $i,SV17: $i,SV21: $i] :
( ( ( SV21 = SV17 )
= $false )
| ( ( ~ ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ( ( ordered_pair @ SY89 @ SY90 )
!= SV17 )
| ~ ( in @ SY89 @ SV5 )
| ( SY90
!= ( singleton @ SY89 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(250,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 )
| ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) ) )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(251,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(252,plain,
! [SV22: $i,SV5: $i] :
( ( ( ~ ! [SY101: $i] :
( ! [SY102: $i] :
( ( SY102 != SY101 )
| ~ ( in @ SY102 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY101 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY101 @ ( sK6_C @ SV22 @ SV5 ) ) ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(253,plain,
! [SV5: $i,SV22: $i] :
( ( ( ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ ( sK6_C @ SV22 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY105 @ SV22 @ SV5 )
!= SY105 )
| ~ ( in @ ( sK9_E @ SY105 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SY105 @ SV22 @ SV5 ) )
!= SY105 )
| ~ ( in @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY105 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SY105 @ SV22 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(254,plain,
! [SV5: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(255,plain,
! [SV5: $i] :
( ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(256,plain,
! [SV19: $i,SV5: $i,SV25: $i] :
( ( ( ! [SY116: $i] :
( ( SY116 != SV25 )
| ~ ( in @ SY116 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ! [SY117: $i,SY118: $i] :
( ( ( ordered_pair @ SY117 @ SY118 )
!= SV25 )
| ~ ( in @ SY117 @ SV5 )
| ( SY118
!= ( singleton @ SY117 ) ) ) )
= $true )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(257,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 )
| ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(258,plain,
! [SV23: $i,SV5: $i] :
( ( ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( SY107 != SY106 )
| ~ ( in @ SY107 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY106 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY106 @ ( sK6_C @ SV23 @ SV5 ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(259,plain,
! [SV5: $i,SV23: $i] :
( ( ( ~ ! [SY110: $i] :
( ~ ( in @ SY110 @ ( sK6_C @ SV23 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY110 @ SV23 @ SV5 )
!= SY110 )
| ~ ( in @ ( sK9_E @ SY110 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SY110 @ SV23 @ SV5 ) )
!= SY110 )
| ~ ( in @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY110 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SY110 @ SV23 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(260,plain,
! [SV24: $i,SV5: $i] :
( ( ( ~ ! [SY111: $i] :
( ! [SY112: $i] :
( ( SY112 != SY111 )
| ~ ( in @ SY112 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY111 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY111 @ ( sK6_C @ SV24 @ SV5 ) ) ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(261,plain,
! [SV5: $i,SV24: $i] :
( ( ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ ( sK6_C @ SV24 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY115 @ SV24 @ SV5 )
!= SY115 )
| ~ ( in @ ( sK9_E @ SY115 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SY115 @ SV24 @ SV5 ) )
!= SY115 )
| ~ ( in @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY115 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SY115 @ SV24 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(262,plain,
! [SV20: $i,SV5: $i,SV27: $i] :
( ( ( ! [SY119: $i] :
( ( SY119 != SV27 )
| ~ ( in @ SY119 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ! [SY120: $i,SY121: $i] :
( ( ( ordered_pair @ SY120 @ SY121 )
!= SV27 )
| ~ ( in @ SY120 @ SV5 )
| ( SY121
!= ( singleton @ SY120 ) ) ) )
= $true )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(263,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 )
| ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(264,plain,
! [SV17: $i,SV14: $i,SV5: $i,SV21: $i] :
( ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( SV21 = SV17 )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ( ( ordered_pair @ SY89 @ SY90 )
!= SV17 )
| ~ ( in @ SY89 @ SV5 )
| ( SY90
!= ( singleton @ SY89 ) ) ) )
= $true )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 )
| ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(266,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(267,plain,
! [SV22: $i,SV5: $i] :
( ( ( ! [SY101: $i] :
( ! [SY102: $i] :
( ( SY102 != SY101 )
| ~ ( in @ SY102 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY101 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY101 @ ( sK6_C @ SV22 @ SV5 ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(268,plain,
! [SV5: $i,SV22: $i] :
( ( ( ! [SY105: $i] :
( ~ ( in @ SY105 @ ( sK6_C @ SV22 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY105 @ SV22 @ SV5 )
!= SY105 )
| ~ ( in @ ( sK9_E @ SY105 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SY105 @ SV22 @ SV5 ) )
!= SY105 )
| ~ ( in @ ( sK7_J @ SY105 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY105 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SY105 @ SV22 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(269,plain,
! [SV5: $i] :
( ( ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) )
| ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(270,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY122: $i] :
( ! [SY123: $i] :
( ( SY123 != SY122 )
| ~ ( in @ SY123 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY122 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY122 @ ( sK6_C @ SV29 @ SV5 ) ) )
| ~ ! [SY126: $i] :
( ~ ( in @ SY126 @ ( sK6_C @ SV29 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY126 @ SV29 @ SV5 )
!= SY126 )
| ~ ( in @ ( sK9_E @ SY126 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SY126 @ SV29 @ SV5 ) )
!= SY126 )
| ~ ( in @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY126 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SY126 @ SV29 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(271,plain,
! [SV19: $i,SV5: $i,SV25: $i] :
( ( ( ! [SY116: $i] :
( ( SY116 != SV25 )
| ~ ( in @ SY116 @ ( cartesian_product2 @ SV5 @ SV19 ) ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ( ( ordered_pair @ SY117 @ SY118 )
!= SV25 )
| ~ ( in @ SY117 @ SV5 )
| ( SY118
!= ( singleton @ SY117 ) ) ) )
= $true )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(272,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 )
| ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(273,plain,
! [SV23: $i,SV5: $i] :
( ( ( ! [SY106: $i] :
( ! [SY107: $i] :
( ( SY107 != SY106 )
| ~ ( in @ SY107 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY106 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY106 @ ( sK6_C @ SV23 @ SV5 ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(274,plain,
! [SV5: $i,SV23: $i] :
( ( ( ! [SY110: $i] :
( ~ ( in @ SY110 @ ( sK6_C @ SV23 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY110 @ SV23 @ SV5 )
!= SY110 )
| ~ ( in @ ( sK9_E @ SY110 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SY110 @ SV23 @ SV5 ) )
!= SY110 )
| ~ ( in @ ( sK7_J @ SY110 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY110 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SY110 @ SV23 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(275,plain,
! [SV24: $i,SV5: $i] :
( ( ( ! [SY111: $i] :
( ! [SY112: $i] :
( ( SY112 != SY111 )
| ~ ( in @ SY112 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY111 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY111 @ ( sK6_C @ SV24 @ SV5 ) ) ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(276,plain,
! [SV5: $i,SV24: $i] :
( ( ( ! [SY115: $i] :
( ~ ( in @ SY115 @ ( sK6_C @ SV24 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY115 @ SV24 @ SV5 )
!= SY115 )
| ~ ( in @ ( sK9_E @ SY115 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SY115 @ SV24 @ SV5 ) )
!= SY115 )
| ~ ( in @ ( sK7_J @ SY115 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY115 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SY115 @ SV24 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(277,plain,
! [SV20: $i,SV5: $i,SV27: $i] :
( ( ( ! [SY119: $i] :
( ( SY119 != SV27 )
| ~ ( in @ SY119 @ ( cartesian_product2 @ SV5 @ SV20 ) ) ) )
= $true )
| ( ( ! [SY120: $i,SY121: $i] :
( ( ( ordered_pair @ SY120 @ SY121 )
!= SV27 )
| ~ ( in @ SY120 @ SV5 )
| ( SY121
!= ( singleton @ SY120 ) ) ) )
= $true )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(278,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 )
| ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(279,plain,
! [SV14: $i,SV21: $i,SV5: $i,SV17: $i,SV30: $i] :
( ( ( ! [SY127: $i] :
( ( ( ordered_pair @ SV30 @ SY127 )
!= SV17 )
| ~ ( in @ SV30 @ SV5 )
| ( SY127
!= ( singleton @ SV30 ) ) ) )
= $true )
| ( ( SV21 = SV17 )
= $false )
| ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(280,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
!= SV18 ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(281,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(282,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(283,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
!= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(284,plain,
! [SV22: $i,SV5: $i,SV31: $i] :
( ( ( ! [SY128: $i] :
( ( SY128 != SV31 )
| ~ ( in @ SY128 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ! [SY129: $i,SY130: $i] :
( ( ( ordered_pair @ SY129 @ SY130 )
!= SV31 )
| ~ ( in @ SY129 @ SV5 )
| ( SY130
!= ( singleton @ SY129 ) ) )
| ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(285,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 )
| ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(286,plain,
! [SV5: $i] :
( ( ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
!= ( sK11_SY55 @ SV5 ) ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(287,plain,
! [SV5: $i] :
( ( ( ~ ( in @ ( sK15_SY62 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(288,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ! [SY122: $i] :
( ! [SY123: $i] :
( ( SY123 != SY122 )
| ~ ( in @ SY123 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY122 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY122 @ ( sK6_C @ SV29 @ SV5 ) ) )
| ~ ! [SY126: $i] :
( ~ ( in @ SY126 @ ( sK6_C @ SV29 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY126 @ SV29 @ SV5 )
!= SY126 )
| ~ ( in @ ( sK9_E @ SY126 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SY126 @ SV29 @ SV5 ) )
!= SY126 )
| ~ ( in @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY126 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SY126 @ SV29 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(289,plain,
! [SV19: $i,SV5: $i,SV25: $i,SV33: $i] :
( ( ( ( SV33 != SV25 )
| ~ ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ( ( ordered_pair @ SY117 @ SY118 )
!= SV25 )
| ~ ( in @ SY117 @ SV5 )
| ( SY118
!= ( singleton @ SY117 ) ) ) )
= $true )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(290,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 )
| ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(291,plain,
! [SV23: $i,SV5: $i,SV34: $i] :
( ( ( ! [SY131: $i] :
( ( SY131 != SV34 )
| ~ ( in @ SY131 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ! [SY132: $i,SY133: $i] :
( ( ( ordered_pair @ SY132 @ SY133 )
!= SV34 )
| ~ ( in @ SY132 @ SV5 )
| ( SY133
!= ( singleton @ SY132 ) ) )
| ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(292,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 )
| ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(293,plain,
! [SV24: $i,SV5: $i,SV36: $i] :
( ( ( ! [SY134: $i] :
( ( SY134 != SV36 )
| ~ ( in @ SY134 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ! [SY135: $i,SY136: $i] :
( ( ( ordered_pair @ SY135 @ SY136 )
!= SV36 )
| ~ ( in @ SY135 @ SV5 )
| ( SY136
!= ( singleton @ SY135 ) ) )
| ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(294,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 )
| ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(295,plain,
! [SV20: $i,SV5: $i,SV27: $i,SV38: $i] :
( ( ( ( SV38 != SV27 )
| ~ ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
= $true )
| ( ( ! [SY120: $i,SY121: $i] :
( ( ( ordered_pair @ SY120 @ SY121 )
!= SV27 )
| ~ ( in @ SY120 @ SV5 )
| ( SY121
!= ( singleton @ SY120 ) ) ) )
= $true )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(296,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 )
| ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(297,plain,
! [SV14: $i,SV21: $i,SV5: $i,SV17: $i,SV39: $i,SV30: $i] :
( ( ( ( ( ordered_pair @ SV30 @ SV39 )
!= SV17 )
| ~ ( in @ SV30 @ SV5 )
| ( SV39
!= ( singleton @ SV30 ) ) )
= $true )
| ( ( SV21 = SV17 )
= $false )
| ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(298,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( sK9_E @ SV18 @ SV14 @ SV5 )
= SV18 )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(299,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( in @ ( sK9_E @ SV18 @ SV14 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(300,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(301,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( sK8_SY54 @ SV18 @ SV14 @ SV5 )
= ( singleton @ ( sK7_J @ SV18 @ SV14 @ SV5 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(302,plain,
! [SV22: $i,SV5: $i,SV31: $i] :
( ( ( ! [SY128: $i] :
( ( SY128 != SV31 )
| ~ ( in @ SY128 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ! [SY129: $i,SY130: $i] :
( ( ( ordered_pair @ SY129 @ SY130 )
!= SV31 )
| ~ ( in @ SY129 @ SV5 )
| ( SY130
!= ( singleton @ SY129 ) ) ) )
= $true )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(303,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 )
| ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(304,plain,
! [SV5: $i] :
( ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(305,plain,
! [SV5: $i] :
( ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true )
| ( ( ! [SY74: $i] :
~ ( ~ ! [SY75: $i] :
( ! [SY76: $i] :
( ( SY76 != SY75 )
| ~ ( in @ SY76 @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY75 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY75 @ ( sK6_C @ SY74 @ SV5 ) ) )
| ~ ! [SY79: $i] :
( ~ ( in @ SY79 @ ( sK6_C @ SY74 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY79 @ SY74 @ SV5 )
!= SY79 )
| ~ ( in @ ( sK9_E @ SY79 @ SY74 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SY74 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ ( sK8_SY54 @ SY79 @ SY74 @ SV5 ) )
!= SY79 )
| ~ ( in @ ( sK7_J @ SY79 @ SY74 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY79 @ SY74 @ SV5 )
!= ( singleton @ ( sK7_J @ SY79 @ SY74 @ SV5 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(306,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ! [SY122: $i] :
( ! [SY123: $i] :
( ( SY123 != SY122 )
| ~ ( in @ SY123 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY122 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY122 @ ( sK6_C @ SV29 @ SV5 ) ) ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(307,plain,
! [SV5: $i,SV29: $i] :
( ( ( ~ ! [SY126: $i] :
( ~ ( in @ SY126 @ ( sK6_C @ SV29 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY126 @ SV29 @ SV5 )
!= SY126 )
| ~ ( in @ ( sK9_E @ SY126 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SY126 @ SV29 @ SV5 ) )
!= SY126 )
| ~ ( in @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY126 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SY126 @ SV29 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(308,plain,
! [SV19: $i,SV5: $i,SV25: $i,SV33: $i] :
( ( ( ( SV33 != SV25 ) )
= $true )
| ( ( ~ ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ( ( ordered_pair @ SY117 @ SY118 )
!= SV25 )
| ~ ( in @ SY117 @ SV5 )
| ( SY118
!= ( singleton @ SY117 ) ) ) )
= $true )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(309,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 )
| ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(310,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(311,plain,
! [SV23: $i,SV5: $i,SV34: $i] :
( ( ( ! [SY131: $i] :
( ( SY131 != SV34 )
| ~ ( in @ SY131 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ! [SY132: $i,SY133: $i] :
( ( ( ordered_pair @ SY132 @ SY133 )
!= SV34 )
| ~ ( in @ SY132 @ SV5 )
| ( SY133
!= ( singleton @ SY132 ) ) ) )
= $true )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(312,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 )
| ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(313,plain,
! [SV24: $i,SV5: $i,SV36: $i] :
( ( ( ! [SY134: $i] :
( ( SY134 != SV36 )
| ~ ( in @ SY134 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ! [SY135: $i,SY136: $i] :
( ( ( ordered_pair @ SY135 @ SY136 )
!= SV36 )
| ~ ( in @ SY135 @ SV5 )
| ( SY136
!= ( singleton @ SY135 ) ) ) )
= $true )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(314,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 )
| ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(315,plain,
! [SV20: $i,SV5: $i,SV27: $i,SV38: $i] :
( ( ( ( SV38 != SV27 ) )
= $true )
| ( ( ~ ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
= $true )
| ( ( ! [SY120: $i,SY121: $i] :
( ( ( ordered_pair @ SY120 @ SY121 )
!= SV27 )
| ~ ( in @ SY120 @ SV5 )
| ( SY121
!= ( singleton @ SY120 ) ) ) )
= $true )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(316,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 )
| ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(317,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(318,plain,
! [SV14: $i,SV21: $i,SV5: $i,SV17: $i,SV39: $i,SV30: $i] :
( ( ( ( ( ordered_pair @ SV30 @ SV39 )
!= SV17 )
| ~ ( in @ SV30 @ SV5 ) )
= $true )
| ( ( ( SV39
!= ( singleton @ SV30 ) ) )
= $true )
| ( ( SV21 = SV17 )
= $false )
| ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(319,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 )
| ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(320,plain,
! [SV22: $i,SV5: $i,SV31: $i] :
( ( ( ! [SY128: $i] :
( ( SY128 != SV31 )
| ~ ( in @ SY128 @ ( cartesian_product2 @ SV5 @ SV22 ) ) ) )
= $true )
| ( ( ! [SY129: $i,SY130: $i] :
( ( ( ordered_pair @ SY129 @ SY130 )
!= SV31 )
| ~ ( in @ SY129 @ SV5 )
| ( SY130
!= ( singleton @ SY129 ) ) ) )
= $true )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(321,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 )
| ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(322,plain,
! [SV40: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
( ( SY138 != SY137 )
| ~ ( in @ SY138 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY137 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY137 @ ( sK6_C @ SV40 @ SV5 ) ) )
| ~ ! [SY141: $i] :
( ~ ( in @ SY141 @ ( sK6_C @ SV40 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY141 @ SV40 @ SV5 )
!= SY141 )
| ~ ( in @ ( sK9_E @ SY141 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SY141 @ SV40 @ SV5 ) )
!= SY141 )
| ~ ( in @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY141 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SY141 @ SV40 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(323,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( ~ ! [SY142: $i] :
( ! [SY143: $i] :
( ( SY143 != SY142 )
| ~ ( in @ SY143 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY142 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY142 @ ( sK6_C @ SV41 @ SV5 ) ) )
| ~ ! [SY146: $i] :
( ~ ( in @ SY146 @ ( sK6_C @ SV41 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY146 @ SV41 @ SV5 )
!= SY146 )
| ~ ( in @ ( sK9_E @ SY146 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SY146 @ SV41 @ SV5 ) )
!= SY146 )
| ~ ( in @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY146 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SY146 @ SV41 @ SV5 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(324,plain,
! [SV29: $i,SV5: $i] :
( ( ( ! [SY122: $i] :
( ! [SY123: $i] :
( ( SY123 != SY122 )
| ~ ( in @ SY123 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY122 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY122 @ ( sK6_C @ SV29 @ SV5 ) ) ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(325,plain,
! [SV5: $i,SV29: $i] :
( ( ( ! [SY126: $i] :
( ~ ( in @ SY126 @ ( sK6_C @ SV29 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY126 @ SV29 @ SV5 )
!= SY126 )
| ~ ( in @ ( sK9_E @ SY126 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SY126 @ SV29 @ SV5 ) )
!= SY126 )
| ~ ( in @ ( sK7_J @ SY126 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY126 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SY126 @ SV29 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(326,plain,
! [SV19: $i,SV5: $i,SV25: $i,SV33: $i] :
( ( ( SV33 = SV25 )
= $false )
| ( ( ~ ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ( ( ordered_pair @ SY117 @ SY118 )
!= SV25 )
| ~ ( in @ SY117 @ SV5 )
| ( SY118
!= ( singleton @ SY117 ) ) ) )
= $true )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(327,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 )
| ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) ) )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(328,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(329,plain,
! [SV23: $i,SV5: $i,SV34: $i] :
( ( ( ! [SY131: $i] :
( ( SY131 != SV34 )
| ~ ( in @ SY131 @ ( cartesian_product2 @ SV5 @ SV23 ) ) ) )
= $true )
| ( ( ! [SY132: $i,SY133: $i] :
( ( ( ordered_pair @ SY132 @ SY133 )
!= SV34 )
| ~ ( in @ SY132 @ SV5 )
| ( SY133
!= ( singleton @ SY132 ) ) ) )
= $true )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(330,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 )
| ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(331,plain,
! [SV24: $i,SV5: $i,SV36: $i] :
( ( ( ! [SY134: $i] :
( ( SY134 != SV36 )
| ~ ( in @ SY134 @ ( cartesian_product2 @ SV5 @ SV24 ) ) ) )
= $true )
| ( ( ! [SY135: $i,SY136: $i] :
( ( ( ordered_pair @ SY135 @ SY136 )
!= SV36 )
| ~ ( in @ SY135 @ SV5 )
| ( SY136
!= ( singleton @ SY135 ) ) ) )
= $true )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(332,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 )
| ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(333,plain,
! [SV20: $i,SV5: $i,SV27: $i,SV38: $i] :
( ( ( SV38 = SV27 )
= $false )
| ( ( ~ ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
= $true )
| ( ( ! [SY120: $i,SY121: $i] :
( ( ( ordered_pair @ SY120 @ SY121 )
!= SV27 )
| ~ ( in @ SY120 @ SV5 )
| ( SY121
!= ( singleton @ SY120 ) ) ) )
= $true )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(334,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 )
| ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) ) )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(335,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(336,plain,
! [SV14: $i,SV21: $i,SV5: $i,SV17: $i,SV39: $i,SV30: $i] :
( ( ( ( ( ordered_pair @ SV30 @ SV39 )
!= SV17 ) )
= $true )
| ( ( ~ ( in @ SV30 @ SV5 ) )
= $true )
| ( ( ( SV39
!= ( singleton @ SV30 ) ) )
= $true )
| ( ( SV21 = SV17 )
= $false )
| ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(337,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
!= SV18 ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(338,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(339,plain,
! [SV22: $i,SV5: $i,SV31: $i,SV42: $i] :
( ( ( ( SV42 != SV31 )
| ~ ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
= $true )
| ( ( ! [SY129: $i,SY130: $i] :
( ( ( ordered_pair @ SY129 @ SY130 )
!= SV31 )
| ~ ( in @ SY129 @ SV5 )
| ( SY130
!= ( singleton @ SY129 ) ) ) )
= $true )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(340,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 )
| ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(341,plain,
! [SV40: $i,SV5: $i] :
( ( ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
( ( SY138 != SY137 )
| ~ ( in @ SY138 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY137 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY137 @ ( sK6_C @ SV40 @ SV5 ) ) )
| ~ ! [SY141: $i] :
( ~ ( in @ SY141 @ ( sK6_C @ SV40 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY141 @ SV40 @ SV5 )
!= SY141 )
| ~ ( in @ ( sK9_E @ SY141 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SY141 @ SV40 @ SV5 ) )
!= SY141 )
| ~ ( in @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY141 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SY141 @ SV40 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(342,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ! [SY142: $i] :
( ! [SY143: $i] :
( ( SY143 != SY142 )
| ~ ( in @ SY143 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY142 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY142 @ ( sK6_C @ SV41 @ SV5 ) ) )
| ~ ! [SY146: $i] :
( ~ ( in @ SY146 @ ( sK6_C @ SV41 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY146 @ SV41 @ SV5 )
!= SY146 )
| ~ ( in @ ( sK9_E @ SY146 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SY146 @ SV41 @ SV5 ) )
!= SY146 )
| ~ ( in @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY146 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SY146 @ SV41 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(343,plain,
! [SV29: $i,SV5: $i,SV43: $i] :
( ( ( ! [SY147: $i] :
( ( SY147 != SV43 )
| ~ ( in @ SY147 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ! [SY148: $i,SY149: $i] :
( ( ( ordered_pair @ SY148 @ SY149 )
!= SV43 )
| ~ ( in @ SY148 @ SV5 )
| ( SY149
!= ( singleton @ SY148 ) ) )
| ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(344,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 )
| ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(345,plain,
! [SV25: $i,SV19: $i,SV5: $i,SV33: $i] :
( ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( SV33 = SV25 )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ( ( ordered_pair @ SY117 @ SY118 )
!= SV25 )
| ~ ( in @ SY117 @ SV5 )
| ( SY118
!= ( singleton @ SY117 ) ) ) )
= $true )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(346,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 )
| ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(347,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(348,plain,
! [SV23: $i,SV5: $i,SV34: $i,SV45: $i] :
( ( ( ( SV45 != SV34 )
| ~ ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
= $true )
| ( ( ! [SY132: $i,SY133: $i] :
( ( ( ordered_pair @ SY132 @ SY133 )
!= SV34 )
| ~ ( in @ SY132 @ SV5 )
| ( SY133
!= ( singleton @ SY132 ) ) ) )
= $true )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(349,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 )
| ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(350,plain,
! [SV24: $i,SV5: $i,SV36: $i,SV46: $i] :
( ( ( ( SV46 != SV36 )
| ~ ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
= $true )
| ( ( ! [SY135: $i,SY136: $i] :
( ( ( ordered_pair @ SY135 @ SY136 )
!= SV36 )
| ~ ( in @ SY135 @ SV5 )
| ( SY136
!= ( singleton @ SY135 ) ) ) )
= $true )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(351,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 )
| ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(352,plain,
! [SV27: $i,SV20: $i,SV5: $i,SV38: $i] :
( ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( SV38 = SV27 )
= $false )
| ( ( ! [SY120: $i,SY121: $i] :
( ( ( ordered_pair @ SY120 @ SY121 )
!= SV27 )
| ~ ( in @ SY120 @ SV5 )
| ( SY121
!= ( singleton @ SY120 ) ) ) )
= $true )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(353,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 )
| ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(354,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(355,plain,
! [SV14: $i,SV21: $i,SV5: $i,SV17: $i,SV39: $i,SV30: $i] :
( ( ( ( ordered_pair @ SV30 @ SV39 )
= SV17 )
= $false )
| ( ( ~ ( in @ SV30 @ SV5 ) )
= $true )
| ( ( ( SV39
!= ( singleton @ SV30 ) ) )
= $true )
| ( ( SV21 = SV17 )
= $false )
| ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(356,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ ( sK8_SY54 @ SV18 @ SV14 @ SV5 ) )
= SV18 )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(357,plain,
! [SV5: $i,SV14: $i,SV18: $i] :
( ( ( in @ ( sK7_J @ SV18 @ SV14 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV18 @ ( sK6_C @ SV14 @ SV5 ) )
= $false )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(358,plain,
! [SV22: $i,SV5: $i,SV31: $i,SV42: $i] :
( ( ( ( SV42 != SV31 ) )
= $true )
| ( ( ~ ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
= $true )
| ( ( ! [SY129: $i,SY130: $i] :
( ( ( ordered_pair @ SY129 @ SY130 )
!= SV31 )
| ~ ( in @ SY129 @ SV5 )
| ( SY130
!= ( singleton @ SY129 ) ) ) )
= $true )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(359,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 )
| ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(360,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(361,plain,
! [SV40: $i,SV5: $i] :
( ( ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
( ( SY138 != SY137 )
| ~ ( in @ SY138 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY137 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY137 @ ( sK6_C @ SV40 @ SV5 ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(362,plain,
! [SV5: $i,SV40: $i] :
( ( ( ~ ! [SY141: $i] :
( ~ ( in @ SY141 @ ( sK6_C @ SV40 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY141 @ SV40 @ SV5 )
!= SY141 )
| ~ ( in @ ( sK9_E @ SY141 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SY141 @ SV40 @ SV5 ) )
!= SY141 )
| ~ ( in @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY141 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SY141 @ SV40 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(363,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ! [SY142: $i] :
( ! [SY143: $i] :
( ( SY143 != SY142 )
| ~ ( in @ SY143 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY142 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY142 @ ( sK6_C @ SV41 @ SV5 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(364,plain,
! [SV5: $i,SV41: $i] :
( ( ( ~ ! [SY146: $i] :
( ~ ( in @ SY146 @ ( sK6_C @ SV41 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY146 @ SV41 @ SV5 )
!= SY146 )
| ~ ( in @ ( sK9_E @ SY146 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SY146 @ SV41 @ SV5 ) )
!= SY146 )
| ~ ( in @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY146 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SY146 @ SV41 @ SV5 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(365,plain,
! [SV29: $i,SV5: $i,SV43: $i] :
( ( ( ! [SY147: $i] :
( ( SY147 != SV43 )
| ~ ( in @ SY147 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ! [SY148: $i,SY149: $i] :
( ( ( ordered_pair @ SY148 @ SY149 )
!= SV43 )
| ~ ( in @ SY148 @ SV5 )
| ( SY149
!= ( singleton @ SY148 ) ) ) )
= $true )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(366,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 )
| ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(367,plain,
! [SV19: $i,SV33: $i,SV5: $i,SV25: $i,SV47: $i] :
( ( ( ! [SY150: $i] :
( ( ( ordered_pair @ SV47 @ SY150 )
!= SV25 )
| ~ ( in @ SV47 @ SV5 )
| ( SY150
!= ( singleton @ SV47 ) ) ) )
= $true )
| ( ( SV33 = SV25 )
= $false )
| ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(368,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
!= SV26 ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(369,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(370,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(371,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
!= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(372,plain,
! [SV23: $i,SV5: $i,SV34: $i,SV45: $i] :
( ( ( ( SV45 != SV34 ) )
= $true )
| ( ( ~ ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
= $true )
| ( ( ! [SY132: $i,SY133: $i] :
( ( ( ordered_pair @ SY132 @ SY133 )
!= SV34 )
| ~ ( in @ SY132 @ SV5 )
| ( SY133
!= ( singleton @ SY132 ) ) ) )
= $true )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(373,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 )
| ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(374,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(375,plain,
! [SV24: $i,SV5: $i,SV36: $i,SV46: $i] :
( ( ( ( SV46 != SV36 ) )
= $true )
| ( ( ~ ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
= $true )
| ( ( ! [SY135: $i,SY136: $i] :
( ( ( ordered_pair @ SY135 @ SY136 )
!= SV36 )
| ~ ( in @ SY135 @ SV5 )
| ( SY136
!= ( singleton @ SY135 ) ) ) )
= $true )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(376,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 )
| ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(377,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(378,plain,
! [SV20: $i,SV38: $i,SV5: $i,SV27: $i,SV48: $i] :
( ( ( ! [SY151: $i] :
( ( ( ordered_pair @ SV48 @ SY151 )
!= SV27 )
| ~ ( in @ SV48 @ SV5 )
| ( SY151
!= ( singleton @ SV48 ) ) ) )
= $true )
| ( ( SV38 = SV27 )
= $false )
| ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(379,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
!= SV28 ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(380,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(381,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(382,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
!= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(383,plain,
! [SV14: $i,SV21: $i,SV17: $i,SV39: $i,SV5: $i,SV30: $i] :
( ( ( in @ SV30 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV30 @ SV39 )
= SV17 )
= $false )
| ( ( ( SV39
!= ( singleton @ SV30 ) ) )
= $true )
| ( ( SV21 = SV17 )
= $false )
| ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(384,plain,
! [SV22: $i,SV5: $i,SV31: $i,SV42: $i] :
( ( ( SV42 = SV31 )
= $false )
| ( ( ~ ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
= $true )
| ( ( ! [SY129: $i,SY130: $i] :
( ( ( ordered_pair @ SY129 @ SY130 )
!= SV31 )
| ~ ( in @ SY129 @ SV5 )
| ( SY130
!= ( singleton @ SY129 ) ) ) )
= $true )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(385,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 )
| ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) ) )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(386,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(387,plain,
! [SV40: $i,SV5: $i] :
( ( ( ! [SY137: $i] :
( ! [SY138: $i] :
( ( SY138 != SY137 )
| ~ ( in @ SY138 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY137 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY137 @ ( sK6_C @ SV40 @ SV5 ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(388,plain,
! [SV5: $i,SV40: $i] :
( ( ( ! [SY141: $i] :
( ~ ( in @ SY141 @ ( sK6_C @ SV40 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY141 @ SV40 @ SV5 )
!= SY141 )
| ~ ( in @ ( sK9_E @ SY141 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SY141 @ SV40 @ SV5 ) )
!= SY141 )
| ~ ( in @ ( sK7_J @ SY141 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY141 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SY141 @ SV40 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(389,plain,
! [SV41: $i,SV5: $i] :
( ( ( ! [SY142: $i] :
( ! [SY143: $i] :
( ( SY143 != SY142 )
| ~ ( in @ SY143 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ! [SY77: $i,SY78: $i] :
( ( ( ordered_pair @ SY77 @ SY78 )
!= SY142 )
| ~ ( in @ SY77 @ SV5 )
| ( SY78
!= ( singleton @ SY77 ) ) )
| ( in @ SY142 @ ( sK6_C @ SV41 @ SV5 ) ) ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(390,plain,
! [SV5: $i,SV41: $i] :
( ( ( ! [SY146: $i] :
( ~ ( in @ SY146 @ ( sK6_C @ SV41 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SY146 @ SV41 @ SV5 )
!= SY146 )
| ~ ( in @ ( sK9_E @ SY146 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SY146 @ SV41 @ SV5 ) )
!= SY146 )
| ~ ( in @ ( sK7_J @ SY146 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SY146 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SY146 @ SV41 @ SV5 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(391,plain,
! [SV29: $i,SV5: $i,SV43: $i] :
( ( ( ! [SY147: $i] :
( ( SY147 != SV43 )
| ~ ( in @ SY147 @ ( cartesian_product2 @ SV5 @ SV29 ) ) ) )
= $true )
| ( ( ! [SY148: $i,SY149: $i] :
( ( ( ordered_pair @ SY148 @ SY149 )
!= SV43 )
| ~ ( in @ SY148 @ SV5 )
| ( SY149
!= ( singleton @ SY148 ) ) ) )
= $true )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(392,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 )
| ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(393,plain,
! [SV19: $i,SV33: $i,SV5: $i,SV25: $i,SV49: $i,SV47: $i] :
( ( ( ( ( ordered_pair @ SV47 @ SV49 )
!= SV25 )
| ~ ( in @ SV47 @ SV5 )
| ( SV49
!= ( singleton @ SV47 ) ) )
= $true )
| ( ( SV33 = SV25 )
= $false )
| ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(394,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( sK9_E @ SV26 @ SV19 @ SV5 )
= SV26 )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(395,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( in @ ( sK9_E @ SV26 @ SV19 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(396,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(397,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( sK8_SY54 @ SV26 @ SV19 @ SV5 )
= ( singleton @ ( sK7_J @ SV26 @ SV19 @ SV5 ) ) )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(398,plain,
! [SV23: $i,SV5: $i,SV34: $i,SV45: $i] :
( ( ( SV45 = SV34 )
= $false )
| ( ( ~ ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
= $true )
| ( ( ! [SY132: $i,SY133: $i] :
( ( ( ordered_pair @ SY132 @ SY133 )
!= SV34 )
| ~ ( in @ SY132 @ SV5 )
| ( SY133
!= ( singleton @ SY132 ) ) ) )
= $true )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(399,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 )
| ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) ) )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(400,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(401,plain,
! [SV24: $i,SV5: $i,SV36: $i,SV46: $i] :
( ( ( SV46 = SV36 )
= $false )
| ( ( ~ ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
= $true )
| ( ( ! [SY135: $i,SY136: $i] :
( ( ( ordered_pair @ SY135 @ SY136 )
!= SV36 )
| ~ ( in @ SY135 @ SV5 )
| ( SY136
!= ( singleton @ SY135 ) ) ) )
= $true )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(402,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 )
| ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) ) )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(403,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(404,plain,
! [SV20: $i,SV38: $i,SV5: $i,SV27: $i,SV50: $i,SV48: $i] :
( ( ( ( ( ordered_pair @ SV48 @ SV50 )
!= SV27 )
| ~ ( in @ SV48 @ SV5 )
| ( SV50
!= ( singleton @ SV48 ) ) )
= $true )
| ( ( SV38 = SV27 )
= $false )
| ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(405,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( sK9_E @ SV28 @ SV20 @ SV5 )
= SV28 )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(406,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( in @ ( sK9_E @ SV28 @ SV20 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(407,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(408,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( sK8_SY54 @ SV28 @ SV20 @ SV5 )
= ( singleton @ ( sK7_J @ SV28 @ SV20 @ SV5 ) ) )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(409,plain,
! [SV14: $i,SV21: $i,SV5: $i,SV17: $i,SV30: $i,SV39: $i] :
( ( ( SV39
= ( singleton @ SV30 ) )
= $false )
| ( ( ( ordered_pair @ SV30 @ SV39 )
= SV17 )
= $false )
| ( ( in @ SV30 @ SV5 )
= $false )
| ( ( SV21 = SV17 )
= $false )
| ( ( in @ SV21 @ ( cartesian_product2 @ SV5 @ SV14 ) )
= $false )
| ( ( in @ SV17 @ ( sK6_C @ SV14 @ SV5 ) )
= $true )
| ( ( ( sK11_SY55 @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(410,plain,
! [SV31: $i,SV22: $i,SV5: $i,SV42: $i] :
( ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( SV42 = SV31 )
= $false )
| ( ( ! [SY129: $i,SY130: $i] :
( ( ( ordered_pair @ SY129 @ SY130 )
!= SV31 )
| ~ ( in @ SY129 @ SV5 )
| ( SY130
!= ( singleton @ SY129 ) ) ) )
= $true )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(411,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 )
| ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(412,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(413,plain,
! [SV40: $i,SV5: $i,SV51: $i] :
( ( ( ! [SY152: $i] :
( ( SY152 != SV51 )
| ~ ( in @ SY152 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ! [SY153: $i,SY154: $i] :
( ( ( ordered_pair @ SY153 @ SY154 )
!= SV51 )
| ~ ( in @ SY153 @ SV5 )
| ( SY154
!= ( singleton @ SY153 ) ) )
| ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(414,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 )
| ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(415,plain,
! [SV41: $i,SV5: $i,SV53: $i] :
( ( ( ! [SY155: $i] :
( ( SY155 != SV53 )
| ~ ( in @ SY155 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ! [SY156: $i,SY157: $i] :
( ( ( ordered_pair @ SY156 @ SY157 )
!= SV53 )
| ~ ( in @ SY156 @ SV5 )
| ( SY157
!= ( singleton @ SY156 ) ) )
| ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(416,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
| ~ ( ~ ~ ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 )
| ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(417,plain,
! [SV29: $i,SV5: $i,SV43: $i,SV55: $i] :
( ( ( ( SV55 != SV43 )
| ~ ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
= $true )
| ( ( ! [SY148: $i,SY149: $i] :
( ( ( ordered_pair @ SY148 @ SY149 )
!= SV43 )
| ~ ( in @ SY148 @ SV5 )
| ( SY149
!= ( singleton @ SY148 ) ) ) )
= $true )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(418,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 )
| ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(419,plain,
! [SV19: $i,SV33: $i,SV5: $i,SV25: $i,SV49: $i,SV47: $i] :
( ( ( ( ( ordered_pair @ SV47 @ SV49 )
!= SV25 )
| ~ ( in @ SV47 @ SV5 ) )
= $true )
| ( ( ( SV49
!= ( singleton @ SV47 ) ) )
= $true )
| ( ( SV33 = SV25 )
= $false )
| ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(420,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 )
| ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(421,plain,
! [SV34: $i,SV23: $i,SV5: $i,SV45: $i] :
( ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( SV45 = SV34 )
= $false )
| ( ( ! [SY132: $i,SY133: $i] :
( ( ( ordered_pair @ SY132 @ SY133 )
!= SV34 )
| ~ ( in @ SY132 @ SV5 )
| ( SY133
!= ( singleton @ SY132 ) ) ) )
= $true )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(422,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 )
| ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(423,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(424,plain,
! [SV36: $i,SV24: $i,SV5: $i,SV46: $i] :
( ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( SV46 = SV36 )
= $false )
| ( ( ! [SY135: $i,SY136: $i] :
( ( ( ordered_pair @ SY135 @ SY136 )
!= SV36 )
| ~ ( in @ SY135 @ SV5 )
| ( SY136
!= ( singleton @ SY135 ) ) ) )
= $true )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(425,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 )
| ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(426,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(427,plain,
! [SV20: $i,SV38: $i,SV5: $i,SV27: $i,SV50: $i,SV48: $i] :
( ( ( ( ( ordered_pair @ SV48 @ SV50 )
!= SV27 )
| ~ ( in @ SV48 @ SV5 ) )
= $true )
| ( ( ( SV50
!= ( singleton @ SV48 ) ) )
= $true )
| ( ( SV38 = SV27 )
= $false )
| ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(428,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 )
| ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(429,plain,
! [SV22: $i,SV42: $i,SV5: $i,SV31: $i,SV56: $i] :
( ( ( ! [SY158: $i] :
( ( ( ordered_pair @ SV56 @ SY158 )
!= SV31 )
| ~ ( in @ SV56 @ SV5 )
| ( SY158
!= ( singleton @ SV56 ) ) ) )
= $true )
| ( ( SV42 = SV31 )
= $false )
| ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(430,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
!= SV32 ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(431,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(432,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(433,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
!= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(434,plain,
! [SV40: $i,SV5: $i,SV51: $i] :
( ( ( ! [SY152: $i] :
( ( SY152 != SV51 )
| ~ ( in @ SY152 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ! [SY153: $i,SY154: $i] :
( ( ( ordered_pair @ SY153 @ SY154 )
!= SV51 )
| ~ ( in @ SY153 @ SV5 )
| ( SY154
!= ( singleton @ SY153 ) ) ) )
= $true )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(435,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 )
| ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(436,plain,
! [SV41: $i,SV5: $i,SV53: $i] :
( ( ( ! [SY155: $i] :
( ( SY155 != SV53 )
| ~ ( in @ SY155 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ! [SY156: $i,SY157: $i] :
( ( ( ordered_pair @ SY156 @ SY157 )
!= SV53 )
| ~ ( in @ SY156 @ SV5 )
| ( SY157
!= ( singleton @ SY156 ) ) ) )
= $true )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(437,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 )
| ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(438,plain,
! [SV29: $i,SV5: $i,SV43: $i,SV55: $i] :
( ( ( ( SV55 != SV43 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
= $true )
| ( ( ! [SY148: $i,SY149: $i] :
( ( ( ordered_pair @ SY148 @ SY149 )
!= SV43 )
| ~ ( in @ SY148 @ SV5 )
| ( SY149
!= ( singleton @ SY148 ) ) ) )
= $true )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(439,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 )
| ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(440,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(441,plain,
! [SV19: $i,SV33: $i,SV5: $i,SV25: $i,SV49: $i,SV47: $i] :
( ( ( ( ( ordered_pair @ SV47 @ SV49 )
!= SV25 ) )
= $true )
| ( ( ~ ( in @ SV47 @ SV5 ) )
= $true )
| ( ( ( SV49
!= ( singleton @ SV47 ) ) )
= $true )
| ( ( SV33 = SV25 )
= $false )
| ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(442,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
!= SV26 ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(443,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(444,plain,
! [SV23: $i,SV45: $i,SV5: $i,SV34: $i,SV57: $i] :
( ( ( ! [SY159: $i] :
( ( ( ordered_pair @ SV57 @ SY159 )
!= SV34 )
| ~ ( in @ SV57 @ SV5 )
| ( SY159
!= ( singleton @ SV57 ) ) ) )
= $true )
| ( ( SV45 = SV34 )
= $false )
| ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(445,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
!= SV35 ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(446,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(447,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(448,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
!= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(449,plain,
! [SV24: $i,SV46: $i,SV5: $i,SV36: $i,SV58: $i] :
( ( ( ! [SY160: $i] :
( ( ( ordered_pair @ SV58 @ SY160 )
!= SV36 )
| ~ ( in @ SV58 @ SV5 )
| ( SY160
!= ( singleton @ SV58 ) ) ) )
= $true )
| ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(450,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
!= SV37 ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(451,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(452,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(453,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
!= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(454,plain,
! [SV20: $i,SV38: $i,SV5: $i,SV27: $i,SV50: $i,SV48: $i] :
( ( ( ( ( ordered_pair @ SV48 @ SV50 )
!= SV27 ) )
= $true )
| ( ( ~ ( in @ SV48 @ SV5 ) )
= $true )
| ( ( ( SV50
!= ( singleton @ SV48 ) ) )
= $true )
| ( ( SV38 = SV27 )
= $false )
| ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(455,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
!= SV28 ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(456,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(457,plain,
! [SV22: $i,SV42: $i,SV5: $i,SV31: $i,SV59: $i,SV56: $i] :
( ( ( ( ( ordered_pair @ SV56 @ SV59 )
!= SV31 )
| ~ ( in @ SV56 @ SV5 )
| ( SV59
!= ( singleton @ SV56 ) ) )
= $true )
| ( ( SV42 = SV31 )
= $false )
| ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(458,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( sK9_E @ SV32 @ SV22 @ SV5 )
= SV32 )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(459,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( in @ ( sK9_E @ SV32 @ SV22 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(460,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(461,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( sK8_SY54 @ SV32 @ SV22 @ SV5 )
= ( singleton @ ( sK7_J @ SV32 @ SV22 @ SV5 ) ) )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(462,plain,
! [SV40: $i,SV5: $i,SV51: $i] :
( ( ( ! [SY152: $i] :
( ( SY152 != SV51 )
| ~ ( in @ SY152 @ ( cartesian_product2 @ SV5 @ SV40 ) ) ) )
= $true )
| ( ( ! [SY153: $i,SY154: $i] :
( ( ( ordered_pair @ SY153 @ SY154 )
!= SV51 )
| ~ ( in @ SY153 @ SV5 )
| ( SY154
!= ( singleton @ SY153 ) ) ) )
= $true )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(463,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 )
| ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(464,plain,
! [SV41: $i,SV5: $i,SV53: $i] :
( ( ( ! [SY155: $i] :
( ( SY155 != SV53 )
| ~ ( in @ SY155 @ ( cartesian_product2 @ SV5 @ SV41 ) ) ) )
= $true )
| ( ( ! [SY156: $i,SY157: $i] :
( ( ( ordered_pair @ SY156 @ SY157 )
!= SV53 )
| ~ ( in @ SY156 @ SV5 )
| ( SY157
!= ( singleton @ SY156 ) ) ) )
= $true )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(465,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 )
| ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(466,plain,
! [SV29: $i,SV5: $i,SV43: $i,SV55: $i] :
( ( ( SV55 = SV43 )
= $false )
| ( ( ~ ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
= $true )
| ( ( ! [SY148: $i,SY149: $i] :
( ( ( ordered_pair @ SY148 @ SY149 )
!= SV43 )
| ~ ( in @ SY148 @ SV5 )
| ( SY149
!= ( singleton @ SY148 ) ) ) )
= $true )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(467,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 )
| ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) ) )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(468,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(469,plain,
! [SV19: $i,SV33: $i,SV5: $i,SV25: $i,SV49: $i,SV47: $i] :
( ( ( ( ordered_pair @ SV47 @ SV49 )
= SV25 )
= $false )
| ( ( ~ ( in @ SV47 @ SV5 ) )
= $true )
| ( ( ( SV49
!= ( singleton @ SV47 ) ) )
= $true )
| ( ( SV33 = SV25 )
= $false )
| ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(470,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ ( sK8_SY54 @ SV26 @ SV19 @ SV5 ) )
= SV26 )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(471,plain,
! [SV5: $i,SV19: $i,SV26: $i] :
( ( ( in @ ( sK7_J @ SV26 @ SV19 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV26 @ ( sK6_C @ SV19 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(472,plain,
! [SV23: $i,SV45: $i,SV5: $i,SV34: $i,SV60: $i,SV57: $i] :
( ( ( ( ( ordered_pair @ SV57 @ SV60 )
!= SV34 )
| ~ ( in @ SV57 @ SV5 )
| ( SV60
!= ( singleton @ SV57 ) ) )
= $true )
| ( ( SV45 = SV34 )
= $false )
| ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(473,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( sK9_E @ SV35 @ SV23 @ SV5 )
= SV35 )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(474,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( in @ ( sK9_E @ SV35 @ SV23 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(475,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(476,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( sK8_SY54 @ SV35 @ SV23 @ SV5 )
= ( singleton @ ( sK7_J @ SV35 @ SV23 @ SV5 ) ) )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(477,plain,
! [SV24: $i,SV46: $i,SV5: $i,SV36: $i,SV61: $i,SV58: $i] :
( ( ( ( ( ordered_pair @ SV58 @ SV61 )
!= SV36 )
| ~ ( in @ SV58 @ SV5 )
| ( SV61
!= ( singleton @ SV58 ) ) )
= $true )
| ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(478,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( sK9_E @ SV37 @ SV24 @ SV5 )
= SV37 )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(479,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( in @ ( sK9_E @ SV37 @ SV24 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(480,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(481,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( sK8_SY54 @ SV37 @ SV24 @ SV5 )
= ( singleton @ ( sK7_J @ SV37 @ SV24 @ SV5 ) ) )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(482,plain,
! [SV20: $i,SV38: $i,SV5: $i,SV27: $i,SV50: $i,SV48: $i] :
( ( ( ( ordered_pair @ SV48 @ SV50 )
= SV27 )
= $false )
| ( ( ~ ( in @ SV48 @ SV5 ) )
= $true )
| ( ( ( SV50
!= ( singleton @ SV48 ) ) )
= $true )
| ( ( SV38 = SV27 )
= $false )
| ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(483,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ ( sK8_SY54 @ SV28 @ SV20 @ SV5 ) )
= SV28 )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(484,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( in @ ( sK7_J @ SV28 @ SV20 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV28 @ ( sK6_C @ SV20 @ SV5 ) )
= $false )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(485,plain,
! [SV22: $i,SV42: $i,SV5: $i,SV31: $i,SV59: $i,SV56: $i] :
( ( ( ( ( ordered_pair @ SV56 @ SV59 )
!= SV31 )
| ~ ( in @ SV56 @ SV5 ) )
= $true )
| ( ( ( SV59
!= ( singleton @ SV56 ) ) )
= $true )
| ( ( SV42 = SV31 )
= $false )
| ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(486,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 )
| ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(487,plain,
! [SV40: $i,SV5: $i,SV51: $i,SV62: $i] :
( ( ( ( SV62 != SV51 )
| ~ ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
= $true )
| ( ( ! [SY153: $i,SY154: $i] :
( ( ( ordered_pair @ SY153 @ SY154 )
!= SV51 )
| ~ ( in @ SY153 @ SV5 )
| ( SY154
!= ( singleton @ SY153 ) ) ) )
= $true )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(488,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 )
| ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(489,plain,
! [SV41: $i,SV5: $i,SV53: $i,SV63: $i] :
( ( ( ( SV63 != SV53 )
| ~ ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
= $true )
| ( ( ! [SY156: $i,SY157: $i] :
( ( ( ordered_pair @ SY156 @ SY157 )
!= SV53 )
| ~ ( in @ SY156 @ SV5 )
| ( SY157
!= ( singleton @ SY156 ) ) ) )
= $true )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(490,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 )
| ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(491,plain,
! [SV43: $i,SV29: $i,SV5: $i,SV55: $i] :
( ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( SV55 = SV43 )
= $false )
| ( ( ! [SY148: $i,SY149: $i] :
( ( ( ordered_pair @ SY148 @ SY149 )
!= SV43 )
| ~ ( in @ SY148 @ SV5 )
| ( SY149
!= ( singleton @ SY148 ) ) ) )
= $true )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(492,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 )
| ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(493,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(494,plain,
! [SV19: $i,SV33: $i,SV25: $i,SV49: $i,SV5: $i,SV47: $i] :
( ( ( in @ SV47 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV47 @ SV49 )
= SV25 )
= $false )
| ( ( ( SV49
!= ( singleton @ SV47 ) ) )
= $true )
| ( ( SV33 = SV25 )
= $false )
| ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(495,plain,
! [SV23: $i,SV45: $i,SV5: $i,SV34: $i,SV60: $i,SV57: $i] :
( ( ( ( ( ordered_pair @ SV57 @ SV60 )
!= SV34 )
| ~ ( in @ SV57 @ SV5 ) )
= $true )
| ( ( ( SV60
!= ( singleton @ SV57 ) ) )
= $true )
| ( ( SV45 = SV34 )
= $false )
| ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(496,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 )
| ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(497,plain,
! [SV24: $i,SV46: $i,SV5: $i,SV36: $i,SV61: $i,SV58: $i] :
( ( ( ( ( ordered_pair @ SV58 @ SV61 )
!= SV36 )
| ~ ( in @ SV58 @ SV5 ) )
= $true )
| ( ( ( SV61
!= ( singleton @ SV58 ) ) )
= $true )
| ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(498,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 )
| ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(499,plain,
! [SV20: $i,SV38: $i,SV27: $i,SV50: $i,SV5: $i,SV48: $i] :
( ( ( in @ SV48 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV48 @ SV50 )
= SV27 )
= $false )
| ( ( ( SV50
!= ( singleton @ SV48 ) ) )
= $true )
| ( ( SV38 = SV27 )
= $false )
| ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(500,plain,
! [SV22: $i,SV42: $i,SV5: $i,SV31: $i,SV59: $i,SV56: $i] :
( ( ( ( ( ordered_pair @ SV56 @ SV59 )
!= SV31 ) )
= $true )
| ( ( ~ ( in @ SV56 @ SV5 ) )
= $true )
| ( ( ( SV59
!= ( singleton @ SV56 ) ) )
= $true )
| ( ( SV42 = SV31 )
= $false )
| ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(501,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
!= SV32 ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(502,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(503,plain,
! [SV40: $i,SV5: $i,SV51: $i,SV62: $i] :
( ( ( ( SV62 != SV51 ) )
= $true )
| ( ( ~ ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
= $true )
| ( ( ! [SY153: $i,SY154: $i] :
( ( ( ordered_pair @ SY153 @ SY154 )
!= SV51 )
| ~ ( in @ SY153 @ SV5 )
| ( SY154
!= ( singleton @ SY153 ) ) ) )
= $true )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(504,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 )
| ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(505,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(506,plain,
! [SV41: $i,SV5: $i,SV53: $i,SV63: $i] :
( ( ( ( SV63 != SV53 ) )
= $true )
| ( ( ~ ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
= $true )
| ( ( ! [SY156: $i,SY157: $i] :
( ( ( ordered_pair @ SY156 @ SY157 )
!= SV53 )
| ~ ( in @ SY156 @ SV5 )
| ( SY157
!= ( singleton @ SY156 ) ) ) )
= $true )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(507,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ~ ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 )
| ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(508,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(509,plain,
! [SV29: $i,SV55: $i,SV5: $i,SV43: $i,SV64: $i] :
( ( ( ! [SY161: $i] :
( ( ( ordered_pair @ SV64 @ SY161 )
!= SV43 )
| ~ ( in @ SV64 @ SV5 )
| ( SY161
!= ( singleton @ SV64 ) ) ) )
= $true )
| ( ( SV55 = SV43 )
= $false )
| ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(510,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
!= SV44 ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(511,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(512,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(513,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
!= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(514,plain,
! [SV19: $i,SV33: $i,SV5: $i,SV25: $i,SV47: $i,SV49: $i] :
( ( ( SV49
= ( singleton @ SV47 ) )
= $false )
| ( ( ( ordered_pair @ SV47 @ SV49 )
= SV25 )
= $false )
| ( ( in @ SV47 @ SV5 )
= $false )
| ( ( SV33 = SV25 )
= $false )
| ( ( in @ SV33 @ ( cartesian_product2 @ SV5 @ SV19 ) )
= $false )
| ( ( in @ SV25 @ ( sK6_C @ SV19 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(515,plain,
! [SV23: $i,SV45: $i,SV5: $i,SV34: $i,SV60: $i,SV57: $i] :
( ( ( ( ( ordered_pair @ SV57 @ SV60 )
!= SV34 ) )
= $true )
| ( ( ~ ( in @ SV57 @ SV5 ) )
= $true )
| ( ( ( SV60
!= ( singleton @ SV57 ) ) )
= $true )
| ( ( SV45 = SV34 )
= $false )
| ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(516,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
!= SV35 ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(517,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(518,plain,
! [SV24: $i,SV46: $i,SV5: $i,SV36: $i,SV61: $i,SV58: $i] :
( ( ( ( ( ordered_pair @ SV58 @ SV61 )
!= SV36 ) )
= $true )
| ( ( ~ ( in @ SV58 @ SV5 ) )
= $true )
| ( ( ( SV61
!= ( singleton @ SV58 ) ) )
= $true )
| ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(519,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
!= SV37 ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(520,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(521,plain,
! [SV20: $i,SV38: $i,SV5: $i,SV27: $i,SV48: $i,SV50: $i] :
( ( ( SV50
= ( singleton @ SV48 ) )
= $false )
| ( ( ( ordered_pair @ SV48 @ SV50 )
= SV27 )
= $false )
| ( ( in @ SV48 @ SV5 )
= $false )
| ( ( SV38 = SV27 )
= $false )
| ( ( in @ SV38 @ ( cartesian_product2 @ SV5 @ SV20 ) )
= $false )
| ( ( in @ SV27 @ ( sK6_C @ SV20 @ SV5 ) )
= $true )
| ( ( ( sK14_SY70 @ SV5 )
= ( singleton @ ( sK13_SY68 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(522,plain,
! [SV22: $i,SV42: $i,SV5: $i,SV31: $i,SV59: $i,SV56: $i] :
( ( ( ( ordered_pair @ SV56 @ SV59 )
= SV31 )
= $false )
| ( ( ~ ( in @ SV56 @ SV5 ) )
= $true )
| ( ( ( SV59
!= ( singleton @ SV56 ) ) )
= $true )
| ( ( SV42 = SV31 )
= $false )
| ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(523,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ ( sK8_SY54 @ SV32 @ SV22 @ SV5 ) )
= SV32 )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(524,plain,
! [SV5: $i,SV22: $i,SV32: $i] :
( ( ( in @ ( sK7_J @ SV32 @ SV22 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV32 @ ( sK6_C @ SV22 @ SV5 ) )
= $false )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(525,plain,
! [SV40: $i,SV5: $i,SV51: $i,SV62: $i] :
( ( ( SV62 = SV51 )
= $false )
| ( ( ~ ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
= $true )
| ( ( ! [SY153: $i,SY154: $i] :
( ( ( ordered_pair @ SY153 @ SY154 )
!= SV51 )
| ~ ( in @ SY153 @ SV5 )
| ( SY154
!= ( singleton @ SY153 ) ) ) )
= $true )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(526,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 )
| ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) ) )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(527,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(528,plain,
! [SV41: $i,SV5: $i,SV53: $i,SV63: $i] :
( ( ( SV63 = SV53 )
= $false )
| ( ( ~ ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
= $true )
| ( ( ! [SY156: $i,SY157: $i] :
( ( ( ordered_pair @ SY156 @ SY157 )
!= SV53 )
| ~ ( in @ SY156 @ SV5 )
| ( SY157
!= ( singleton @ SY156 ) ) ) )
= $true )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(529,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 )
| ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) ) )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(530,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) ) )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(531,plain,
! [SV29: $i,SV55: $i,SV5: $i,SV43: $i,SV65: $i,SV64: $i] :
( ( ( ( ( ordered_pair @ SV64 @ SV65 )
!= SV43 )
| ~ ( in @ SV64 @ SV5 )
| ( SV65
!= ( singleton @ SV64 ) ) )
= $true )
| ( ( SV55 = SV43 )
= $false )
| ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(532,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( sK9_E @ SV44 @ SV29 @ SV5 )
= SV44 )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(533,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( in @ ( sK9_E @ SV44 @ SV29 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(534,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(535,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( sK8_SY54 @ SV44 @ SV29 @ SV5 )
= ( singleton @ ( sK7_J @ SV44 @ SV29 @ SV5 ) ) )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(536,plain,
! [SV23: $i,SV45: $i,SV5: $i,SV34: $i,SV60: $i,SV57: $i] :
( ( ( ( ordered_pair @ SV57 @ SV60 )
= SV34 )
= $false )
| ( ( ~ ( in @ SV57 @ SV5 ) )
= $true )
| ( ( ( SV60
!= ( singleton @ SV57 ) ) )
= $true )
| ( ( SV45 = SV34 )
= $false )
| ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(537,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ ( sK8_SY54 @ SV35 @ SV23 @ SV5 ) )
= SV35 )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(538,plain,
! [SV5: $i,SV23: $i,SV35: $i] :
( ( ( in @ ( sK7_J @ SV35 @ SV23 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV35 @ ( sK6_C @ SV23 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(539,plain,
! [SV24: $i,SV46: $i,SV5: $i,SV36: $i,SV61: $i,SV58: $i] :
( ( ( ( ordered_pair @ SV58 @ SV61 )
= SV36 )
= $false )
| ( ( ~ ( in @ SV58 @ SV5 ) )
= $true )
| ( ( ( SV61
!= ( singleton @ SV58 ) ) )
= $true )
| ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(540,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ ( sK8_SY54 @ SV37 @ SV24 @ SV5 ) )
= SV37 )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(541,plain,
! [SV5: $i,SV24: $i,SV37: $i] :
( ( ( in @ ( sK7_J @ SV37 @ SV24 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV37 @ ( sK6_C @ SV24 @ SV5 ) )
= $false )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(542,plain,
! [SV22: $i,SV42: $i,SV31: $i,SV59: $i,SV5: $i,SV56: $i] :
( ( ( in @ SV56 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV56 @ SV59 )
= SV31 )
= $false )
| ( ( ( SV59
!= ( singleton @ SV56 ) ) )
= $true )
| ( ( SV42 = SV31 )
= $false )
| ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(543,plain,
! [SV51: $i,SV40: $i,SV5: $i,SV62: $i] :
( ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( SV62 = SV51 )
= $false )
| ( ( ! [SY153: $i,SY154: $i] :
( ( ( ordered_pair @ SY153 @ SY154 )
!= SV51 )
| ~ ( in @ SY153 @ SV5 )
| ( SY154
!= ( singleton @ SY153 ) ) ) )
= $true )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(544,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 )
| ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(545,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(546,plain,
! [SV53: $i,SV41: $i,SV5: $i,SV63: $i] :
( ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( SV63 = SV53 )
= $false )
| ( ( ! [SY156: $i,SY157: $i] :
( ( ( ordered_pair @ SY156 @ SY157 )
!= SV53 )
| ~ ( in @ SY156 @ SV5 )
| ( SY157
!= ( singleton @ SY156 ) ) ) )
= $true )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(547,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 )
| ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(548,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
| ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(549,plain,
! [SV29: $i,SV55: $i,SV5: $i,SV43: $i,SV65: $i,SV64: $i] :
( ( ( ( ( ordered_pair @ SV64 @ SV65 )
!= SV43 )
| ~ ( in @ SV64 @ SV5 ) )
= $true )
| ( ( ( SV65
!= ( singleton @ SV64 ) ) )
= $true )
| ( ( SV55 = SV43 )
= $false )
| ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(550,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 )
| ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(551,plain,
! [SV23: $i,SV45: $i,SV34: $i,SV60: $i,SV5: $i,SV57: $i] :
( ( ( in @ SV57 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV57 @ SV60 )
= SV34 )
= $false )
| ( ( ( SV60
!= ( singleton @ SV57 ) ) )
= $true )
| ( ( SV45 = SV34 )
= $false )
| ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(552,plain,
! [SV24: $i,SV46: $i,SV36: $i,SV61: $i,SV5: $i,SV58: $i] :
( ( ( in @ SV58 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV58 @ SV61 )
= SV36 )
= $false )
| ( ( ( SV61
!= ( singleton @ SV58 ) ) )
= $true )
| ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(553,plain,
! [SV22: $i,SV42: $i,SV5: $i,SV31: $i,SV56: $i,SV59: $i] :
( ( ( SV59
= ( singleton @ SV56 ) )
= $false )
| ( ( ( ordered_pair @ SV56 @ SV59 )
= SV31 )
= $false )
| ( ( in @ SV56 @ SV5 )
= $false )
| ( ( SV42 = SV31 )
= $false )
| ( ( in @ SV42 @ ( cartesian_product2 @ SV5 @ SV22 ) )
= $false )
| ( ( in @ SV31 @ ( sK6_C @ SV22 @ SV5 ) )
= $true )
| ( ( ( sK10_C @ SV5 )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(554,plain,
! [SV40: $i,SV62: $i,SV5: $i,SV51: $i,SV66: $i] :
( ( ( ! [SY162: $i] :
( ( ( ordered_pair @ SV66 @ SY162 )
!= SV51 )
| ~ ( in @ SV66 @ SV5 )
| ( SY162
!= ( singleton @ SV66 ) ) ) )
= $true )
| ( ( SV62 = SV51 )
= $false )
| ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(555,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
!= SV52 ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(556,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(557,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(558,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
!= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(559,plain,
! [SV41: $i,SV63: $i,SV5: $i,SV53: $i,SV67: $i] :
( ( ( ! [SY163: $i] :
( ( ( ordered_pair @ SV67 @ SY163 )
!= SV53 )
| ~ ( in @ SV67 @ SV5 )
| ( SY163
!= ( singleton @ SV67 ) ) ) )
= $true )
| ( ( SV63 = SV53 )
= $false )
| ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(560,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
!= SV54 ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(561,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[547]) ).
thf(562,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(563,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
!= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(564,plain,
! [SV29: $i,SV55: $i,SV5: $i,SV43: $i,SV65: $i,SV64: $i] :
( ( ( ( ( ordered_pair @ SV64 @ SV65 )
!= SV43 ) )
= $true )
| ( ( ~ ( in @ SV64 @ SV5 ) )
= $true )
| ( ( ( SV65
!= ( singleton @ SV64 ) ) )
= $true )
| ( ( SV55 = SV43 )
= $false )
| ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(565,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
!= SV44 ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(566,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(567,plain,
! [SV23: $i,SV45: $i,SV5: $i,SV34: $i,SV57: $i,SV60: $i] :
( ( ( SV60
= ( singleton @ SV57 ) )
= $false )
| ( ( ( ordered_pair @ SV57 @ SV60 )
= SV34 )
= $false )
| ( ( in @ SV57 @ SV5 )
= $false )
| ( ( SV45 = SV34 )
= $false )
| ( ( in @ SV45 @ ( cartesian_product2 @ SV5 @ SV23 ) )
= $false )
| ( ( in @ SV34 @ ( sK6_C @ SV23 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK13_SY68 @ SV5 ) @ ( sK14_SY70 @ SV5 ) )
= ( sK12_SY61 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(568,plain,
! [SV24: $i,SV46: $i,SV5: $i,SV36: $i,SV58: $i,SV61: $i] :
( ( ( SV61
= ( singleton @ SV58 ) )
= $false )
| ( ( ( ordered_pair @ SV58 @ SV61 )
= SV36 )
= $false )
| ( ( in @ SV58 @ SV5 )
= $false )
| ( ( SV46 = SV36 )
= $false )
| ( ( in @ SV46 @ ( cartesian_product2 @ SV5 @ SV24 ) )
= $false )
| ( ( in @ SV36 @ ( sK6_C @ SV24 @ SV5 ) )
= $true )
| ( ( in @ ( sK13_SY68 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(569,plain,
! [SV40: $i,SV62: $i,SV5: $i,SV51: $i,SV68: $i,SV66: $i] :
( ( ( ( ( ordered_pair @ SV66 @ SV68 )
!= SV51 )
| ~ ( in @ SV66 @ SV5 )
| ( SV68
!= ( singleton @ SV66 ) ) )
= $true )
| ( ( SV62 = SV51 )
= $false )
| ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(570,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( sK9_E @ SV52 @ SV40 @ SV5 )
= SV52 )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(571,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( in @ ( sK9_E @ SV52 @ SV40 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(572,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(573,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( sK8_SY54 @ SV52 @ SV40 @ SV5 )
= ( singleton @ ( sK7_J @ SV52 @ SV40 @ SV5 ) ) )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(574,plain,
! [SV41: $i,SV63: $i,SV5: $i,SV53: $i,SV69: $i,SV67: $i] :
( ( ( ( ( ordered_pair @ SV67 @ SV69 )
!= SV53 )
| ~ ( in @ SV67 @ SV5 )
| ( SV69
!= ( singleton @ SV67 ) ) )
= $true )
| ( ( SV63 = SV53 )
= $false )
| ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(575,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( sK9_E @ SV54 @ SV41 @ SV5 )
= SV54 )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(576,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( in @ ( sK9_E @ SV54 @ SV41 @ SV5 ) @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(577,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(578,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( sK8_SY54 @ SV54 @ SV41 @ SV5 )
= ( singleton @ ( sK7_J @ SV54 @ SV41 @ SV5 ) ) )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(579,plain,
! [SV29: $i,SV55: $i,SV5: $i,SV43: $i,SV65: $i,SV64: $i] :
( ( ( ( ordered_pair @ SV64 @ SV65 )
= SV43 )
= $false )
| ( ( ~ ( in @ SV64 @ SV5 ) )
= $true )
| ( ( ( SV65
!= ( singleton @ SV64 ) ) )
= $true )
| ( ( SV55 = SV43 )
= $false )
| ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(580,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ ( sK8_SY54 @ SV44 @ SV29 @ SV5 ) )
= SV44 )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(581,plain,
! [SV5: $i,SV29: $i,SV44: $i] :
( ( ( in @ ( sK7_J @ SV44 @ SV29 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV44 @ ( sK6_C @ SV29 @ SV5 ) )
= $false )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(582,plain,
! [SV40: $i,SV62: $i,SV5: $i,SV51: $i,SV68: $i,SV66: $i] :
( ( ( ( ( ordered_pair @ SV66 @ SV68 )
!= SV51 )
| ~ ( in @ SV66 @ SV5 ) )
= $true )
| ( ( ( SV68
!= ( singleton @ SV66 ) ) )
= $true )
| ( ( SV62 = SV51 )
= $false )
| ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(583,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 )
| ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(584,plain,
! [SV41: $i,SV63: $i,SV5: $i,SV53: $i,SV69: $i,SV67: $i] :
( ( ( ( ( ordered_pair @ SV67 @ SV69 )
!= SV53 )
| ~ ( in @ SV67 @ SV5 ) )
= $true )
| ( ( ( SV69
!= ( singleton @ SV67 ) ) )
= $true )
| ( ( SV63 = SV53 )
= $false )
| ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(585,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 )
| ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(586,plain,
! [SV29: $i,SV55: $i,SV43: $i,SV65: $i,SV5: $i,SV64: $i] :
( ( ( in @ SV64 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV64 @ SV65 )
= SV43 )
= $false )
| ( ( ( SV65
!= ( singleton @ SV64 ) ) )
= $true )
| ( ( SV55 = SV43 )
= $false )
| ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(587,plain,
! [SV40: $i,SV62: $i,SV5: $i,SV51: $i,SV68: $i,SV66: $i] :
( ( ( ( ( ordered_pair @ SV66 @ SV68 )
!= SV51 ) )
= $true )
| ( ( ~ ( in @ SV66 @ SV5 ) )
= $true )
| ( ( ( SV68
!= ( singleton @ SV66 ) ) )
= $true )
| ( ( SV62 = SV51 )
= $false )
| ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(588,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
!= SV52 ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(589,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(590,plain,
! [SV41: $i,SV63: $i,SV5: $i,SV53: $i,SV69: $i,SV67: $i] :
( ( ( ( ( ordered_pair @ SV67 @ SV69 )
!= SV53 ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV5 ) )
= $true )
| ( ( ( SV69
!= ( singleton @ SV67 ) ) )
= $true )
| ( ( SV63 = SV53 )
= $false )
| ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(591,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
!= SV54 ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(592,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ~ ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(593,plain,
! [SV29: $i,SV55: $i,SV5: $i,SV43: $i,SV64: $i,SV65: $i] :
( ( ( SV65
= ( singleton @ SV64 ) )
= $false )
| ( ( ( ordered_pair @ SV64 @ SV65 )
= SV43 )
= $false )
| ( ( in @ SV64 @ SV5 )
= $false )
| ( ( SV55 = SV43 )
= $false )
| ( ( in @ SV55 @ ( cartesian_product2 @ SV5 @ SV29 ) )
= $false )
| ( ( in @ SV43 @ ( sK6_C @ SV29 @ SV5 ) )
= $true )
| ( ( ( sK16_SY71 @ SV5 )
= ( singleton @ ( sK15_SY62 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(594,plain,
! [SV40: $i,SV62: $i,SV5: $i,SV51: $i,SV68: $i,SV66: $i] :
( ( ( ( ordered_pair @ SV66 @ SV68 )
= SV51 )
= $false )
| ( ( ~ ( in @ SV66 @ SV5 ) )
= $true )
| ( ( ( SV68
!= ( singleton @ SV66 ) ) )
= $true )
| ( ( SV62 = SV51 )
= $false )
| ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(595,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ ( sK8_SY54 @ SV52 @ SV40 @ SV5 ) )
= SV52 )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(596,plain,
! [SV5: $i,SV40: $i,SV52: $i] :
( ( ( in @ ( sK7_J @ SV52 @ SV40 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV52 @ ( sK6_C @ SV40 @ SV5 ) )
= $false )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(597,plain,
! [SV41: $i,SV63: $i,SV5: $i,SV53: $i,SV69: $i,SV67: $i] :
( ( ( ( ordered_pair @ SV67 @ SV69 )
= SV53 )
= $false )
| ( ( ~ ( in @ SV67 @ SV5 ) )
= $true )
| ( ( ( SV69
!= ( singleton @ SV67 ) ) )
= $true )
| ( ( SV63 = SV53 )
= $false )
| ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(598,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( ( ordered_pair @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ ( sK8_SY54 @ SV54 @ SV41 @ SV5 ) )
= SV54 )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(599,plain,
! [SV5: $i,SV41: $i,SV54: $i] :
( ( ( in @ ( sK7_J @ SV54 @ SV41 @ SV5 ) @ SV5 )
= $true )
| ( ( in @ SV54 @ ( sK6_C @ SV41 @ SV5 ) )
= $false )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(600,plain,
! [SV40: $i,SV62: $i,SV51: $i,SV68: $i,SV5: $i,SV66: $i] :
( ( ( in @ SV66 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV66 @ SV68 )
= SV51 )
= $false )
| ( ( ( SV68
!= ( singleton @ SV66 ) ) )
= $true )
| ( ( SV62 = SV51 )
= $false )
| ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(601,plain,
! [SV41: $i,SV63: $i,SV53: $i,SV69: $i,SV5: $i,SV67: $i] :
( ( ( in @ SV67 @ SV5 )
= $false )
| ( ( ( ordered_pair @ SV67 @ SV69 )
= SV53 )
= $false )
| ( ( ( SV69
!= ( singleton @ SV67 ) ) )
= $true )
| ( ( SV63 = SV53 )
= $false )
| ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(602,plain,
! [SV40: $i,SV62: $i,SV5: $i,SV51: $i,SV66: $i,SV68: $i] :
( ( ( SV68
= ( singleton @ SV66 ) )
= $false )
| ( ( ( ordered_pair @ SV66 @ SV68 )
= SV51 )
= $false )
| ( ( in @ SV66 @ SV5 )
= $false )
| ( ( SV62 = SV51 )
= $false )
| ( ( in @ SV62 @ ( cartesian_product2 @ SV5 @ SV40 ) )
= $false )
| ( ( in @ SV51 @ ( sK6_C @ SV40 @ SV5 ) )
= $true )
| ( ( ( ordered_pair @ ( sK15_SY62 @ SV5 ) @ ( sK16_SY71 @ SV5 ) )
= ( sK11_SY55 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(603,plain,
! [SV41: $i,SV63: $i,SV5: $i,SV53: $i,SV67: $i,SV69: $i] :
( ( ( SV69
= ( singleton @ SV67 ) )
= $false )
| ( ( ( ordered_pair @ SV67 @ SV69 )
= SV53 )
= $false )
| ( ( in @ SV67 @ SV5 )
= $false )
| ( ( SV63 = SV53 )
= $false )
| ( ( in @ SV63 @ ( cartesian_product2 @ SV5 @ SV41 ) )
= $false )
| ( ( in @ SV53 @ ( sK6_C @ SV41 @ SV5 ) )
= $true )
| ( ( in @ ( sK15_SY62 @ SV5 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(604,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,603,602,599,598,596,595,593,581,580,578,576,575,573,571,570,568,567,553,541,540,538,537,535,533,532,524,523,521,514,484,483,481,479,478,476,474,473,471,470,461,459,458,409,408,406,405,397,395,394,357,356,301,299,298,239,227,226,195,186,176,168,167,164,147,140,139,138,137,136,120,119,106,101,95,93,69,57,56,55]) ).
thf(605,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 02:54:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 14
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:16,loop_count:0,foatp_calls:0,translation:fof_full).............................
% 26.55/26.77
% 26.55/26.77 ********************************
% 26.55/26.77 * All subproblems solved! *
% 26.55/26.77 ********************************
% 26.55/26.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:604,loop_count:0,foatp_calls:1,translation:fof_full)
% 26.77/27.03
% 26.77/27.03 %**** Beginning of derivation protocol ****
% 26.77/27.03 % SZS output start CNFRefutation
% See solution above
% 26.77/27.03
% 26.77/27.03 %**** End of derivation protocol ****
% 26.77/27.03 %**** no. of clauses in derivation: 605 ****
% 26.77/27.03 %**** clause counter: 604 ****
% 26.77/27.03
% 26.77/27.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:604,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------