%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:43:39 AM UTC 2026
% Result : Theorem 1.15s 0.41s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of formulae : 427 ( 114 unt; 0 typ; 0 def)
% Number of atoms : 4160 (1111 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 6740 (2102 ~;1460 |; 32 &;3071 @)
% ( 33 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 3 con; 0-2 aty)
% Number of variables : 505 ( 0 ^; 505 !; 0 ?; 505 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(1,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(3,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(7,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
thf(8,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(9,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_wellord1) ).
thf(10,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
thf(11,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
thf(12,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
thf(13,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(15,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_wellord1) ).
thf(16,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
$true = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(32,plain,
( ( ( relation @ sK1_A )
=> ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
<=> ( well_ordering @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(33,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[32]) ).
thf(34,plain,
( ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
<=> ( well_ordering @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[32]) ).
thf(35,plain,
( ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
=> ( well_ordering @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[34]) ).
thf(36,plain,
( ( ( well_ordering @ sK1_A )
=> ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[34]) ).
thf(37,plain,
( ( ~ ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
=> ( well_ordering @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(38,plain,
( ( ~ ( ( well_ordering @ sK1_A )
=> ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(47,plain,
$true = $true,
inference(copy,[status(thm)],[23]) ).
thf(48,plain,
$true = $true,
inference(copy,[status(thm)],[22]) ).
thf(49,plain,
$true = $true,
inference(copy,[status(thm)],[21]) ).
thf(50,plain,
$true = $true,
inference(copy,[status(thm)],[20]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(53,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(54,plain,
( ( ~ ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
=> ( well_ordering @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(55,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( well_ordering @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 ) )
| ~ ( antisymmetric @ SX0 ) )
| ~ ( connected @ SX0 ) )
| ~ ( well_founded_relation @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 ) )
| ~ ( antisymmetric @ SX0 ) )
| ~ ( connected @ SX0 ) )
| ~ ( well_founded_relation @ SX0 ) )
| ( well_ordering @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(56,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(57,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(58,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(59,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ~ ( well_orders @ SX0 @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ~ ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ( is_antisymmetric_in @ SX0 @ SX1 ) )
| ~ ( is_connected_in @ SX0 @ SX1 ) )
| ~ ( is_well_founded_in @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ~ ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ( is_antisymmetric_in @ SX0 @ SX1 ) )
| ~ ( is_connected_in @ SX0 @ SX1 ) )
| ~ ( is_well_founded_in @ SX0 @ SX1 ) )
| ( well_orders @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(60,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_field @ SX0 )
= ( set_union2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(61,plain,
( ( ~ ( ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
| ( well_ordering @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(62,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(63,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(64,plain,
! [SV1: $i] :
( ( ! [SY14: $i] :
( ( set_union2 @ SV1 @ SY14 )
= ( set_union2 @ SY14 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(65,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
( ( set_union2 @ SV2 @ SV2 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV3: $i] :
( ( ~ ( relation @ SV3 )
| ~ ( ~ ( ~ ( well_ordering @ SV3 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
| ( well_ordering @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV4: $i] :
( ( ~ ( relation @ SV4 )
| ~ ( ~ ( ~ ( reflexive @ SV4 )
| ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
| ( reflexive @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ~ ( ~ ( ~ ( transitive @ SV5 )
| ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) ) )
| ~ ( ~ ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
| ( transitive @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ~ ( ~ ( ~ ( connected @ SV6 )
| ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) ) )
| ~ ( ~ ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
| ( connected @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV7: $i] :
( ( ~ ( relation @ SV7 )
| ! [SY16: $i] :
~ ( ~ ( ~ ( well_orders @ SV7 @ SY16 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SY16 )
| ~ ( is_transitive_in @ SV7 @ SY16 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SY16 ) )
| ~ ( is_connected_in @ SV7 @ SY16 ) )
| ~ ( is_well_founded_in @ SV7 @ SY16 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SY16 )
| ~ ( is_transitive_in @ SV7 @ SY16 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SY16 ) )
| ~ ( is_connected_in @ SV7 @ SY16 ) )
| ~ ( is_well_founded_in @ SV7 @ SY16 ) )
| ( well_orders @ SV7 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ( ( relation_field @ SV8 )
= ( set_union2 @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(72,plain,
( ( ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
| ( well_ordering @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(73,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ~ ( ~ ( ~ ( well_founded_relation @ SV9 )
| ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
| ( well_founded_relation @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(74,plain,
! [SV10: $i] :
( ( ~ ( relation @ SV10 )
| ~ ( ~ ( ~ ( antisymmetric @ SV10 )
| ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
| ( antisymmetric @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(75,plain,
! [SV11: $i,SV1: $i] :
( ( ( set_union2 @ SV1 @ SV11 )
= ( set_union2 @ SV11 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(76,plain,
! [SV2: $i] :
( ( ( set_union2 @ SV2 @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(77,plain,
! [SV3: $i] :
( ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( well_ordering @ SV3 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
| ( well_ordering @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(78,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( reflexive @ SV4 )
| ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
| ( reflexive @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(79,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( transitive @ SV5 )
| ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) ) )
| ~ ( ~ ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
| ( transitive @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(80,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( connected @ SV6 )
| ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) ) )
| ~ ( ~ ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
| ( connected @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(81,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY16: $i] :
~ ( ~ ( ~ ( well_orders @ SV7 @ SY16 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SY16 )
| ~ ( is_transitive_in @ SV7 @ SY16 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SY16 ) )
| ~ ( is_connected_in @ SV7 @ SY16 ) )
| ~ ( is_well_founded_in @ SV7 @ SY16 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SY16 )
| ~ ( is_transitive_in @ SV7 @ SY16 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SY16 ) )
| ~ ( is_connected_in @ SV7 @ SY16 ) )
| ~ ( is_well_founded_in @ SV7 @ SY16 ) )
| ( well_orders @ SV7 @ SY16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(82,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ( relation_field @ SV8 )
= ( set_union2 @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(83,plain,
( ( ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(84,plain,
( ( well_ordering @ sK1_A )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(85,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( well_founded_relation @ SV9 )
| ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
| ( well_founded_relation @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( antisymmetric @ SV10 )
| ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
| ( antisymmetric @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( ~ ( ~ ( ~ ( well_ordering @ SV3 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
| ( well_ordering @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( ~ ( ~ ( ~ ( reflexive @ SV4 )
| ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
| ( reflexive @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ~ ( ~ ( ~ ( transitive @ SV5 )
| ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) ) )
| ~ ( ~ ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
| ( transitive @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ~ ( ~ ( ~ ( connected @ SV6 )
| ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) ) )
| ~ ( ~ ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
| ( connected @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ! [SY16: $i] :
~ ( ~ ( ~ ( well_orders @ SV7 @ SY16 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SY16 )
| ~ ( is_transitive_in @ SV7 @ SY16 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SY16 ) )
| ~ ( is_connected_in @ SV7 @ SY16 ) )
| ~ ( is_well_founded_in @ SV7 @ SY16 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SY16 )
| ~ ( is_transitive_in @ SV7 @ SY16 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SY16 ) )
| ~ ( is_connected_in @ SV7 @ SY16 ) )
| ~ ( is_well_founded_in @ SV7 @ SY16 ) )
| ( well_orders @ SV7 @ SY16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ( relation_field @ SV8 )
= ( set_union2 @ ( relation_dom @ SV8 ) @ ( relation_rng @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(94,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ~ ( ~ ( ~ ( well_founded_relation @ SV9 )
| ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
| ( well_founded_relation @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ~ ( ~ ( ~ ( antisymmetric @ SV10 )
| ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
| ( antisymmetric @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( well_ordering @ SV3 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
| ( well_ordering @ SV3 ) ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( reflexive @ SV4 )
| ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
| ( reflexive @ SV4 ) ) )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( transitive @ SV5 )
| ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) ) )
| ~ ( ~ ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
| ( transitive @ SV5 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( connected @ SV6 )
| ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) ) )
| ~ ( ~ ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
| ( connected @ SV6 ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ( ~ ( well_orders @ SV7 @ SV13 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) )
| ( well_orders @ SV7 @ SV13 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( well_founded_relation @ SV9 )
| ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
| ( well_founded_relation @ SV9 ) ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( antisymmetric @ SV10 )
| ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
| ( antisymmetric @ SV10 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( well_ordering @ SV3 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(104,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
| ( well_ordering @ SV3 ) ) )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( reflexive @ SV4 )
| ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) ) ) )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(106,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
| ( reflexive @ SV4 ) ) )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(107,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( transitive @ SV5 )
| ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(108,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
| ( transitive @ SV5 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(109,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( connected @ SV6 )
| ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(110,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
| ( connected @ SV6 ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(111,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ( well_orders @ SV7 @ SV13 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) )
| ( well_orders @ SV7 @ SV13 ) ) )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( well_founded_relation @ SV9 )
| ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) ) ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(113,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
| ( well_founded_relation @ SV9 ) ) )
= $false )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(114,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( antisymmetric @ SV10 )
| ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) ) ) )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(115,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
| ( antisymmetric @ SV10 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(116,plain,
! [SV3: $i] :
( ( ( ~ ( well_ordering @ SV3 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(117,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
| ( well_ordering @ SV3 ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(118,plain,
! [SV4: $i] :
( ( ( ~ ( reflexive @ SV4 )
| ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(119,plain,
! [SV4: $i] :
( ( ( ~ ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
| ( reflexive @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(120,plain,
! [SV5: $i] :
( ( ( ~ ( transitive @ SV5 )
| ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(121,plain,
! [SV5: $i] :
( ( ( ~ ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
| ( transitive @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(122,plain,
! [SV6: $i] :
( ( ( ~ ( connected @ SV6 )
| ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(123,plain,
! [SV6: $i] :
( ( ( ~ ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
| ( connected @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(124,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ( well_orders @ SV7 @ SV13 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) ) )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(125,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) )
| ( well_orders @ SV7 @ SV13 ) ) )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(126,plain,
! [SV9: $i] :
( ( ( ~ ( well_founded_relation @ SV9 )
| ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(127,plain,
! [SV9: $i] :
( ( ( ~ ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
| ( well_founded_relation @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(128,plain,
! [SV10: $i] :
( ( ( ~ ( antisymmetric @ SV10 )
| ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(129,plain,
! [SV10: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
| ( antisymmetric @ SV10 ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(130,plain,
! [SV3: $i] :
( ( ( ~ ( well_ordering @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV4: $i] :
( ( ( ~ ( reflexive @ SV4 ) )
= $true )
| ( ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV4: $i] :
( ( ( ~ ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) ) )
= $true )
| ( ( reflexive @ SV4 )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV5: $i] :
( ( ( ~ ( transitive @ SV5 ) )
= $true )
| ( ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV5: $i] :
( ( ( ~ ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) ) )
= $true )
| ( ( transitive @ SV5 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV6: $i] :
( ( ( ~ ( connected @ SV6 ) )
= $true )
| ( ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV6: $i] :
( ( ( ~ ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) ) )
= $true )
| ( ( connected @ SV6 )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( well_orders @ SV7 @ SV13 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(139,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) )
| ( well_orders @ SV7 @ SV13 ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(140,plain,
! [SV9: $i] :
( ( ( ~ ( well_founded_relation @ SV9 ) )
= $true )
| ( ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV9: $i] :
( ( ( ~ ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) ) )
= $true )
| ( ( well_founded_relation @ SV9 )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV10: $i] :
( ( ( ~ ( antisymmetric @ SV10 ) )
= $true )
| ( ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV10: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) ) )
= $true )
| ( ( antisymmetric @ SV10 )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV3: $i] :
( ( ( well_ordering @ SV3 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) ) )
= $false )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV4: $i] :
( ( ( reflexive @ SV4 )
= $false )
| ( ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV4: $i] :
( ( ( is_reflexive_in @ SV4 @ ( relation_field @ SV4 ) )
= $false )
| ( ( reflexive @ SV4 )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV5: $i] :
( ( ( transitive @ SV5 )
= $false )
| ( ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV5: $i] :
( ( ( is_transitive_in @ SV5 @ ( relation_field @ SV5 ) )
= $false )
| ( ( transitive @ SV5 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV6: $i] :
( ( ( connected @ SV6 )
= $false )
| ( ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV6: $i] :
( ( ( is_connected_in @ SV6 @ ( relation_field @ SV6 ) )
= $false )
| ( ( connected @ SV6 )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( well_orders @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV9: $i] :
( ( ( well_founded_relation @ SV9 )
= $false )
| ( ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV9: $i] :
( ( ( is_well_founded_in @ SV9 @ ( relation_field @ SV9 ) )
= $false )
| ( ( well_founded_relation @ SV9 )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV10: $i] :
( ( ( antisymmetric @ SV10 )
= $false )
| ( ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV10: $i] :
( ( ( is_antisymmetric_in @ SV10 @ ( relation_field @ SV10 ) )
= $false )
| ( ( antisymmetric @ SV10 )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
| ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(160,plain,
! [SV13: $i,SV7: $i] :
( ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV3: $i] :
( ( ( ~ ( well_founded_relation @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(164,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(165,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
| ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(167,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) ) )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(168,plain,
! [SV3: $i] :
( ( ( well_founded_relation @ SV3 )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(169,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) ) )
= $false )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(170,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(171,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(172,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(173,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(174,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
| ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(175,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(176,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_well_founded_in @ SV7 @ SV13 )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(177,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) ) )
= $false )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(179,plain,
! [SV3: $i] :
( ( ( ~ ( connected @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(180,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(181,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(182,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
| ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(183,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) ) )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(184,plain,
! [SV3: $i] :
( ( ( connected @ SV3 )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(185,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) ) )
= $false )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(186,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(187,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(188,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(189,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(190,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
| ~ ( antisymmetric @ SV3 ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(191,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(192,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_connected_in @ SV7 @ SV13 )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(193,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) ) )
= $false )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(194,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(195,plain,
! [SV3: $i] :
( ( ( ~ ( antisymmetric @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(196,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) ) )
= $true )
| ( ( ~ ( antisymmetric @ SV3 ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(197,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(198,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
| ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(199,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) ) )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(200,plain,
! [SV3: $i] :
( ( ( antisymmetric @ SV3 )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(201,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) ) )
= $false )
| ( ( ~ ( antisymmetric @ SV3 ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(202,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(203,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(204,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV3: $i] :
( ( ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(206,plain,
! [SV3: $i] :
( ( ( ~ ( reflexive @ SV3 )
| ~ ( transitive @ SV3 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV3 ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(207,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(208,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_antisymmetric_in @ SV7 @ SV13 )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(209,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) ) )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(210,plain,
! [SV3: $i] :
( ( ( ~ ( reflexive @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV3: $i] :
( ( ( ~ ( transitive @ SV3 ) )
= $false )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(212,plain,
! [SV3: $i] :
( ( ( ~ ( reflexive @ SV3 ) )
= $true )
| ( ( ~ ( transitive @ SV3 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV3 ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(213,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(214,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_reflexive_in @ SV7 @ SV13 )
| ~ ( is_transitive_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(215,plain,
! [SV3: $i] :
( ( ( reflexive @ SV3 )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(216,plain,
! [SV3: $i] :
( ( ( transitive @ SV3 )
= $true )
| ( ( well_ordering @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(217,plain,
! [SV3: $i] :
( ( ( reflexive @ SV3 )
= $false )
| ( ( ~ ( transitive @ SV3 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV3 ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(218,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_reflexive_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(219,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_transitive_in @ SV7 @ SV13 ) )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( is_reflexive_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(221,plain,
! [SV3: $i] :
( ( ( transitive @ SV3 )
= $false )
| ( ( reflexive @ SV3 )
= $false )
| ( ( ~ ( antisymmetric @ SV3 ) )
= $true )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(222,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_reflexive_in @ SV7 @ SV13 )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(223,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_transitive_in @ SV7 @ SV13 )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(224,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_reflexive_in @ SV7 @ SV13 )
= $false )
| ( ( ~ ( is_transitive_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(225,plain,
! [SV3: $i] :
( ( ( antisymmetric @ SV3 )
= $false )
| ( ( reflexive @ SV3 )
= $false )
| ( ( transitive @ SV3 )
= $false )
| ( ( ~ ( connected @ SV3 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_transitive_in @ SV7 @ SV13 )
= $false )
| ( ( is_reflexive_in @ SV7 @ SV13 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(227,plain,
! [SV3: $i] :
( ( ( connected @ SV3 )
= $false )
| ( ( transitive @ SV3 )
= $false )
| ( ( reflexive @ SV3 )
= $false )
| ( ( antisymmetric @ SV3 )
= $false )
| ( ( ~ ( well_founded_relation @ SV3 ) )
= $true )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(228,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_antisymmetric_in @ SV7 @ SV13 )
= $false )
| ( ( is_reflexive_in @ SV7 @ SV13 )
= $false )
| ( ( is_transitive_in @ SV7 @ SV13 )
= $false )
| ( ( ~ ( is_connected_in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(229,plain,
! [SV3: $i] :
( ( ( well_founded_relation @ SV3 )
= $false )
| ( ( antisymmetric @ SV3 )
= $false )
| ( ( reflexive @ SV3 )
= $false )
| ( ( transitive @ SV3 )
= $false )
| ( ( connected @ SV3 )
= $false )
| ( ( well_ordering @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(230,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_connected_in @ SV7 @ SV13 )
= $false )
| ( ( is_transitive_in @ SV7 @ SV13 )
= $false )
| ( ( is_reflexive_in @ SV7 @ SV13 )
= $false )
| ( ( is_antisymmetric_in @ SV7 @ SV13 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV7 @ SV13 ) )
= $true )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(231,plain,
! [SV13: $i,SV7: $i] :
( ( ( is_well_founded_in @ SV7 @ SV13 )
= $false )
| ( ( is_antisymmetric_in @ SV7 @ SV13 )
= $false )
| ( ( is_reflexive_in @ SV7 @ SV13 )
= $false )
| ( ( is_transitive_in @ SV7 @ SV13 )
= $false )
| ( ( is_connected_in @ SV7 @ SV13 )
= $false )
| ( ( well_orders @ SV7 @ SV13 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(232,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,231,229,223,222,216,215,208,200,192,184,176,168,157,156,155,154,151,150,149,148,147,146,93,92,84,76,75,53,50,49,48]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(234,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(235,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(236,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(237,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(238,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(239,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(240,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(241,plain,
$true = $true,
inference(copy,[status(thm)],[23]) ).
thf(242,plain,
$true = $true,
inference(copy,[status(thm)],[22]) ).
thf(243,plain,
$true = $true,
inference(copy,[status(thm)],[21]) ).
thf(244,plain,
$true = $true,
inference(copy,[status(thm)],[20]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(246,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(247,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(248,plain,
( ( ~ ( ( well_ordering @ sK1_A )
=> ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(249,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ~ ( well_orders @ SX0 @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ~ ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ( is_antisymmetric_in @ SX0 @ SX1 ) )
| ~ ( is_connected_in @ SX0 @ SX1 ) )
| ~ ( is_well_founded_in @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ~ ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ( is_antisymmetric_in @ SX0 @ SX1 ) )
| ~ ( is_connected_in @ SX0 @ SX1 ) )
| ~ ( is_well_founded_in @ SX0 @ SX1 ) )
| ( well_orders @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(250,plain,
( ( ~ ( ~ ( well_ordering @ sK1_A )
| ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(251,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(252,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(253,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(254,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( well_ordering @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 ) )
| ~ ( antisymmetric @ SX0 ) )
| ~ ( connected @ SX0 ) )
| ~ ( well_founded_relation @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 ) )
| ~ ( antisymmetric @ SX0 ) )
| ~ ( connected @ SX0 ) )
| ~ ( well_founded_relation @ SX0 ) )
| ( well_ordering @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(255,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(256,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ( ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(257,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_field @ SX0 )
= ( set_union2 @ ( relation_dom @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(258,plain,
! [SV14: $i] :
( ( ! [SY17: $i] :
( ( set_union2 @ SV14 @ SY17 )
= ( set_union2 @ SY17 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(259,plain,
! [SV15: $i] :
( ( ! [SY18: $i] :
( ( set_union2 @ SV15 @ SV15 )
= SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(260,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ! [SY19: $i] :
~ ( ~ ( ~ ( well_orders @ SV16 @ SY19 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SY19 )
| ~ ( is_transitive_in @ SV16 @ SY19 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SY19 ) )
| ~ ( is_connected_in @ SV16 @ SY19 ) )
| ~ ( is_well_founded_in @ SV16 @ SY19 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SY19 )
| ~ ( is_transitive_in @ SV16 @ SY19 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SY19 ) )
| ~ ( is_connected_in @ SV16 @ SY19 ) )
| ~ ( is_well_founded_in @ SV16 @ SY19 ) )
| ( well_orders @ SV16 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(261,plain,
( ( ~ ( well_ordering @ sK1_A )
| ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(262,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ~ ( ~ ( ~ ( reflexive @ SV17 )
| ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
| ( reflexive @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(263,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ~ ( ~ ( ~ ( antisymmetric @ SV18 )
| ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
| ( antisymmetric @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ~ ( ~ ( ~ ( transitive @ SV19 )
| ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) ) )
| ~ ( ~ ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
| ( transitive @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ~ ( ~ ( ~ ( well_ordering @ SV20 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
| ( well_ordering @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV21: $i] :
( ( ~ ( relation @ SV21 )
| ~ ( ~ ( ~ ( well_founded_relation @ SV21 )
| ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
| ( well_founded_relation @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(267,plain,
! [SV22: $i] :
( ( ~ ( relation @ SV22 )
| ~ ( ~ ( ~ ( connected @ SV22 )
| ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) ) )
| ~ ( ~ ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
| ( connected @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(268,plain,
! [SV23: $i] :
( ( ~ ( relation @ SV23 )
| ( ( relation_field @ SV23 )
= ( set_union2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(269,plain,
! [SV24: $i,SV14: $i] :
( ( ( set_union2 @ SV14 @ SV24 )
= ( set_union2 @ SV24 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV15: $i] :
( ( ( set_union2 @ SV15 @ SV15 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ! [SY19: $i] :
~ ( ~ ( ~ ( well_orders @ SV16 @ SY19 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SY19 )
| ~ ( is_transitive_in @ SV16 @ SY19 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SY19 ) )
| ~ ( is_connected_in @ SV16 @ SY19 ) )
| ~ ( is_well_founded_in @ SV16 @ SY19 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SY19 )
| ~ ( is_transitive_in @ SV16 @ SY19 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SY19 ) )
| ~ ( is_connected_in @ SV16 @ SY19 ) )
| ~ ( is_well_founded_in @ SV16 @ SY19 ) )
| ( well_orders @ SV16 @ SY19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(272,plain,
( ( ~ ( well_ordering @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(273,plain,
( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(274,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( reflexive @ SV17 )
| ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
| ( reflexive @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(275,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( antisymmetric @ SV18 )
| ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
| ( antisymmetric @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(276,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( transitive @ SV19 )
| ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) ) )
| ~ ( ~ ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
| ( transitive @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(277,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( well_ordering @ SV20 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
| ( well_ordering @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(278,plain,
! [SV21: $i] :
( ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( well_founded_relation @ SV21 )
| ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
| ( well_founded_relation @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(279,plain,
! [SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( connected @ SV22 )
| ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) ) )
| ~ ( ~ ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
| ( connected @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(280,plain,
! [SV23: $i] :
( ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ( relation_field @ SV23 )
= ( set_union2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(281,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ! [SY19: $i] :
~ ( ~ ( ~ ( well_orders @ SV16 @ SY19 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SY19 )
| ~ ( is_transitive_in @ SV16 @ SY19 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SY19 ) )
| ~ ( is_connected_in @ SV16 @ SY19 ) )
| ~ ( is_well_founded_in @ SV16 @ SY19 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SY19 )
| ~ ( is_transitive_in @ SV16 @ SY19 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SY19 ) )
| ~ ( is_connected_in @ SV16 @ SY19 ) )
| ~ ( is_well_founded_in @ SV16 @ SY19 ) )
| ( well_orders @ SV16 @ SY19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(282,plain,
( ( well_ordering @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(283,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ~ ( ~ ( ~ ( reflexive @ SV17 )
| ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
| ( reflexive @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(284,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( ~ ( ~ ( antisymmetric @ SV18 )
| ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
| ( antisymmetric @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(285,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ~ ( ~ ( ~ ( transitive @ SV19 )
| ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) ) )
| ~ ( ~ ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
| ( transitive @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(286,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ~ ( ~ ( ~ ( well_ordering @ SV20 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
| ( well_ordering @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(287,plain,
! [SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( ~ ( ~ ( ~ ( well_founded_relation @ SV21 )
| ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
| ( well_founded_relation @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(288,plain,
! [SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( ~ ( ~ ( ~ ( connected @ SV22 )
| ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) ) )
| ~ ( ~ ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
| ( connected @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(289,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( ( relation_field @ SV23 )
= ( set_union2 @ ( relation_dom @ SV23 ) @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(290,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( well_orders @ SV16 @ SV26 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) )
| ( well_orders @ SV16 @ SV26 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(291,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( reflexive @ SV17 )
| ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) ) )
| ~ ( ~ ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
| ( reflexive @ SV17 ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(292,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ( antisymmetric @ SV18 )
| ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) ) )
| ~ ( ~ ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
| ( antisymmetric @ SV18 ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(293,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( transitive @ SV19 )
| ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) ) )
| ~ ( ~ ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
| ( transitive @ SV19 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(294,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( well_ordering @ SV20 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
| ( well_ordering @ SV20 ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(295,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( well_founded_relation @ SV21 )
| ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) ) )
| ~ ( ~ ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
| ( well_founded_relation @ SV21 ) ) )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(296,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( connected @ SV22 )
| ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) ) )
| ~ ( ~ ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
| ( connected @ SV22 ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(297,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ( well_orders @ SV16 @ SV26 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) )
| ( well_orders @ SV16 @ SV26 ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(298,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( reflexive @ SV17 )
| ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(299,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
| ( reflexive @ SV17 ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(300,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ( antisymmetric @ SV18 )
| ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(301,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
| ( antisymmetric @ SV18 ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(302,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( transitive @ SV19 )
| ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(303,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
| ( transitive @ SV19 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(304,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( well_ordering @ SV20 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(305,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
| ( well_ordering @ SV20 ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(306,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( well_founded_relation @ SV21 )
| ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) ) ) )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(307,plain,
! [SV21: $i] :
( ( ( ~ ( ~ ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
| ( well_founded_relation @ SV21 ) ) )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(308,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( connected @ SV22 )
| ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(309,plain,
! [SV22: $i] :
( ( ( ~ ( ~ ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
| ( connected @ SV22 ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(310,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ( well_orders @ SV16 @ SV26 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(311,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) )
| ( well_orders @ SV16 @ SV26 ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(312,plain,
! [SV17: $i] :
( ( ( ~ ( reflexive @ SV17 )
| ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(313,plain,
! [SV17: $i] :
( ( ( ~ ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
| ( reflexive @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(314,plain,
! [SV18: $i] :
( ( ( ~ ( antisymmetric @ SV18 )
| ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(315,plain,
! [SV18: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
| ( antisymmetric @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(316,plain,
! [SV19: $i] :
( ( ( ~ ( transitive @ SV19 )
| ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(317,plain,
! [SV19: $i] :
( ( ( ~ ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
| ( transitive @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(318,plain,
! [SV20: $i] :
( ( ( ~ ( well_ordering @ SV20 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(319,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
| ( well_ordering @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(320,plain,
! [SV21: $i] :
( ( ( ~ ( well_founded_relation @ SV21 )
| ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(321,plain,
! [SV21: $i] :
( ( ( ~ ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
| ( well_founded_relation @ SV21 ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(322,plain,
! [SV22: $i] :
( ( ( ~ ( connected @ SV22 )
| ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(323,plain,
! [SV22: $i] :
( ( ( ~ ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
| ( connected @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(324,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( well_orders @ SV16 @ SV26 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(325,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) )
| ( well_orders @ SV16 @ SV26 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(326,plain,
! [SV17: $i] :
( ( ( ~ ( reflexive @ SV17 ) )
= $true )
| ( ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(327,plain,
! [SV17: $i] :
( ( ( ~ ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) ) )
= $true )
| ( ( reflexive @ SV17 )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(328,plain,
! [SV18: $i] :
( ( ( ~ ( antisymmetric @ SV18 ) )
= $true )
| ( ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(329,plain,
! [SV18: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) ) )
= $true )
| ( ( antisymmetric @ SV18 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(330,plain,
! [SV19: $i] :
( ( ( ~ ( transitive @ SV19 ) )
= $true )
| ( ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(331,plain,
! [SV19: $i] :
( ( ( ~ ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) ) )
= $true )
| ( ( transitive @ SV19 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(332,plain,
! [SV20: $i] :
( ( ( ~ ( well_ordering @ SV20 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(333,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(334,plain,
! [SV21: $i] :
( ( ( ~ ( well_founded_relation @ SV21 ) )
= $true )
| ( ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(335,plain,
! [SV21: $i] :
( ( ( ~ ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) ) )
= $true )
| ( ( well_founded_relation @ SV21 )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(336,plain,
! [SV22: $i] :
( ( ( ~ ( connected @ SV22 ) )
= $true )
| ( ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(337,plain,
! [SV22: $i] :
( ( ( ~ ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) ) )
= $true )
| ( ( connected @ SV22 )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(338,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( well_orders @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(339,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(340,plain,
! [SV17: $i] :
( ( ( reflexive @ SV17 )
= $false )
| ( ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(341,plain,
! [SV17: $i] :
( ( ( is_reflexive_in @ SV17 @ ( relation_field @ SV17 ) )
= $false )
| ( ( reflexive @ SV17 )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(342,plain,
! [SV18: $i] :
( ( ( antisymmetric @ SV18 )
= $false )
| ( ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(343,plain,
! [SV18: $i] :
( ( ( is_antisymmetric_in @ SV18 @ ( relation_field @ SV18 ) )
= $false )
| ( ( antisymmetric @ SV18 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(344,plain,
! [SV19: $i] :
( ( ( transitive @ SV19 )
= $false )
| ( ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(345,plain,
! [SV19: $i] :
( ( ( is_transitive_in @ SV19 @ ( relation_field @ SV19 ) )
= $false )
| ( ( transitive @ SV19 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(346,plain,
! [SV20: $i] :
( ( ( well_ordering @ SV20 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(347,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) ) )
= $false )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(348,plain,
! [SV21: $i] :
( ( ( well_founded_relation @ SV21 )
= $false )
| ( ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(349,plain,
! [SV21: $i] :
( ( ( is_well_founded_in @ SV21 @ ( relation_field @ SV21 ) )
= $false )
| ( ( well_founded_relation @ SV21 )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(350,plain,
! [SV22: $i] :
( ( ( connected @ SV22 )
= $false )
| ( ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(351,plain,
! [SV22: $i] :
( ( ( is_connected_in @ SV22 @ ( relation_field @ SV22 ) )
= $false )
| ( ( connected @ SV22 )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(352,plain,
! [SV26: $i,SV16: $i] :
( ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(353,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(354,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(355,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
| ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(356,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(357,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
| ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(358,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(359,plain,
! [SV20: $i] :
( ( ( ~ ( well_founded_relation @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(360,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(361,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(362,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(363,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(364,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) ) )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(365,plain,
! [SV20: $i] :
( ( ( well_founded_relation @ SV20 )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(366,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) ) )
= $false )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(367,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(368,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_well_founded_in @ SV16 @ SV26 )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(369,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) ) )
= $false )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(370,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(371,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
| ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(372,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(373,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
| ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(374,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(375,plain,
! [SV20: $i] :
( ( ( ~ ( connected @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(376,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(377,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(378,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(379,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(380,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) ) )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(381,plain,
! [SV20: $i] :
( ( ( connected @ SV20 )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(382,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) ) )
= $false )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(383,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(384,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_connected_in @ SV16 @ SV26 )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(385,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) ) )
= $false )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(386,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(387,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
| ~ ( antisymmetric @ SV20 ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(388,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(389,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
| ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(390,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(391,plain,
! [SV20: $i] :
( ( ( ~ ( antisymmetric @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(392,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) ) )
= $true )
| ( ( ~ ( antisymmetric @ SV20 ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(393,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(394,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(395,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(396,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) ) )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(397,plain,
! [SV20: $i] :
( ( ( antisymmetric @ SV20 )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(398,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) ) )
= $false )
| ( ( ~ ( antisymmetric @ SV20 ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(399,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(400,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_antisymmetric_in @ SV16 @ SV26 )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(401,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) ) )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(402,plain,
! [SV20: $i] :
( ( ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(403,plain,
! [SV20: $i] :
( ( ( ~ ( reflexive @ SV20 )
| ~ ( transitive @ SV20 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV20 ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(404,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(405,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_reflexive_in @ SV16 @ SV26 )
| ~ ( is_transitive_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(406,plain,
! [SV20: $i] :
( ( ( ~ ( reflexive @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(407,plain,
! [SV20: $i] :
( ( ( ~ ( transitive @ SV20 ) )
= $false )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(408,plain,
! [SV20: $i] :
( ( ( ~ ( reflexive @ SV20 ) )
= $true )
| ( ( ~ ( transitive @ SV20 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV20 ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(409,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_reflexive_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(410,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_transitive_in @ SV16 @ SV26 ) )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(411,plain,
! [SV26: $i,SV16: $i] :
( ( ( ~ ( is_reflexive_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(412,plain,
! [SV20: $i] :
( ( ( reflexive @ SV20 )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(413,plain,
! [SV20: $i] :
( ( ( transitive @ SV20 )
= $true )
| ( ( well_ordering @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(414,plain,
! [SV20: $i] :
( ( ( reflexive @ SV20 )
= $false )
| ( ( ~ ( transitive @ SV20 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV20 ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(415,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_reflexive_in @ SV16 @ SV26 )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(416,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_transitive_in @ SV16 @ SV26 )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(417,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_reflexive_in @ SV16 @ SV26 )
= $false )
| ( ( ~ ( is_transitive_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(418,plain,
! [SV20: $i] :
( ( ( transitive @ SV20 )
= $false )
| ( ( reflexive @ SV20 )
= $false )
| ( ( ~ ( antisymmetric @ SV20 ) )
= $true )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(419,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_transitive_in @ SV16 @ SV26 )
= $false )
| ( ( is_reflexive_in @ SV16 @ SV26 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(420,plain,
! [SV20: $i] :
( ( ( antisymmetric @ SV20 )
= $false )
| ( ( reflexive @ SV20 )
= $false )
| ( ( transitive @ SV20 )
= $false )
| ( ( ~ ( connected @ SV20 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(421,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_antisymmetric_in @ SV16 @ SV26 )
= $false )
| ( ( is_reflexive_in @ SV16 @ SV26 )
= $false )
| ( ( is_transitive_in @ SV16 @ SV26 )
= $false )
| ( ( ~ ( is_connected_in @ SV16 @ SV26 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(422,plain,
! [SV20: $i] :
( ( ( connected @ SV20 )
= $false )
| ( ( transitive @ SV20 )
= $false )
| ( ( reflexive @ SV20 )
= $false )
| ( ( antisymmetric @ SV20 )
= $false )
| ( ( ~ ( well_founded_relation @ SV20 ) )
= $true )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(423,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_connected_in @ SV16 @ SV26 )
= $false )
| ( ( is_transitive_in @ SV16 @ SV26 )
= $false )
| ( ( is_reflexive_in @ SV16 @ SV26 )
= $false )
| ( ( is_antisymmetric_in @ SV16 @ SV26 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV16 @ SV26 ) )
= $true )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(424,plain,
! [SV20: $i] :
( ( ( well_founded_relation @ SV20 )
= $false )
| ( ( antisymmetric @ SV20 )
= $false )
| ( ( reflexive @ SV20 )
= $false )
| ( ( transitive @ SV20 )
= $false )
| ( ( connected @ SV20 )
= $false )
| ( ( well_ordering @ SV20 )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(425,plain,
! [SV26: $i,SV16: $i] :
( ( ( is_well_founded_in @ SV16 @ SV26 )
= $false )
| ( ( is_antisymmetric_in @ SV16 @ SV26 )
= $false )
| ( ( is_reflexive_in @ SV16 @ SV26 )
= $false )
| ( ( is_transitive_in @ SV16 @ SV26 )
= $false )
| ( ( is_connected_in @ SV16 @ SV26 )
= $false )
| ( ( well_orders @ SV16 @ SV26 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(426,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[241,425,424,416,415,413,412,400,397,384,381,368,365,351,350,349,348,345,344,343,342,341,340,289,282,273,270,269,247,244,243,242]) ).
thf(427,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[426,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU244+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:09:09 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.15/0.41
% 1.15/0.41 No.of.Axioms: 14
% 1.15/0.41
% 1.15/0.41 Length.of.Defs: 0
% 1.15/0.41
% 1.15/0.41 Contains.Choice.Funs: false
% 1.15/0.41 .........
% 1.15/0.41
% 1.15/0.41 ********************************
% 1.15/0.41 * All subproblems solved! *
% 1.15/0.41 ********************************
% 1.15/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,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:426,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.15/0.41
% 1.15/0.41 %**** Beginning of derivation protocol ****
% 1.15/0.41 % SZS output start CNFRefutation
% See solution above
% 1.15/0.41
% 1.15/0.41 %**** End of derivation protocol ****
% 1.15/0.41 %**** no. of clauses in derivation: 427 ****
% 1.15/0.41 %**** clause counter: 426 ****
% 1.15/0.41
% 1.15/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,ps:3,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:426,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------