%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU181+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:18 AM UTC 2026
% Result : Theorem 21.05s 3.87s
% Output : CNFRefutation 21.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 411 ( 106 unt; 0 typ; 0 def)
% Number of atoms : 4326 (1553 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 8988 (1900 ~;1516 |; 9 &;5511 @)
% ( 24 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 6 con; 0-3 aty)
% Number of variables : 1329 ( 0 ^;1317 !; 12 ?;1329 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_SY58,type,
sK10_SY58: $i > $i > $i ).
thf(tp_sK11_SY54,type,
sK11_SY54: $i > $i > $i > $i ).
thf(tp_sK12_SY58,type,
sK12_SY58: $i > $i > $i > $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i ).
thf(tp_sK14_SY83,type,
sK14_SY83: $i > $i > $i ).
thf(tp_sK15_SY89,type,
sK15_SY89: $i > $i > $i ).
thf(tp_sK16_SY94,type,
sK16_SY94: $i > $i > $i ).
thf(tp_sK17_SY105,type,
sK17_SY105: $i > $i > $i ).
thf(tp_sK18_SY96,type,
sK18_SY96: $i > $i > $i > $i ).
thf(tp_sK19_SY100,type,
sK19_SY100: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY99,type,
sK20_SY99: $i > $i > $i ).
thf(tp_sK21_SY103,type,
sK21_SY103: $i > $i > $i ).
thf(tp_sK22_SY99,type,
sK22_SY99: $i > $i > $i > $i ).
thf(tp_sK23_SY103,type,
sK23_SY103: $i > $i > $i > $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i > $i > $i ).
thf(tp_sK4_SY48,type,
sK4_SY48: $i > $i > $i ).
thf(tp_sK5_SY43,type,
sK5_SY43: $i > $i > $i ).
thf(tp_sK6_SY60,type,
sK6_SY60: $i > $i > $i ).
thf(tp_sK7_SY51,type,
sK7_SY51: $i > $i > $i > $i ).
thf(tp_sK8_SY55,type,
sK8_SY55: $i > $i > $i > $i ).
thf(tp_sK9_SY54,type,
sK9_SY54: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(14,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(15,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(24,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(31,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(34,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(39,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(40,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[39]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[40]) ).
thf(42,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(50,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(52,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(56,plain,
( ( ( relation @ sK1_A )
=> ( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( relation_inverse @ sK1_A ) ) )
& ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( relation_inverse @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(57,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(58,plain,
( ( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( relation_inverse @ sK1_A ) ) )
& ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( relation_inverse @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(59,plain,
( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( relation_inverse @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[58]) ).
thf(60,plain,
( ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( relation_inverse @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[58]) ).
thf(61,plain,
( ( ( relation_rng @ sK1_A )
!= ( relation_dom @ ( relation_inverse @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(62,plain,
( ( ( relation_dom @ sK1_A )
!= ( relation_rng @ ( relation_inverse @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[60]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(66,plain,
$true = $true,
inference(copy,[status(thm)],[52]) ).
thf(67,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(68,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(69,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(70,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(71,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(73,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(74,plain,
$true = $true,
inference(copy,[status(thm)],[44]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(76,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(77,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(78,plain,
( ( ( relation_rng @ sK1_A )
!= ( relation_dom @ ( relation_inverse @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(81,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX1
!= ( relation_inverse @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(85,plain,
( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( relation_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV1: $i] :
( ( ~ ( relation @ SV1 )
| ! [SY16: $i] :
~ ( ~ ( ( SY16
!= ( relation_rng @ SV1 ) )
| ! [SY17: $i] :
~ ( ~ ( ~ ( in @ SY17 @ SY16 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY17 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY17 ) @ SV1 )
| ( in @ SY17 @ SY16 ) ) ) )
| ~ ( ~ ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SY16 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY20 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY20 ) @ SV1 )
| ( in @ SY20 @ SY16 ) ) )
| ( SY16
= ( relation_rng @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV2: $i] :
( ( ~ ( relation @ SV2 )
| ( relation @ ( relation_inverse @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV3: $i] :
( ( ~ ( relation @ SV3 )
| ! [SY23: $i] :
( ~ ( relation @ SY23 )
| ~ ( ~ ( ( SY23
!= ( relation_inverse @ SV3 ) )
| ! [SY24: $i,SY25: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY24 @ SY25 ) @ SY23 )
| ( in @ ( ordered_pair @ SY25 @ SY24 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY25 @ SY24 ) @ SV3 )
| ( in @ ( ordered_pair @ SY24 @ SY25 ) @ SY23 ) ) ) )
| ~ ( ~ ! [SY26: $i,SY27: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY26 @ SY27 ) @ SY23 )
| ( in @ ( ordered_pair @ SY27 @ SY26 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY27 @ SY26 ) @ SV3 )
| ( in @ ( ordered_pair @ SY26 @ SY27 ) @ SY23 ) ) )
| ( SY23
= ( relation_inverse @ SV3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV4: $i] :
( ( ~ ( relation @ SV4 )
| ( ( relation_inverse @ ( relation_inverse @ SV4 ) )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV5 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV5 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV5 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV1: $i] :
( ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( ! [SY16: $i] :
~ ( ~ ( ( SY16
!= ( relation_rng @ SV1 ) )
| ! [SY17: $i] :
~ ( ~ ( ~ ( in @ SY17 @ SY16 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY17 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY17 ) @ SV1 )
| ( in @ SY17 @ SY16 ) ) ) )
| ~ ( ~ ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SY16 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY20 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY20 ) @ SV1 )
| ( in @ SY20 @ SY16 ) ) )
| ( SY16
= ( relation_rng @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV3: $i] :
( ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( relation @ SY23 )
| ~ ( ~ ( ( SY23
!= ( relation_inverse @ SV3 ) )
| ! [SY24: $i,SY25: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY24 @ SY25 ) @ SY23 )
| ( in @ ( ordered_pair @ SY25 @ SY24 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY25 @ SY24 ) @ SV3 )
| ( in @ ( ordered_pair @ SY24 @ SY25 ) @ SY23 ) ) ) )
| ~ ( ~ ! [SY26: $i,SY27: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY26 @ SY27 ) @ SY23 )
| ( in @ ( ordered_pair @ SY27 @ SY26 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY27 @ SY26 ) @ SV3 )
| ( in @ ( ordered_pair @ SY26 @ SY27 ) @ SY23 ) ) )
| ( SY23
= ( relation_inverse @ SV3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV4 ) )
= SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV5 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV5 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV5 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(97,plain,
( ( ~ ~ ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(98,plain,
! [SV1: $i] :
( ( ( relation @ SV1 )
= $false )
| ( ( ! [SY16: $i] :
~ ( ~ ( ( SY16
!= ( relation_rng @ SV1 ) )
| ! [SY17: $i] :
~ ( ~ ( ~ ( in @ SY17 @ SY16 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY17 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY17 ) @ SV1 )
| ( in @ SY17 @ SY16 ) ) ) )
| ~ ( ~ ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SY16 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY20 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY20 ) @ SV1 )
| ( in @ SY20 @ SY16 ) ) )
| ( SY16
= ( relation_rng @ SV1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(99,plain,
! [SV2: $i] :
( ( ( relation @ SV2 )
= $false )
| ( ( relation @ ( relation_inverse @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( relation @ SY23 )
| ~ ( ~ ( ( SY23
!= ( relation_inverse @ SV3 ) )
| ! [SY24: $i,SY25: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY24 @ SY25 ) @ SY23 )
| ( in @ ( ordered_pair @ SY25 @ SY24 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY25 @ SY24 ) @ SV3 )
| ( in @ ( ordered_pair @ SY24 @ SY25 ) @ SY23 ) ) ) )
| ~ ( ~ ! [SY26: $i,SY27: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY26 @ SY27 ) @ SY23 )
| ( in @ ( ordered_pair @ SY27 @ SY26 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY27 @ SY26 ) @ SV3 )
| ( in @ ( ordered_pair @ SY26 @ SY27 ) @ SY23 ) ) )
| ( SY23
= ( relation_inverse @ SV3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV4 ) )
= SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV5 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV5 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV5 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(103,plain,
( ( ~ ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ( ~ ( ( SV6
!= ( relation_rng @ SV1 ) )
| ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV6 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY35 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY35 ) @ SV1 )
| ( in @ SY35 @ SV6 ) ) ) )
| ~ ( ~ ! [SY38: $i] :
~ ( ~ ( ~ ( in @ SY38 @ SV6 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY38 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY38 ) @ SV1 )
| ( in @ SY38 @ SV6 ) ) )
| ( SV6
= ( relation_rng @ SV1 ) ) ) ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( relation @ SV7 )
| ~ ( ~ ( ( SV7
!= ( relation_inverse @ SV3 ) )
| ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) )
| ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) )
| ( SV7
= ( relation_inverse @ SV3 ) ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV5: $i,SV8: $i] :
( ( ( ~ ( ~ ( ( SV8
!= ( relation_dom @ SV5 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV8 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY31 ) @ SV5 )
| ( in @ SY45 @ SV8 ) ) ) )
| ~ ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SV8 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY34 ) @ SV5 )
| ( in @ SY48 @ SV8 ) ) )
| ( SV8
= ( relation_dom @ SV5 ) ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(107,plain,
( ( ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ( ( SV6
!= ( relation_rng @ SV1 ) )
| ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV6 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY35 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY35 ) @ SV1 )
| ( in @ SY35 @ SV6 ) ) ) )
| ~ ( ~ ! [SY38: $i] :
~ ( ~ ( ~ ( in @ SY38 @ SV6 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY38 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY38 ) @ SV1 )
| ( in @ SY38 @ SV6 ) ) )
| ( SV6
= ( relation_rng @ SV1 ) ) ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( ( SV7
!= ( relation_inverse @ SV3 ) )
| ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) )
| ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) )
| ( SV7
= ( relation_inverse @ SV3 ) ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV5: $i,SV8: $i] :
( ( ( ~ ( ( SV8
!= ( relation_dom @ SV5 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV8 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY31 ) @ SV5 )
| ( in @ SY45 @ SV8 ) ) ) )
| ~ ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SV8 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY34 ) @ SV5 )
| ( in @ SY48 @ SV8 ) ) )
| ( SV8
= ( relation_dom @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(112,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(113,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ( ( SV6
!= ( relation_rng @ SV1 ) )
| ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV6 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY35 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY35 ) @ SV1 )
| ( in @ SY35 @ SV6 ) ) ) ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(114,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ( ~ ! [SY38: $i] :
~ ( ~ ( ~ ( in @ SY38 @ SV6 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY38 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY38 ) @ SV1 )
| ( in @ SY38 @ SV6 ) ) )
| ( SV6
= ( relation_rng @ SV1 ) ) ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(115,plain,
! [SV3: $i,SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ~ ( ~ ( ( SV7
!= ( relation_inverse @ SV3 ) )
| ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) )
| ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) )
| ( SV7
= ( relation_inverse @ SV3 ) ) ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(116,plain,
! [SV5: $i,SV8: $i] :
( ( ( ~ ( ( SV8
!= ( relation_dom @ SV5 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV8 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY31 ) @ SV5 )
| ( in @ SY45 @ SV8 ) ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(117,plain,
! [SV5: $i,SV8: $i] :
( ( ( ~ ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SV8 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY34 ) @ SV5 )
| ( in @ SY48 @ SV8 ) ) )
| ( SV8
= ( relation_dom @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(118,plain,
( ( empty @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(119,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(120,plain,
! [SV1: $i,SV6: $i] :
( ( ( ( SV6
!= ( relation_rng @ SV1 ) )
| ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV6 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY35 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY35 ) @ SV1 )
| ( in @ SY35 @ SV6 ) ) ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(121,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ! [SY38: $i] :
~ ( ~ ( ~ ( in @ SY38 @ SV6 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY38 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY38 ) @ SV1 )
| ( in @ SY38 @ SV6 ) ) )
| ( SV6
= ( relation_rng @ SV1 ) ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( ( SV7
!= ( relation_inverse @ SV3 ) )
| ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) )
| ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) )
| ( SV7
= ( relation_inverse @ SV3 ) ) ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV5: $i,SV8: $i] :
( ( ( ( SV8
!= ( relation_dom @ SV5 ) )
| ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV8 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY31 ) @ SV5 )
| ( in @ SY45 @ SV8 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(124,plain,
! [SV5: $i,SV8: $i] :
( ( ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SV8 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY34 ) @ SV5 )
| ( in @ SY48 @ SV8 ) ) )
| ( SV8
= ( relation_dom @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(125,plain,
! [SV1: $i,SV6: $i] :
( ( ( SV6
!= ( relation_rng @ SV1 ) )
= $true )
| ( ( ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV6 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY35 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY35 ) @ SV1 )
| ( in @ SY35 @ SV6 ) ) ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ! [SY38: $i] :
~ ( ~ ( ~ ( in @ SY38 @ SV6 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY38 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY38 ) @ SV1 )
| ( in @ SY38 @ SV6 ) ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(127,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( ( SV7
!= ( relation_inverse @ SV3 ) )
| ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(128,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( ~ ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) )
| ( SV7
= ( relation_inverse @ SV3 ) ) ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV5: $i,SV8: $i] :
( ( ( SV8
!= ( relation_dom @ SV5 ) )
= $true )
| ( ( ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV8 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY31 ) @ SV5 )
| ( in @ SY45 @ SV8 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV5: $i,SV8: $i] :
( ( ( ~ ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SV8 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY34 ) @ SV5 )
| ( in @ SY48 @ SV8 ) ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV1: $i,SV6: $i] :
( ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( ! [SY35: $i] :
~ ( ~ ( ~ ( in @ SY35 @ SV6 )
| ~ ! [SY18: $i] :
~ ( in @ ( ordered_pair @ SY18 @ SY35 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY19: $i] :
~ ( in @ ( ordered_pair @ SY19 @ SY35 ) @ SV1 )
| ( in @ SY35 @ SV6 ) ) ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV1: $i,SV6: $i] :
( ( ( ! [SY38: $i] :
~ ( ~ ( ~ ( in @ SY38 @ SV6 )
| ~ ! [SY21: $i] :
~ ( in @ ( ordered_pair @ SY21 @ SY38 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY22: $i] :
~ ( in @ ( ordered_pair @ SY22 @ SY38 ) @ SV1 )
| ( in @ SY38 @ SV6 ) ) ) )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV3: $i,SV7: $i] :
( ( ( ( SV7
!= ( relation_inverse @ SV3 ) )
| ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(134,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) )
| ( SV7
= ( relation_inverse @ SV3 ) ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(135,plain,
! [SV5: $i,SV8: $i] :
( ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV8 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY30 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY31 ) @ SV5 )
| ( in @ SY45 @ SV8 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV5: $i,SV8: $i] :
( ( ( ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SY48 @ SV8 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY33 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY48 @ SY34 ) @ SV5 )
| ( in @ SY48 @ SV8 ) ) ) )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV1: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV9 @ SV6 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ SY51 @ SV9 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ SY52 @ SV9 ) @ SV1 )
| ( in @ SV9 @ SV6 ) ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
| ~ ! [SY53: $i] :
~ ( in @ ( ordered_pair @ SY53 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) ) )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[132]) ).
thf(139,plain,
! [SV3: $i,SV7: $i] :
( ( ( SV7
!= ( relation_inverse @ SV3 ) )
= $true )
| ( ( ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV10 @ SV8 )
| ~ ! [SY55: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY55 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY56: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY56 ) @ SV5 )
| ( in @ SV10 @ SV8 ) ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
| ~ ! [SY57: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY57 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) ) )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[136]) ).
thf(143,plain,
! [SV1: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV6 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ SY51 @ SV9 ) @ SV1 ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ SY52 @ SV9 ) @ SV1 )
| ( in @ SV9 @ SV6 ) ) )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(144,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
| ~ ! [SY53: $i] :
~ ( in @ ( ordered_pair @ SY53 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
| ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(145,plain,
! [SV3: $i,SV7: $i] :
( ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 )
| ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY42 @ SY41 ) @ SV3 )
| ( in @ ( ordered_pair @ SY41 @ SY42 ) @ SV7 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(146,plain,
! [SV3: $i,SV7: $i] :
( ( ( ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 )
| ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY44 @ SY43 ) @ SV3 )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV8 )
| ~ ! [SY55: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY55 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY56: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY56 ) @ SV5 )
| ( in @ SV10 @ SV8 ) ) )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
| ~ ! [SY57: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY57 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(149,plain,
! [SV1: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV6 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ SY51 @ SV9 ) @ SV1 ) ) )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(150,plain,
! [SV6: $i,SV1: $i,SV9: $i] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ SY52 @ SV9 ) @ SV1 )
| ( in @ SV9 @ SV6 ) ) )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
| ~ ! [SY53: $i] :
~ ( in @ ( ordered_pair @ SY53 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV3: $i,SV7: $i,SV11: $i] :
( ( ( ! [SY59: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SY59 ) @ SV7 )
| ( in @ ( ordered_pair @ SY59 @ SV11 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY59 @ SV11 ) @ SV3 )
| ( in @ ( ordered_pair @ SV11 @ SY59 ) @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV7: $i,SV3: $i] :
( ( ( ! [SY60: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ SY60 ) @ SV7 )
| ( in @ ( ordered_pair @ SY60 @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY60 @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ SY60 ) @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[146]) ).
thf(154,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV8 )
| ~ ! [SY55: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY55 ) @ SV5 ) ) )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV8: $i,SV5: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ! [SY56: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY56 ) @ SV5 )
| ( in @ SV10 @ SV8 ) ) )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
| ~ ! [SY57: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY57 ) @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(157,plain,
! [SV1: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV6 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ SY51 @ SV9 ) @ SV1 ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(158,plain,
! [SV6: $i,SV1: $i,SV9: $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ SY52 @ SV9 ) @ SV1 )
| ( in @ SV9 @ SV6 ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(159,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
| ~ ! [SY53: $i] :
~ ( in @ ( ordered_pair @ SY53 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV3: $i,SV7: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 )
| ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 )
| ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
| ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(162,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV8 )
| ~ ! [SY55: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY55 ) @ SV5 ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV8: $i,SV5: $i,SV10: $i] :
( ( ( ~ ~ ! [SY56: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY56 ) @ SV5 )
| ( in @ SV10 @ SV8 ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(164,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
| ~ ! [SY57: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY57 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV1: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV6 ) )
= $true )
| ( ( ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ SY51 @ SV9 ) @ SV1 ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(166,plain,
! [SV6: $i,SV1: $i,SV9: $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ SY52 @ SV9 ) @ SV1 ) )
= $true )
| ( ( in @ SV9 @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(168,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ! [SY53: $i] :
~ ( in @ ( ordered_pair @ SY53 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(169,plain,
! [SV3: $i,SV7: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 )
| ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 )
| ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 ) ) )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
| ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(171,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV8 ) )
= $true )
| ( ( ~ ! [SY55: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY55 ) @ SV5 ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV8: $i,SV5: $i,SV10: $i] :
( ( ( ~ ~ ! [SY56: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY56 ) @ SV5 ) )
= $true )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(173,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(174,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ! [SY57: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY57 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(175,plain,
! [SV1: $i,SV6: $i,SV9: $i] :
( ( ( in @ SV9 @ SV6 )
= $false )
| ( ( ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ SY51 @ SV9 ) @ SV1 ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV6: $i,SV1: $i,SV9: $i] :
( ( ( ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ SY52 @ SV9 ) @ SV1 ) )
= $false )
| ( ( in @ SV9 @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV6: $i,SV1: $i] :
( ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV6: $i,SV1: $i] :
( ( ( ! [SY53: $i] :
~ ( in @ ( ordered_pair @ SY53 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(179,plain,
! [SV3: $i,SV7: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 )
| ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 ) ) )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(180,plain,
! [SV7: $i,SV3: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 )
| ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 ) ) )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(181,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
| ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( in @ SV10 @ SV8 )
= $false )
| ( ( ~ ! [SY55: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY55 ) @ SV5 ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV8: $i,SV5: $i,SV10: $i] :
( ( ( ~ ! [SY56: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY56 ) @ SV5 ) )
= $false )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV8: $i,SV5: $i] :
( ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(185,plain,
! [SV8: $i,SV5: $i] :
( ( ( ! [SY57: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY57 ) @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(186,plain,
! [SV6: $i,SV1: $i,SV9: $i] :
( ( ( ! [SY51: $i] :
~ ( in @ ( ordered_pair @ SY51 @ SV9 ) @ SV1 ) )
= $false )
| ( ( in @ SV9 @ SV6 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV6: $i,SV1: $i,SV9: $i] :
( ( ( ! [SY52: $i] :
~ ( in @ ( ordered_pair @ SY52 @ SV9 ) @ SV1 ) )
= $true )
| ( ( in @ SV9 @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(188,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV6: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(190,plain,
! [SV3: $i,SV7: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 )
| ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(191,plain,
! [SV7: $i,SV3: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 )
| ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(192,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
| ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV8: $i,SV5: $i,SV10: $i] :
( ( ( ! [SY55: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY55 ) @ SV5 ) )
= $false )
| ( ( in @ SV10 @ SV8 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV8: $i,SV5: $i,SV10: $i] :
( ( ( ! [SY56: $i] :
~ ( in @ ( ordered_pair @ SV10 @ SY56 ) @ SV5 ) )
= $true )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(195,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV9: $i,SV1: $i,SV6: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_SY51 @ SV6 @ SV1 @ SV9 ) @ SV9 ) @ SV1 ) )
= $false )
| ( ( in @ SV9 @ SV6 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[186]) ).
thf(198,plain,
! [SV6: $i,SV1: $i,SV9: $i,SV15: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV15 @ SV9 ) @ SV1 ) )
= $true )
| ( ( in @ SV9 @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(200,plain,
! [SV6: $i,SV1: $i] :
( ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(201,plain,
! [SV6: $i,SV1: $i,SV13: $i] :
( ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( ~ ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV3: $i,SV7: $i,SV12: $i,SV11: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(203,plain,
! [SV7: $i,SV3: $i,SV11: $i,SV12: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(204,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(205,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(206,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV10 @ ( sK8_SY55 @ SV8 @ SV5 @ SV10 ) ) @ SV5 ) )
= $false )
| ( ( in @ SV10 @ SV8 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[193]) ).
thf(207,plain,
! [SV8: $i,SV5: $i,SV16: $i,SV10: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV10 @ SV16 ) @ SV5 ) )
= $true )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(208,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(209,plain,
! [SV8: $i,SV5: $i] :
( ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $false )
| ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(210,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( ~ ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) ) )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(211,plain,
! [SV9: $i,SV1: $i,SV6: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_SY51 @ SV6 @ SV1 @ SV9 ) @ SV9 ) @ SV1 )
= $true )
| ( ( in @ SV9 @ SV6 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(212,plain,
! [SV6: $i,SV1: $i,SV9: $i,SV15: $i] :
( ( ( in @ ( ordered_pair @ SV15 @ SV9 ) @ SV1 )
= $false )
| ( ( in @ SV9 @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $false )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(213,plain,
! [SV6: $i,SV1: $i] :
( ( ( ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $true )
| ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(214,plain,
! [SV13: $i,SV6: $i,SV1: $i] :
( ( ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
| ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(215,plain,
! [SV3: $i,SV7: $i,SV12: $i,SV11: $i] :
( ( ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 )
= $false )
| ( ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(216,plain,
! [SV7: $i,SV3: $i,SV11: $i,SV12: $i] :
( ( ( in @ ( ordered_pair @ SV12 @ SV11 ) @ SV3 )
= $false )
| ( ( in @ ( ordered_pair @ SV11 @ SV12 ) @ SV7 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(217,plain,
! [SV7: $i,SV3: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(218,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(219,plain,
! [SV5: $i,SV8: $i,SV10: $i] :
( ( ( in @ ( ordered_pair @ SV10 @ ( sK8_SY55 @ SV8 @ SV5 @ SV10 ) ) @ SV5 )
= $true )
| ( ( in @ SV10 @ SV8 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(220,plain,
! [SV8: $i,SV5: $i,SV16: $i,SV10: $i] :
( ( ( in @ ( ordered_pair @ SV10 @ SV16 ) @ SV5 )
= $false )
| ( ( in @ SV10 @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(221,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 ) )
= $true )
| ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(222,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 )
| ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(223,plain,
! [SV6: $i,SV1: $i] :
( ( ( ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(224,plain,
! [SV13: $i,SV6: $i,SV1: $i] :
( ( ( ~ ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(225,plain,
! [SV13: $i,SV6: $i,SV1: $i] :
( ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(226,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
| ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(227,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(228,plain,
! [SV7: $i,SV3: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(229,plain,
! [SV8: $i,SV5: $i] :
( ( ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(230,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( ~ ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(231,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(232,plain,
! [SV1: $i,SV6: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_SY54 @ SV6 @ SV1 ) @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[223]) ).
thf(233,plain,
! [SV13: $i,SV6: $i,SV1: $i] :
( ( ( ~ ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(234,plain,
! [SV3: $i,SV7: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(235,plain,
! [SV7: $i,SV3: $i] :
( ( ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(236,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
= $false )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(237,plain,
! [SV8: $i,SV5: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ ( sK10_SY58 @ SV8 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[229]) ).
thf(238,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( ~ ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(239,plain,
! [SV1: $i,SV6: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_SY54 @ SV6 @ SV1 ) @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $true )
| ( ( in @ ( sK3_SY38 @ SV1 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(240,plain,
! [SV13: $i,SV6: $i,SV1: $i] :
( ( ( ! [SY54: $i] :
~ ( in @ ( ordered_pair @ SY54 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(241,plain,
! [SV3: $i,SV7: $i] :
( ( ( in @ ( ordered_pair @ ( sK6_SY60 @ SV7 @ SV3 ) @ ( sK5_SY43 @ SV3 @ SV7 ) ) @ SV3 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK5_SY43 @ SV3 @ SV7 ) @ ( sK6_SY60 @ SV7 @ SV3 ) ) @ SV7 )
= $true )
| ( ( SV7
= ( relation_inverse @ SV3 ) )
= $true )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(242,plain,
! [SV8: $i,SV5: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ ( sK10_SY58 @ SV8 @ SV5 ) ) @ SV5 )
= $true )
| ( ( in @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV8 )
= $true )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(243,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( ! [SY58: $i] :
~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SY58 ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(244,plain,
! [SV1: $i,SV6: $i,SV13: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY54 @ SV13 @ SV6 @ SV1 ) @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[240]) ).
thf(245,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ ( sK12_SY58 @ SV14 @ SV8 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[243]) ).
thf(246,plain,
! [SV1: $i,SV6: $i,SV13: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY54 @ SV13 @ SV6 @ SV1 ) @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $true )
| ( ( in @ ( ordered_pair @ SV13 @ ( sK3_SY38 @ SV1 @ SV6 ) ) @ SV1 )
= $false )
| ( ( SV6
= ( relation_rng @ SV1 ) )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(247,plain,
! [SV14: $i,SV8: $i,SV5: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ ( sK12_SY58 @ SV14 @ SV8 @ SV5 ) ) @ SV5 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK4_SY48 @ SV5 @ SV8 ) @ SV14 ) @ SV5 )
= $false )
| ( ( SV8
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(248,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,247,246,242,241,239,236,235,231,228,225,220,219,216,215,212,211,209,200,119,118,101,99,85,77,74,73,71,70,69,68,67]) ).
thf(249,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(250,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(251,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(252,plain,
$true = $true,
inference(copy,[status(thm)],[52]) ).
thf(253,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(254,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(255,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(256,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(257,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(258,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(259,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(260,plain,
$true = $true,
inference(copy,[status(thm)],[44]) ).
thf(261,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(262,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(263,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(264,plain,
( ( ( relation_dom @ sK1_A )
!= ( relation_rng @ ( relation_inverse @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(265,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(266,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(267,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(268,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(269,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( SX1
!= ( relation_inverse @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(270,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(271,plain,
( ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( relation_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(272,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(273,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ( relation @ ( relation_inverse @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(274,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ! [SY61: $i] :
~ ( ~ ( ( SY61
!= ( relation_dom @ SV19 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY64 ) @ SV19 )
| ( in @ SY62 @ SY61 ) ) ) )
| ~ ( ~ ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SY61 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY67 ) @ SV19 )
| ( in @ SY65 @ SY61 ) ) )
| ( SY61
= ( relation_dom @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(275,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ! [SY68: $i] :
~ ( ~ ( ( SY68
!= ( relation_rng @ SV20 ) )
| ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SY68 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY69 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY69 ) @ SV20 )
| ( in @ SY69 @ SY68 ) ) ) )
| ~ ( ~ ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SY68 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY72 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY72 ) @ SV20 )
| ( in @ SY72 @ SY68 ) ) )
| ( SY68
= ( relation_rng @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(276,plain,
! [SV21: $i] :
( ( ~ ( relation @ SV21 )
| ! [SY75: $i] :
( ~ ( relation @ SY75 )
| ~ ( ~ ( ( SY75
!= ( relation_inverse @ SV21 ) )
| ! [SY76: $i,SY77: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY76 @ SY77 ) @ SY75 )
| ( in @ ( ordered_pair @ SY77 @ SY76 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY77 @ SY76 ) @ SV21 )
| ( in @ ( ordered_pair @ SY76 @ SY77 ) @ SY75 ) ) ) )
| ~ ( ~ ! [SY78: $i,SY79: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SY75 )
| ( in @ ( ordered_pair @ SY79 @ SY78 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SY78 ) @ SV21 )
| ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SY75 ) ) )
| ( SY75
= ( relation_inverse @ SV21 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(277,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(278,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(279,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(280,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ! [SY61: $i] :
~ ( ~ ( ( SY61
!= ( relation_dom @ SV19 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY64 ) @ SV19 )
| ( in @ SY62 @ SY61 ) ) ) )
| ~ ( ~ ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SY61 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY67 ) @ SV19 )
| ( in @ SY65 @ SY61 ) ) )
| ( SY61
= ( relation_dom @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(281,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ! [SY68: $i] :
~ ( ~ ( ( SY68
!= ( relation_rng @ SV20 ) )
| ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SY68 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY69 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY69 ) @ SV20 )
| ( in @ SY69 @ SY68 ) ) ) )
| ~ ( ~ ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SY68 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY72 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY72 ) @ SV20 )
| ( in @ SY72 @ SY68 ) ) )
| ( SY68
= ( relation_rng @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(282,plain,
! [SV21: $i] :
( ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( relation @ SY75 )
| ~ ( ~ ( ( SY75
!= ( relation_inverse @ SV21 ) )
| ! [SY76: $i,SY77: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY76 @ SY77 ) @ SY75 )
| ( in @ ( ordered_pair @ SY77 @ SY76 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY77 @ SY76 ) @ SV21 )
| ( in @ ( ordered_pair @ SY76 @ SY77 ) @ SY75 ) ) ) )
| ~ ( ~ ! [SY78: $i,SY79: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SY75 )
| ( in @ ( ordered_pair @ SY79 @ SY78 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SY78 ) @ SV21 )
| ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SY75 ) ) )
| ( SY75
= ( relation_inverse @ SV21 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(283,plain,
( ( ~ ~ ( ~ ( empty @ sK13_SX0 )
| ~ ( relation @ sK13_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[277]) ).
thf(284,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV17 ) )
= SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(285,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( relation @ ( relation_inverse @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(286,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ! [SY61: $i] :
~ ( ~ ( ( SY61
!= ( relation_dom @ SV19 ) )
| ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY62 @ SY64 ) @ SV19 )
| ( in @ SY62 @ SY61 ) ) ) )
| ~ ( ~ ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SY61 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY65 @ SY67 ) @ SV19 )
| ( in @ SY65 @ SY61 ) ) )
| ( SY61
= ( relation_dom @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(287,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ! [SY68: $i] :
~ ( ~ ( ( SY68
!= ( relation_rng @ SV20 ) )
| ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SY68 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY69 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY69 ) @ SV20 )
| ( in @ SY69 @ SY68 ) ) ) )
| ~ ( ~ ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SY68 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY72 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY72 ) @ SV20 )
| ( in @ SY72 @ SY68 ) ) )
| ( SY68
= ( relation_rng @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(288,plain,
! [SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( relation @ SY75 )
| ~ ( ~ ( ( SY75
!= ( relation_inverse @ SV21 ) )
| ! [SY76: $i,SY77: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY76 @ SY77 ) @ SY75 )
| ( in @ ( ordered_pair @ SY77 @ SY76 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY77 @ SY76 ) @ SV21 )
| ( in @ ( ordered_pair @ SY76 @ SY77 ) @ SY75 ) ) ) )
| ~ ( ~ ! [SY78: $i,SY79: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SY75 )
| ( in @ ( ordered_pair @ SY79 @ SY78 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY79 @ SY78 ) @ SV21 )
| ( in @ ( ordered_pair @ SY78 @ SY79 ) @ SY75 ) ) )
| ( SY75
= ( relation_inverse @ SV21 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(289,plain,
( ( ~ ( ~ ( empty @ sK13_SX0 )
| ~ ( relation @ sK13_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(290,plain,
! [SV19: $i,SV22: $i] :
( ( ( ~ ( ~ ( ( SV22
!= ( relation_dom @ SV19 ) )
| ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV22 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY64 ) @ SV19 )
| ( in @ SY80 @ SV22 ) ) ) )
| ~ ( ~ ! [SY83: $i] :
~ ( ~ ( ~ ( in @ SY83 @ SV22 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY67 ) @ SV19 )
| ( in @ SY83 @ SV22 ) ) )
| ( SV22
= ( relation_dom @ SV19 ) ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(291,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ( ( SV23
!= ( relation_rng @ SV20 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV23 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY86 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY86 ) @ SV20 )
| ( in @ SY86 @ SV23 ) ) ) )
| ~ ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV23 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY89 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY89 ) @ SV20 )
| ( in @ SY89 @ SV23 ) ) )
| ( SV23
= ( relation_rng @ SV20 ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(292,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( relation @ SV24 )
| ~ ( ~ ( ( SV24
!= ( relation_inverse @ SV21 ) )
| ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) )
| ~ ( ~ ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) )
| ( SV24
= ( relation_inverse @ SV21 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(293,plain,
( ( ~ ( empty @ sK13_SX0 )
| ~ ( relation @ sK13_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(294,plain,
! [SV19: $i,SV22: $i] :
( ( ( ~ ( ( SV22
!= ( relation_dom @ SV19 ) )
| ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV22 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY64 ) @ SV19 )
| ( in @ SY80 @ SV22 ) ) ) )
| ~ ( ~ ! [SY83: $i] :
~ ( ~ ( ~ ( in @ SY83 @ SV22 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY67 ) @ SV19 )
| ( in @ SY83 @ SV22 ) ) )
| ( SV22
= ( relation_dom @ SV19 ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(295,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ( ( SV23
!= ( relation_rng @ SV20 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV23 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY86 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY86 ) @ SV20 )
| ( in @ SY86 @ SV23 ) ) ) )
| ~ ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV23 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY89 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY89 ) @ SV20 )
| ( in @ SY89 @ SV23 ) ) )
| ( SV23
= ( relation_rng @ SV20 ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(296,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ~ ( ~ ( ( SV24
!= ( relation_inverse @ SV21 ) )
| ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) )
| ~ ( ~ ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) )
| ( SV24
= ( relation_inverse @ SV21 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(297,plain,
( ( ~ ( empty @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(298,plain,
( ( ~ ( relation @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(299,plain,
! [SV19: $i,SV22: $i] :
( ( ( ~ ( ( SV22
!= ( relation_dom @ SV19 ) )
| ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV22 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY64 ) @ SV19 )
| ( in @ SY80 @ SV22 ) ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(300,plain,
! [SV19: $i,SV22: $i] :
( ( ( ~ ( ~ ! [SY83: $i] :
~ ( ~ ( ~ ( in @ SY83 @ SV22 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY67 ) @ SV19 )
| ( in @ SY83 @ SV22 ) ) )
| ( SV22
= ( relation_dom @ SV19 ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(301,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ( ( SV23
!= ( relation_rng @ SV20 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV23 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY86 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY86 ) @ SV20 )
| ( in @ SY86 @ SV23 ) ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(302,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV23 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY89 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY89 ) @ SV20 )
| ( in @ SY89 @ SV23 ) ) )
| ( SV23
= ( relation_rng @ SV20 ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(303,plain,
! [SV21: $i,SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( ~ ( ~ ( ( SV24
!= ( relation_inverse @ SV21 ) )
| ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) )
| ~ ( ~ ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) )
| ( SV24
= ( relation_inverse @ SV21 ) ) ) ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(304,plain,
( ( empty @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(305,plain,
( ( relation @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(306,plain,
! [SV19: $i,SV22: $i] :
( ( ( ( SV22
!= ( relation_dom @ SV19 ) )
| ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV22 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY64 ) @ SV19 )
| ( in @ SY80 @ SV22 ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(307,plain,
! [SV19: $i,SV22: $i] :
( ( ( ~ ! [SY83: $i] :
~ ( ~ ( ~ ( in @ SY83 @ SV22 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY67 ) @ SV19 )
| ( in @ SY83 @ SV22 ) ) )
| ( SV22
= ( relation_dom @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(308,plain,
! [SV20: $i,SV23: $i] :
( ( ( ( SV23
!= ( relation_rng @ SV20 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV23 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY86 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY86 ) @ SV20 )
| ( in @ SY86 @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(309,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV23 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY89 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY89 ) @ SV20 )
| ( in @ SY89 @ SV23 ) ) )
| ( SV23
= ( relation_rng @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(310,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( relation_inverse @ SV21 ) )
| ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) )
| ~ ( ~ ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) )
| ( SV24
= ( relation_inverse @ SV21 ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(311,plain,
! [SV19: $i,SV22: $i] :
( ( ( SV22
!= ( relation_dom @ SV19 ) )
= $true )
| ( ( ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV22 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY64 ) @ SV19 )
| ( in @ SY80 @ SV22 ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(312,plain,
! [SV19: $i,SV22: $i] :
( ( ( ~ ! [SY83: $i] :
~ ( ~ ( ~ ( in @ SY83 @ SV22 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY67 ) @ SV19 )
| ( in @ SY83 @ SV22 ) ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(313,plain,
! [SV20: $i,SV23: $i] :
( ( ( SV23
!= ( relation_rng @ SV20 ) )
= $true )
| ( ( ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV23 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY86 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY86 ) @ SV20 )
| ( in @ SY86 @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(314,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV23 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY89 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY89 ) @ SV20 )
| ( in @ SY89 @ SV23 ) ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(315,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( ( SV24
!= ( relation_inverse @ SV21 ) )
| ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(316,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( ~ ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) )
| ( SV24
= ( relation_inverse @ SV21 ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(317,plain,
! [SV19: $i,SV22: $i] :
( ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( ! [SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ SV22 )
| ~ ! [SY63: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY63 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY80 @ SY64 ) @ SV19 )
| ( in @ SY80 @ SV22 ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(318,plain,
! [SV19: $i,SV22: $i] :
( ( ( ! [SY83: $i] :
~ ( ~ ( ~ ( in @ SY83 @ SV22 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY66 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ SY83 @ SY67 ) @ SV19 )
| ( in @ SY83 @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(319,plain,
! [SV20: $i,SV23: $i] :
( ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SV23 )
| ~ ! [SY70: $i] :
~ ( in @ ( ordered_pair @ SY70 @ SY86 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY71: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY86 ) @ SV20 )
| ( in @ SY86 @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(320,plain,
! [SV20: $i,SV23: $i] :
( ( ( ! [SY89: $i] :
~ ( ~ ( ~ ( in @ SY89 @ SV23 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SY73 @ SY89 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SY74 @ SY89 ) @ SV20 )
| ( in @ SY89 @ SV23 ) ) ) )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(321,plain,
! [SV21: $i,SV24: $i] :
( ( ( ( SV24
!= ( relation_inverse @ SV21 ) )
| ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(322,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) )
| ( SV24
= ( relation_inverse @ SV21 ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(323,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV25 @ SV22 )
| ~ ! [SY96: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY96 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY97 ) @ SV19 )
| ( in @ SV25 @ SV22 ) ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(324,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
| ~ ! [SY98: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY98 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) ) )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[318]) ).
thf(325,plain,
! [SV20: $i,SV23: $i,SV26: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV26 @ SV23 )
| ~ ! [SY100: $i] :
~ ( in @ ( ordered_pair @ SY100 @ SV26 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SY101 @ SV26 ) @ SV20 )
| ( in @ SV26 @ SV23 ) ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(326,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
| ~ ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
| ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) ) )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[320]) ).
thf(327,plain,
! [SV21: $i,SV24: $i] :
( ( ( SV24
!= ( relation_inverse @ SV21 ) )
= $true )
| ( ( ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(328,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(329,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ SV25 @ SV22 )
| ~ ! [SY96: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY96 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY97: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY97 ) @ SV19 )
| ( in @ SV25 @ SV22 ) ) )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(330,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
| ~ ! [SY98: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY98 ) @ SV19 ) )
| ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(331,plain,
! [SV20: $i,SV23: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ SV26 @ SV23 )
| ~ ! [SY100: $i] :
~ ( in @ ( ordered_pair @ SY100 @ SV26 ) @ SV20 ) )
| ~ ( ~ ~ ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SY101 @ SV26 ) @ SV20 )
| ( in @ SV26 @ SV23 ) ) )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(332,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
| ~ ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
| ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(333,plain,
! [SV21: $i,SV24: $i] :
( ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( ! [SY92: $i,SY93: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 )
| ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY93 @ SY92 ) @ SV21 )
| ( in @ ( ordered_pair @ SY92 @ SY93 ) @ SV24 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(334,plain,
! [SV21: $i,SV24: $i] :
( ( ( ! [SY94: $i,SY95: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 )
| ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY95 @ SY94 ) @ SV21 )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV24 ) ) ) )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(335,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ SV25 @ SV22 )
| ~ ! [SY96: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY96 ) @ SV19 ) ) )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(336,plain,
! [SV22: $i,SV19: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ! [SY97: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY97 ) @ SV19 )
| ( in @ SV25 @ SV22 ) ) )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(337,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
| ~ ! [SY98: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY98 ) @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(338,plain,
! [SV20: $i,SV23: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ SV26 @ SV23 )
| ~ ! [SY100: $i] :
~ ( in @ ( ordered_pair @ SY100 @ SV26 ) @ SV20 ) ) )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(339,plain,
! [SV23: $i,SV20: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SY101 @ SV26 ) @ SV20 )
| ( in @ SV26 @ SV23 ) ) )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(340,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
| ~ ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(341,plain,
! [SV21: $i,SV24: $i,SV27: $i] :
( ( ( ! [SY104: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SY104 ) @ SV24 )
| ( in @ ( ordered_pair @ SY104 @ SV27 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY104 @ SV27 ) @ SV21 )
| ( in @ ( ordered_pair @ SV27 @ SY104 ) @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(342,plain,
! [SV24: $i,SV21: $i] :
( ( ( ! [SY105: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ SY105 ) @ SV24 )
| ( in @ ( ordered_pair @ SY105 @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY105 @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ SY105 ) @ SV24 ) ) ) )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[334]) ).
thf(343,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV22 )
| ~ ! [SY96: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY96 ) @ SV19 ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(344,plain,
! [SV22: $i,SV19: $i,SV25: $i] :
( ( ( ~ ~ ! [SY97: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY97 ) @ SV19 )
| ( in @ SV25 @ SV22 ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(345,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
| ~ ! [SY98: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY98 ) @ SV19 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(346,plain,
! [SV20: $i,SV23: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV23 )
| ~ ! [SY100: $i] :
~ ( in @ ( ordered_pair @ SY100 @ SV26 ) @ SV20 ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(347,plain,
! [SV23: $i,SV20: $i,SV26: $i] :
( ( ( ~ ~ ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SY101 @ SV26 ) @ SV20 )
| ( in @ SV26 @ SV23 ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(348,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
| ~ ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(349,plain,
! [SV21: $i,SV24: $i,SV28: $i,SV27: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 )
| ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 )
| ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(350,plain,
! [SV24: $i,SV21: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) ) ) )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[342]) ).
thf(351,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV22 ) )
= $true )
| ( ( ~ ! [SY96: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY96 ) @ SV19 ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(352,plain,
! [SV22: $i,SV19: $i,SV25: $i] :
( ( ( ~ ~ ! [SY97: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY97 ) @ SV19 ) )
= $true )
| ( ( in @ SV25 @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(353,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(354,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ! [SY98: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY98 ) @ SV19 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(355,plain,
! [SV20: $i,SV23: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV23 ) )
= $true )
| ( ( ~ ! [SY100: $i] :
~ ( in @ ( ordered_pair @ SY100 @ SV26 ) @ SV20 ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(356,plain,
! [SV23: $i,SV20: $i,SV26: $i] :
( ( ( ~ ~ ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SY101 @ SV26 ) @ SV20 ) )
= $true )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(357,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(358,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(359,plain,
! [SV21: $i,SV24: $i,SV28: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 )
| ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 )
| ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 ) ) )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(360,plain,
! [SV24: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 ) )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(361,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( in @ SV25 @ SV22 )
= $false )
| ( ( ~ ! [SY96: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY96 ) @ SV19 ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(362,plain,
! [SV22: $i,SV19: $i,SV25: $i] :
( ( ( ~ ! [SY97: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY97 ) @ SV19 ) )
= $false )
| ( ( in @ SV25 @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(363,plain,
! [SV22: $i,SV19: $i] :
( ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(364,plain,
! [SV22: $i,SV19: $i] :
( ( ( ! [SY98: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY98 ) @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(365,plain,
! [SV20: $i,SV23: $i,SV26: $i] :
( ( ( in @ SV26 @ SV23 )
= $false )
| ( ( ~ ! [SY100: $i] :
~ ( in @ ( ordered_pair @ SY100 @ SV26 ) @ SV20 ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(366,plain,
! [SV23: $i,SV20: $i,SV26: $i] :
( ( ( ~ ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SY101 @ SV26 ) @ SV20 ) )
= $false )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(367,plain,
! [SV23: $i,SV20: $i] :
( ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(368,plain,
! [SV23: $i,SV20: $i] :
( ( ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ SY102 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(369,plain,
! [SV21: $i,SV24: $i,SV28: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 )
| ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 ) ) )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(370,plain,
! [SV24: $i,SV21: $i,SV27: $i,SV28: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 )
| ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 ) ) )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(371,plain,
! [SV24: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(372,plain,
! [SV22: $i,SV19: $i,SV25: $i] :
( ( ( ! [SY96: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY96 ) @ SV19 ) )
= $false )
| ( ( in @ SV25 @ SV22 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(373,plain,
! [SV22: $i,SV19: $i,SV25: $i] :
( ( ( ! [SY97: $i] :
~ ( in @ ( ordered_pair @ SV25 @ SY97 ) @ SV19 ) )
= $true )
| ( ( in @ SV25 @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(374,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(375,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(376,plain,
! [SV23: $i,SV20: $i,SV26: $i] :
( ( ( ! [SY100: $i] :
~ ( in @ ( ordered_pair @ SY100 @ SV26 ) @ SV20 ) )
= $false )
| ( ( in @ SV26 @ SV23 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(377,plain,
! [SV23: $i,SV20: $i,SV26: $i] :
( ( ( ! [SY101: $i] :
~ ( in @ ( ordered_pair @ SY101 @ SV26 ) @ SV20 ) )
= $true )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(378,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) )
= $false )
| ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(379,plain,
! [SV23: $i,SV20: $i,SV30: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(380,plain,
! [SV21: $i,SV24: $i,SV28: $i,SV27: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 )
| ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(381,plain,
! [SV24: $i,SV21: $i,SV27: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 )
| ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(382,plain,
! [SV24: $i,SV21: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(383,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV25 @ ( sK18_SY96 @ SV22 @ SV19 @ SV25 ) ) @ SV19 ) )
= $false )
| ( ( in @ SV25 @ SV22 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[372]) ).
thf(384,plain,
! [SV22: $i,SV19: $i,SV31: $i,SV25: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV25 @ SV31 ) @ SV19 ) )
= $true )
| ( ( in @ SV25 @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(385,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 ) )
= $false )
| ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(386,plain,
! [SV22: $i,SV19: $i] :
( ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $false )
| ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(387,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( ~ ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) ) )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(388,plain,
! [SV26: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_SY100 @ SV23 @ SV20 @ SV26 ) @ SV26 ) @ SV20 ) )
= $false )
| ( ( in @ SV26 @ SV23 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[376]) ).
thf(389,plain,
! [SV23: $i,SV20: $i,SV26: $i,SV32: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV32 @ SV26 ) @ SV20 ) )
= $true )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(390,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(391,plain,
! [SV23: $i,SV20: $i] :
( ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(392,plain,
! [SV23: $i,SV20: $i,SV30: $i] :
( ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( ~ ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) ) )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(393,plain,
! [SV21: $i,SV24: $i,SV28: $i,SV27: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(394,plain,
! [SV24: $i,SV21: $i,SV27: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(395,plain,
! [SV24: $i,SV21: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(396,plain,
! [SV21: $i,SV24: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(397,plain,
! [SV19: $i,SV22: $i,SV25: $i] :
( ( ( in @ ( ordered_pair @ SV25 @ ( sK18_SY96 @ SV22 @ SV19 @ SV25 ) ) @ SV19 )
= $true )
| ( ( in @ SV25 @ SV22 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(398,plain,
! [SV22: $i,SV19: $i,SV31: $i,SV25: $i] :
( ( ( in @ ( ordered_pair @ SV25 @ SV31 ) @ SV19 )
= $false )
| ( ( in @ SV25 @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(399,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 ) )
= $true )
| ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(400,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 )
| ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(401,plain,
! [SV26: $i,SV20: $i,SV23: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_SY100 @ SV23 @ SV20 @ SV26 ) @ SV26 ) @ SV20 )
= $true )
| ( ( in @ SV26 @ SV23 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(402,plain,
! [SV23: $i,SV20: $i,SV26: $i,SV32: $i] :
( ( ( in @ ( ordered_pair @ SV32 @ SV26 ) @ SV20 )
= $false )
| ( ( in @ SV26 @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(403,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $true )
| ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(404,plain,
! [SV30: $i,SV23: $i,SV20: $i] :
( ( ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
| ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(405,plain,
! [SV21: $i,SV24: $i,SV28: $i,SV27: $i] :
( ( ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 )
= $false )
| ( ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(406,plain,
! [SV24: $i,SV21: $i,SV27: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ SV28 @ SV27 ) @ SV21 )
= $false )
| ( ( in @ ( ordered_pair @ SV27 @ SV28 ) @ SV24 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(407,plain,
! [SV24: $i,SV21: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(408,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(409,plain,
! [SV22: $i,SV19: $i] :
( ( ( ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 ) )
= $false )
| ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(410,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( ~ ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(411,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(412,plain,
! [SV23: $i,SV20: $i] :
( ( ( ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(413,plain,
! [SV30: $i,SV23: $i,SV20: $i] :
( ( ( ~ ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(414,plain,
! [SV30: $i,SV23: $i,SV20: $i] :
( ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $false )
| ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(415,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(416,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(417,plain,
! [SV24: $i,SV21: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(418,plain,
! [SV22: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ ( sK20_SY99 @ SV22 @ SV19 ) ) @ SV19 ) )
= $false )
| ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[409]) ).
thf(419,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( ~ ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(420,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK21_SY103 @ SV23 @ SV20 ) @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[412]) ).
thf(421,plain,
! [SV30: $i,SV23: $i,SV20: $i] :
( ( ( ~ ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(422,plain,
! [SV21: $i,SV24: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(423,plain,
! [SV24: $i,SV21: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(424,plain,
! [SV21: $i,SV24: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
= $false )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(425,plain,
! [SV22: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ ( sK20_SY99 @ SV22 @ SV19 ) ) @ SV19 )
= $true )
| ( ( in @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV22 )
= $true )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(426,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( ! [SY99: $i] :
~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SY99 ) @ SV19 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(427,plain,
! [SV20: $i,SV23: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_SY103 @ SV23 @ SV20 ) @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $true )
| ( ( in @ ( sK15_SY89 @ SV20 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(428,plain,
! [SV30: $i,SV23: $i,SV20: $i] :
( ( ( ! [SY103: $i] :
~ ( in @ ( ordered_pair @ SY103 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(429,plain,
! [SV21: $i,SV24: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_SY105 @ SV24 @ SV21 ) @ ( sK16_SY94 @ SV21 @ SV24 ) ) @ SV21 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_SY94 @ SV21 @ SV24 ) @ ( sK17_SY105 @ SV24 @ SV21 ) ) @ SV24 )
= $true )
| ( ( SV24
= ( relation_inverse @ SV21 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(430,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ ( sK22_SY99 @ SV29 @ SV22 @ SV19 ) ) @ SV19 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[426]) ).
thf(431,plain,
! [SV20: $i,SV23: $i,SV30: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_SY103 @ SV30 @ SV23 @ SV20 ) @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[428]) ).
thf(432,plain,
! [SV29: $i,SV22: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ ( sK22_SY99 @ SV29 @ SV22 @ SV19 ) ) @ SV19 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_SY83 @ SV19 @ SV22 ) @ SV29 ) @ SV19 )
= $false )
| ( ( SV22
= ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(433,plain,
! [SV20: $i,SV23: $i,SV30: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_SY103 @ SV30 @ SV23 @ SV20 ) @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $true )
| ( ( in @ ( ordered_pair @ SV30 @ ( sK15_SY89 @ SV20 @ SV23 ) ) @ SV20 )
= $false )
| ( ( SV23
= ( relation_rng @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(434,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[252,433,432,429,427,425,424,423,417,414,411,406,405,402,401,398,397,391,386,305,304,285,284,271,263,260,259,257,256,255,254,253]) ).
thf(435,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[434,248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU181+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.14 % Computer : n020.cluster.edu
% 0.09/0.14 % Model : x86_64 x86_64
% 0.09/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.14 % Memory : 8046.5625MB
% 0.09/0.14 % OS : Linux 6.8.0-71-generic
% 0.09/0.14 % CPULimit : 300
% 0.09/0.14 % WCLimit : 300
% 0.09/0.14 % DateTime : Tue Oct 6 15:04:06 UTC 2026
% 0.09/0.14 % CPUTime :
% 0.09/0.14 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.05/3.87
% 21.05/3.87 No.of.Axioms: 14
% 21.05/3.87
% 21.05/3.87 Length.of.Defs: 0
% 21.05/3.87
% 21.05/3.87 Contains.Choice.Funs: false
% 21.05/3.87 .............
% 21.05/3.87
% 21.05/3.87 ********************************
% 21.05/3.87 * All subproblems solved! *
% 21.05/3.87 ********************************
% 21.05/3.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:434,loop_count:0,foatp_calls:1,translation:fof_full)
% 21.05/3.87
% 21.05/3.87 %**** Beginning of derivation protocol ****
% 21.05/3.87 % SZS output start CNFRefutation
% See solution above
% 21.05/3.87
% 21.05/3.87 %**** End of derivation protocol ****
% 21.05/3.87 %**** no. of clauses in derivation: 411 ****
% 21.05/3.87 %**** clause counter: 434 ****
% 21.05/3.87
% 21.05/3.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:434,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------