%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU248+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 : n018.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 10:43:40 AM UTC 2026
% Result : Theorem 0.93s 0.39s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of formulae : 299 ( 124 unt; 0 typ; 0 def)
% Number of atoms : 2797 ( 872 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 5869 (1277 ~; 958 |; 36 &;3554 @)
% ( 18 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 8 con; 0-3 aty)
% Number of variables : 756 ( 0 ^; 744 !; 12 ?; 756 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $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_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY64,type,
sK10_SY64: $i > $i > $i > $i ).
thf(tp_sK11_SY67,type,
sK11_SY67: $i > $i > $i ).
thf(tp_sK12_SY67,type,
sK12_SY67: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY26,type,
sK2_SY26: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SY48,type,
sK6_SY48: $i > $i > $i ).
thf(tp_sK7_SY57,type,
sK7_SY57: $i > $i > $i ).
thf(tp_sK8_SY62,type,
sK8_SY62: $i > $i > $i > $i ).
thf(tp_sK9_SY69,type,
sK9_SY69: $i > $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(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(10,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(14,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(28,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(29,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(32,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(35,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
thf(36,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(40,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(41,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(42,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(50,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(52,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)],[28]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(56,plain,
( ( ! [SY26: $i] :
( ( relation @ SY26 )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ SY26 ) ) @ ( relation_dom @ SY26 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(57,plain,
( ( ( relation @ sK2_SY26 )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY26 ) ) @ ( relation_dom @ sK2_SY26 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(58,plain,
( ( relation @ sK2_SY26 )
= $true ),
inference(standard_cnf,[status(thm)],[57]) ).
thf(59,plain,
( ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY26 ) ) @ ( relation_dom @ sK2_SY26 ) )
= $false ),
inference(standard_cnf,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY26 ) ) @ ( relation_dom @ sK2_SY26 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[59]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(64,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)],[52]) ).
thf(65,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(66,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(67,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(68,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(70,plain,
$true = $true,
inference(copy,[status(thm)],[46]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(72,plain,
$true = $true,
inference(copy,[status(thm)],[44]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(74,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(75,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(76,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(79,plain,
( ( relation @ sK2_SY26 )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(80,plain,
( ( ~ ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY26 ) ) @ ( relation_dom @ sK2_SY26 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(81,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)],[64]) ).
thf(82,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) )
| ~ ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(83,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(85,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(86,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) )
| ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(88,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(91,plain,
! [SV1: $i] :
( ( ! [SY27: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(92,plain,
( ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY26 ) ) @ ( relation_dom @ sK2_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(93,plain,
! [SV2: $i] :
( ( ~ ( relation @ SV2 )
| ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV2 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV2 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV2 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV3: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ( relation @ SY35 )
| ~ ( function @ SY35 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SY35 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV4: $i] :
( ( ! [SY36: $i] :
( ~ ( relation @ SY36 )
| ( relation @ ( relation_rng_restriction @ SV4 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(96,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(97,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( empty @ SV5 ) )
| ~ ( function @ SV5 ) )
| ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV6: $i] :
( ( ! [SY37: $i] :
~ ( ~ ( ~ ( subset @ SV6 @ SY37 )
| ! [SY38: $i] :
( ~ ( in @ SY38 @ SV6 )
| ( in @ SY38 @ SY37 ) ) )
| ~ ( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV6 )
| ( in @ SY39 @ SY37 ) )
| ( subset @ SV6 @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(100,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(101,plain,
! [SV7: $i] :
( ( ! [SY40: $i] :
~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SY40 ) )
| ( subset @ SV7 @ SY40 ) )
| ~ ( ~ ( subset @ SV7 @ SY40 )
| ( element @ SV7 @ ( powerset @ SY40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV8: $i] :
( ( ! [SY41: $i] :
( ~ ( relation @ SY41 )
| ! [SY42: $i] :
( ~ ( relation @ SY42 )
| ~ ( ~ ( ( SY42
!= ( relation_rng_restriction @ SV8 @ SY41 ) )
| ! [SY43: $i,SY44: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SY42 )
| ~ ( ~ ( in @ SY44 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SY41 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY44 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SY41 ) )
| ( in @ ( ordered_pair @ SY43 @ SY44 ) @ SY42 ) ) ) )
| ~ ( ~ ! [SY45: $i,SY46: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY45 @ SY46 ) @ SY42 )
| ~ ( ~ ( in @ SY46 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY45 @ SY46 ) @ SY41 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY46 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY45 @ SY46 ) @ SY41 ) )
| ( in @ ( ordered_pair @ SY45 @ SY46 ) @ SY42 ) ) )
| ( SY42
= ( relation_rng_restriction @ SV8 @ SY41 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV2 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV2 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV2 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ~ ( ~ ( relation @ SV10 )
| ~ ( function @ SV10 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV4: $i,SV11: $i] :
( ( ~ ( relation @ SV11 )
| ( relation @ ( relation_rng_restriction @ SV4 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(107,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( empty @ sK3_SX0 ) )
| ~ ( function @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[96]) ).
thf(108,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(109,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( empty @ SV5 ) )
| ~ ( function @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV6 @ SV12 )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV12 ) ) )
| ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV12 ) )
| ( subset @ SV6 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(111,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
| ~ ( one_to_one @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[100]) ).
thf(112,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV13 ) )
| ( subset @ SV7 @ SV13 ) )
| ~ ( ~ ( subset @ SV7 @ SV13 )
| ( element @ SV7 @ ( powerset @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV8: $i,SV14: $i] :
( ( ~ ( relation @ SV14 )
| ! [SY49: $i] :
( ~ ( relation @ SY49 )
| ~ ( ~ ( ( SY49
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY50: $i,SY51: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SY49 )
| ~ ( ~ ( in @ SY51 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY51 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SY49 ) ) ) )
| ~ ( ~ ! [SY52: $i,SY53: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SY49 )
| ~ ( ~ ( in @ SY53 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY53 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SY49 ) ) )
| ( SY49
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV2: $i] :
( ( ( relation @ SV2 )
= $false )
| ( ( ! [SY28: $i] :
~ ( ~ ( ( SY28
!= ( relation_dom @ SV2 ) )
| ! [SY29: $i] :
~ ( ~ ( ~ ( in @ SY29 @ SY28 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY29 @ SY31 ) @ SV2 )
| ( in @ SY29 @ SY28 ) ) ) )
| ~ ( ~ ! [SY32: $i] :
~ ( ~ ( ~ ( in @ SY32 @ SY28 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY32 @ SY34 ) @ SV2 )
| ( in @ SY32 @ SY28 ) ) )
| ( SY28
= ( relation_dom @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV10 )
| ~ ( function @ SV10 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV4: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV4 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(117,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( empty @ sK3_SX0 ) )
| ~ ( function @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(118,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( empty @ SV5 ) )
| ~ ( function @ SV5 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( subset @ SV6 @ SV12 )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV12 ) ) )
| ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV12 ) )
| ( subset @ SV6 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
| ~ ( one_to_one @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV13 ) )
| ( subset @ SV7 @ SV13 ) )
| ~ ( ~ ( subset @ SV7 @ SV13 )
| ( element @ SV7 @ ( powerset @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( relation @ SY49 )
| ~ ( ~ ( ( SY49
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY50: $i,SY51: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SY49 )
| ~ ( ~ ( in @ SY51 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY51 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SY49 ) ) ) )
| ~ ( ~ ! [SY52: $i,SY53: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SY49 )
| ~ ( ~ ( in @ SY53 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY53 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SY49 ) ) )
| ( SY49
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ~ ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY31 ) @ SV2 )
| ( in @ SY54 @ SV15 ) ) ) )
| ~ ( ~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY34 ) @ SV2 )
| ( in @ SY57 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( ~ ( relation @ SV10 )
| ~ ( function @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV4: $i,SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV4 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( empty @ sK3_SX0 ) )
| ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(128,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( empty @ SV5 ) )
| ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(130,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ( subset @ SV6 @ SV12 )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(131,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV12 ) )
| ( subset @ SV6 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(132,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
| ~ ( one_to_one @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( element @ SV7 @ ( powerset @ SV13 ) )
| ( subset @ SV7 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(134,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( subset @ SV7 @ SV13 )
| ( element @ SV7 @ ( powerset @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(135,plain,
! [SV8: $i,SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( relation @ SY49 )
| ~ ( ~ ( ( SY49
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY50: $i,SY51: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SY49 )
| ~ ( ~ ( in @ SY51 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY51 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY50 @ SY51 ) @ SY49 ) ) ) )
| ~ ( ~ ! [SY52: $i,SY53: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SY49 )
| ~ ( ~ ( in @ SY53 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY53 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY52 @ SY53 ) @ SY49 ) ) )
| ( SY49
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY31 ) @ SV2 )
| ( in @ SY54 @ SV15 ) ) ) )
| ~ ( ~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY34 ) @ SV2 )
| ( in @ SY57 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 )
| ~ ( function @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(138,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( empty @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(139,plain,
( ( ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(140,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(141,plain,
( ( ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(142,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( empty @ SV5 ) ) )
= $true )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(143,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV12 )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(144,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV12 ) )
| ( subset @ SV6 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(145,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(146,plain,
( ( ~ ( one_to_one @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(147,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ ( powerset @ SV13 ) )
| ( subset @ SV7 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(148,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV13 )
| ( element @ SV7 @ ( powerset @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(149,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 )
| ~ ( ~ ( ( SV16
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) )
| ~ ( ~ ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) )
| ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY31 ) @ SV2 )
| ( in @ SY54 @ SV15 ) ) ) ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(151,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY34 ) @ SV2 )
| ( in @ SY57 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(152,plain,
! [SV3: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( function @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(153,plain,
( ( ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( empty @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(154,plain,
( ( function @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(155,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(156,plain,
( ( function @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(157,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( relation @ SV5 )
| ~ ( empty @ SV5 ) ) )
= $false )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV12 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV12 ) ) )
= $true )
| ( ( subset @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(160,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(161,plain,
( ( one_to_one @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(162,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ ( powerset @ SV13 ) ) )
= $true )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV13 ) )
= $true )
| ( ( element @ SV7 @ ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ( SV16
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) )
| ~ ( ~ ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) )
| ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV2: $i,SV15: $i] :
( ( ( ( SV15
!= ( relation_dom @ SV2 ) )
| ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY31 ) @ SV2 )
| ( in @ SY54 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(166,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY34 ) @ SV2 )
| ( in @ SY57 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV2 ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(167,plain,
! [SV3: $i,SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ~ ( function @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
( ( ~ ( relation @ sK3_SX0 )
| ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 )
| ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(170,plain,
! [SV12: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV12 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( in @ SY47 @ SV6 )
| ( in @ SY47 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV12: $i,SV6: $i] :
( ( ( ! [SY48: $i] :
( ~ ( in @ SY48 @ SV6 )
| ( in @ SY48 @ SV12 ) ) )
= $false )
| ( ( subset @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(172,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV13: $i,SV7: $i] :
( ( ( element @ SV7 @ ( powerset @ SV13 ) )
= $false )
| ( ( subset @ SV7 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(174,plain,
! [SV13: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV13 )
= $false )
| ( ( element @ SV7 @ ( powerset @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(175,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ~ ( ~ ( ( SV16
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) )
| ~ ( ~ ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) )
| ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(176,plain,
! [SV2: $i,SV15: $i] :
( ( ( SV15
!= ( relation_dom @ SV2 ) )
= $true )
| ( ( ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY31 ) @ SV2 )
| ( in @ SY54 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(177,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY34 ) @ SV2 )
| ( in @ SY57 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(178,plain,
! [SV3: $i,SV10: $i] :
( ( ( function @ SV10 )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(179,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(180,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(181,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV6 )
| ( in @ SV17 @ SV12 ) )
= $true )
| ( ( subset @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK6_SY48 @ SV12 @ SV6 ) @ SV6 )
| ( in @ ( sK6_SY48 @ SV12 @ SV6 ) @ SV12 ) )
= $false )
| ( ( subset @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(184,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(185,plain,
( ( ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(186,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ( SV16
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) )
| ~ ( ~ ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) )
| ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV2: $i,SV15: $i] :
( ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( ! [SY54: $i] :
~ ( ~ ( ~ ( in @ SY54 @ SV15 )
| ~ ! [SY30: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY30 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY31: $i] :
~ ( in @ ( ordered_pair @ SY54 @ SY31 ) @ SV2 )
| ( in @ SY54 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(188,plain,
! [SV2: $i,SV15: $i] :
( ( ( ! [SY57: $i] :
~ ( ~ ( ~ ( in @ SY57 @ SV15 )
| ~ ! [SY33: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY33 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY34: $i] :
~ ( in @ ( ordered_pair @ SY57 @ SY34 ) @ SV2 )
| ( in @ SY57 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV10: $i,SV3: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( function @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(190,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(191,plain,
( ( empty @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(192,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV6 ) )
= $true )
| ( ( in @ SV17 @ SV12 )
= $true )
| ( ( subset @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV6: $i,SV12: $i] :
( ( ( ~ ( in @ ( sK6_SY48 @ SV12 @ SV6 ) @ SV6 ) )
= $false )
| ( ( subset @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(195,plain,
! [SV6: $i,SV12: $i] :
( ( ( in @ ( sK6_SY48 @ SV12 @ SV6 ) @ SV12 )
= $false )
| ( ( subset @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(196,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(197,plain,
( ( function @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(198,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ( SV16
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(199,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ~ ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) )
| ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(200,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY64 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY65 ) @ SV2 )
| ( in @ SV18 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(201,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY66 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[188]) ).
thf(202,plain,
! [SV10: $i,SV3: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( function @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(203,plain,
! [SV10: $i,SV3: $i] :
( ( ( ~ ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( function @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(204,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(205,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( in @ SV17 @ SV6 )
= $false )
| ( ( in @ SV17 @ SV12 )
= $true )
| ( ( subset @ SV6 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(206,plain,
! [SV6: $i,SV12: $i] :
( ( ( in @ ( sK6_SY48 @ SV12 @ SV6 ) @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(207,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ( SV16
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
| ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(208,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) )
| ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(209,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY64 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY65 ) @ SV2 )
| ( in @ SV18 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(210,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY66 ) @ SV2 ) )
| ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(211,plain,
! [SV10: $i,SV3: $i] :
( ( ( relation @ ( relation_rng_restriction @ SV3 @ SV10 ) )
= $true )
| ( ( relation @ SV10 )
= $false )
| ( ( function @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(212,plain,
! [SV10: $i,SV3: $i] :
( ( ( function @ ( relation_rng_restriction @ SV3 @ SV10 ) )
= $true )
| ( ( relation @ SV10 )
= $false )
| ( ( function @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(213,plain,
! [SV5: $i] :
( ( ( function @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( SV16
!= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(215,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(216,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY64 ) @ SV2 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(217,plain,
! [SV15: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY65 ) @ SV2 )
| ( in @ SV18 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(218,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY66 ) @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(219,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( one_to_one @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(220,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 )
| ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY61 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV16 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(221,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ! [SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 )
| ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY63 @ SV8 )
| ~ ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SY62 @ SY63 ) @ SV16 ) ) ) )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY64 ) @ SV2 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(223,plain,
! [SV15: $i,SV2: $i,SV18: $i] :
( ( ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY65 ) @ SV2 )
| ( in @ SV18 @ SV15 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(224,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
| ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY66 ) @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(226,plain,
! [SV5: $i] :
( ( ( ~ ( one_to_one @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(227,plain,
! [SV14: $i,SV8: $i,SV16: $i,SV19: $i] :
( ( ( ! [SY68: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV19 @ SY68 ) @ SV16 )
| ~ ( ~ ( in @ SY68 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY68 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SY68 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SV19 @ SY68 ) @ SV16 ) ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(228,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ! [SY69: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ SY69 ) @ SV16 )
| ~ ( ~ ( in @ SY69 @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ SY69 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY69 @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ SY69 ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ SY69 ) @ SV16 ) ) ) )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[221]) ).
thf(229,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY64 ) @ SV2 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(230,plain,
! [SV15: $i,SV2: $i,SV18: $i] :
( ( ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY65 ) @ SV2 ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(231,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(232,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ! [SY66: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY66 ) @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(233,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) ) )
= $true )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(234,plain,
! [SV5: $i] :
( ( ( one_to_one @ SV5 )
= $true )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(235,plain,
! [SV14: $i,SV8: $i,SV16: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
| ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 ) ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(236,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
| ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) ) )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[228]) ).
thf(237,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( in @ SV18 @ SV15 )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY64 ) @ SV2 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(238,plain,
! [SV15: $i,SV2: $i,SV18: $i] :
( ( ( ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY65 ) @ SV2 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(239,plain,
! [SV15: $i,SV2: $i] :
( ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY66: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY66 ) @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(241,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(242,plain,
! [SV14: $i,SV8: $i,SV16: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
| ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 ) ) )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(243,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
| ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(244,plain,
! [SV15: $i,SV2: $i,SV18: $i] :
( ( ( ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY64 ) @ SV2 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(245,plain,
! [SV15: $i,SV2: $i,SV18: $i] :
( ( ( ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY65 ) @ SV2 ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(246,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(247,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(248,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(249,plain,
! [SV5: $i] :
( ( ( ~ ( function @ SV5 ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(250,plain,
! [SV14: $i,SV8: $i,SV16: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
| ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) ) )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(251,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 ) ) )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(252,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
| ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(253,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV18 @ ( sK10_SY64 @ SV15 @ SV2 @ SV18 ) ) @ SV2 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[244]) ).
thf(254,plain,
! [SV15: $i,SV2: $i,SV22: $i,SV18: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV18 @ SV22 ) @ SV2 ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(255,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(256,plain,
! [SV15: $i,SV2: $i] :
( ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(257,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(258,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $true )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(259,plain,
! [SV5: $i] :
( ( ( function @ SV5 )
= $true )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(260,plain,
! [SV14: $i,SV8: $i,SV16: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
| ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(261,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
| ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(262,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
| ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(263,plain,
! [SV2: $i,SV15: $i,SV18: $i] :
( ( ( in @ ( ordered_pair @ SV18 @ ( sK10_SY64 @ SV15 @ SV2 @ SV18 ) ) @ SV2 )
= $true )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(264,plain,
! [SV15: $i,SV2: $i,SV22: $i,SV18: $i] :
( ( ( in @ ( ordered_pair @ SV18 @ SV22 ) @ SV2 )
= $false )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $false )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(265,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 ) )
= $true )
| ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(266,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 )
| ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(267,plain,
! [SV14: $i,SV8: $i,SV16: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(268,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(269,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(270,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(271,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 ) )
= $false )
| ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(272,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(273,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(274,plain,
! [SV14: $i,SV8: $i,SV16: $i,SV20: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $false )
| ( ( ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(275,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(276,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(277,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(278,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ ( sK11_SY67 @ SV15 @ SV2 ) ) @ SV2 ) )
= $false )
| ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[271]) ).
thf(279,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( ~ ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(280,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(281,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV8 )
| ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(282,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(283,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(284,plain,
! [SV15: $i,SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ ( sK11_SY67 @ SV15 @ SV2 ) ) @ SV2 )
= $true )
| ( ( in @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(285,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY67: $i] :
~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SY67 ) @ SV2 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(286,plain,
! [SV14: $i,SV16: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(287,plain,
! [SV8: $i,SV16: $i,SV14: $i,SV20: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(288,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV8 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(289,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(290,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(291,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(292,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ ( sK12_SY67 @ SV21 @ SV15 @ SV2 ) ) @ SV2 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[285]) ).
thf(293,plain,
! [SV14: $i,SV16: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( in @ SV20 @ SV8 )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(294,plain,
! [SV8: $i,SV16: $i,SV14: $i,SV20: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(295,plain,
! [SV16: $i,SV14: $i,SV19: $i,SV8: $i,SV20: $i] :
( ( ( in @ SV20 @ SV8 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(296,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(297,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) ) )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(298,plain,
! [SV21: $i,SV15: $i,SV2: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ ( sK12_SY67 @ SV21 @ SV15 @ SV2 ) ) @ SV2 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_SY57 @ SV2 @ SV15 ) @ SV21 ) @ SV2 )
= $false )
| ( ( SV15
= ( relation_dom @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(299,plain,
! [SV16: $i,SV8: $i,SV14: $i,SV20: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV14 )
= $false )
| ( ( in @ SV20 @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ SV20 ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(300,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(301,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
| ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(302,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(303,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(304,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
= $false )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(305,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $false )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(306,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(307,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV16 )
= $true )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(308,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) ) )
= $true )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(309,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
| ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(310,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 ) )
= $false )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(311,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(312,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $true )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(313,plain,
! [SV16: $i,SV8: $i,SV14: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $true )
| ( ( in @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) @ SV8 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY62 @ SV14 @ SV8 @ SV16 ) @ ( sK9_SY69 @ SV16 @ SV8 @ SV14 ) ) @ SV14 )
= $false )
| ( ( SV16
= ( relation_rng_restriction @ SV8 @ SV14 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(314,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,313,312,307,306,305,299,298,294,293,290,284,273,264,263,259,258,256,234,212,211,206,205,197,196,195,191,190,174,173,161,156,155,154,126,103,92,79,72,70,69,68,67,66]) ).
thf(315,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU248+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n018.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Oct 6 15:11:22 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/0.39
% 0.93/0.39 No.of.Axioms: 18
% 0.93/0.39
% 0.93/0.39 Length.of.Defs: 0
% 0.93/0.39
% 0.93/0.39 Contains.Choice.Funs: false
% 0.93/0.39 .........
% 0.93/0.39
% 0.93/0.39 ********************************
% 0.93/0.39 * All subproblems solved! *
% 0.93/0.39 ********************************
% 0.93/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:314,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.93/0.39
% 0.93/0.39 %**** Beginning of derivation protocol ****
% 0.93/0.39 % SZS output start CNFRefutation
% See solution above
% 0.93/0.39
% 0.93/0.39 %**** End of derivation protocol ****
% 0.93/0.39 %**** no. of clauses in derivation: 299 ****
% 0.93/0.39 %**** clause counter: 314 ****
% 0.93/0.39
% 0.93/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:314,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------