TSTP Solution File: SEU199+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU199+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:08:03 EDT 2022
% Result : Theorem 80.76s 81.06s
% Output : CNFRefutation 80.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 54
% Syntax : Number of formulae : 376 ( 183 unt; 24 typ; 0 def)
% Number of atoms : 2530 ( 745 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 5412 ( 775 ~; 798 |; 49 &;3751 @)
% ( 8 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 860 ( 0 ^ 846 !; 14 ?; 860 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_SY56,type,
sK11_SY56: $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_SY57,type,
sK13_SY57: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY55,type,
sK2_SY55: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_B,type,
sK4_B: $i > $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_B,type,
sK9_B: $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(10,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(12,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(13,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(14,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(15,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(16,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(18,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(20,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(21,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(31,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(34,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(36,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(37,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(48,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(49,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(50,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(51,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(52,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(53,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(54,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(56,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(58,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(59,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(60,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(74,plain,
( ( ! [SY55: $i] :
( ( relation @ SY55 )
=> ( subset @ ( relation_rng_restriction @ sK1_A @ SY55 ) @ SY55 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(75,plain,
( ( ( relation @ sK2_SY55 )
=> ( subset @ ( relation_rng_restriction @ sK1_A @ sK2_SY55 ) @ sK2_SY55 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(76,plain,
( ( relation @ sK2_SY55 )
= $true ),
inference(standard_cnf,[status(thm)],[75]) ).
thf(77,plain,
( ( subset @ ( relation_rng_restriction @ sK1_A @ sK2_SY55 ) @ sK2_SY55 )
= $false ),
inference(standard_cnf,[status(thm)],[75]) ).
thf(78,plain,
( ( ~ ( subset @ ( relation_rng_restriction @ sK1_A @ sK2_SY55 ) @ sK2_SY55 ) )
= $true ),
inference(polarity_switch,[status(thm)],[77]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(81,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(82,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(83,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(87,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(88,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( element @ ( sK4_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK4_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(90,plain,
( ( ~ ( empty @ sK5_A )
& ( relation @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(91,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(93,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(94,plain,
( ( ! [A: $i] : ( element @ ( sK9_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(96,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY56 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY56 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK13_SY57 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK13_SY57 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_rng_restriction @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(98,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(101,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK13_SY57 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK13_SY57 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK12_D @ C @ B @ A ) @ ( sK13_SY57 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_rng_restriction @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(104,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY56 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY56 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(113,plain,
( ( ! [A: $i] : ( element @ ( sK9_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(114,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(115,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(117,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(119,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(120,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(122,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(123,plain,
( ( ~ ( empty @ sK5_A )
& ( relation @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(124,plain,
( ( ! [A: $i] :
( ( element @ ( sK4_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK4_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(125,plain,
( ( ~ ( empty @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(126,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(127,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(128,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(130,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(132,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(135,plain,
( ( relation @ sK2_SY55 )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(136,plain,
( ( ~ ( subset @ ( relation_rng_restriction @ sK1_A @ sK2_SY55 ) @ sK2_SY55 ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(137,plain,
( ( ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(139,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(140,plain,
( ( ~ ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(141,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK4_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK4_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(142,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK7_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK7_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY57 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ SX4 @ SX0 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(144,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY56 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY56 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(145,plain,
! [SV1: $i] :
( ( ! [SY58: $i] :
( ~ ( in @ SV1 @ SY58 )
| ~ ( in @ SY58 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(146,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( relation @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(147,plain,
! [SV3: $i] :
( ( ! [SY59: $i] :
( ( unordered_pair @ SV3 @ SY59 )
= ( unordered_pair @ SY59 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(148,plain,
! [SV4: $i] :
( ( ! [SY60: $i] :
( ( ordered_pair @ SV4 @ SY60 )
= ( unordered_pair @ ( unordered_pair @ SV4 @ SY60 ) @ ( singleton @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(149,plain,
! [SV5: $i] :
( ( ! [SY61: $i] :
( ~ ( relation @ SY61 )
| ( relation @ ( relation_rng_restriction @ SV5 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(150,plain,
! [SV6: $i] :
( ( element @ ( sK9_B @ SV6 ) @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(151,plain,
! [SV7: $i] :
( ( ~ ( empty @ ( powerset @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(152,plain,
! [SV8: $i] :
( ( ! [SY62: $i] :
~ ( empty @ ( ordered_pair @ SV8 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(153,plain,
! [SV9: $i] :
( ( ~ ( empty @ ( singleton @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(154,plain,
! [SV10: $i] :
( ( ! [SY63: $i] :
~ ( empty @ ( unordered_pair @ SV10 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(155,plain,
( ( empty @ sK3_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(156,plain,
! [SV11: $i] :
( ( subset @ SV11 @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(157,plain,
! [SV12: $i] :
( ( ! [SY64: $i] :
( ~ ( in @ SV12 @ SY64 )
| ( element @ SV12 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(158,plain,
! [SV13: $i] :
( ( ! [SY65: $i] :
( ~ ( element @ SV13 @ SY65 )
| ( empty @ SY65 )
| ( in @ SV13 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(159,plain,
! [SV14: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( element @ SY66 @ ( powerset @ SY67 ) )
| ~ ( in @ SV14 @ SY66 )
| ( element @ SV14 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(160,plain,
! [SV15: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ~ ( element @ SY68 @ ( powerset @ SY69 ) )
| ~ ( in @ SV15 @ SY68 )
| ~ ( empty @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(161,plain,
! [SV16: $i] :
( ( ~ ( empty @ SV16 )
| ( SV16 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(162,plain,
! [SV17: $i] :
( ( ! [SY70: $i] :
( ~ ( empty @ SY70 )
| ~ ( in @ SV17 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(163,plain,
! [SV18: $i] :
( ( ! [SY71: $i] :
( ( SV18 = SY71 )
| ~ ( empty @ SV18 )
| ~ ( empty @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(164,plain,
( ( subset @ ( relation_rng_restriction @ sK1_A @ sK2_SY55 ) @ sK2_SY55 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(165,plain,
( ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(166,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(167,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(168,plain,
( ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(169,plain,
! [SV19: $i] :
( ( ~ ( ~ ( element @ ( sK4_B @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ( empty @ ( sK4_B @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(170,plain,
! [SV20: $i] :
( ( ( empty @ SV20 )
| ~ ( ~ ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK7_B @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(171,plain,
! [SV21: $i] :
( ( ! [SY72: $i] :
( ~ ( relation @ SY72 )
| ~ ( ~ ! [SY73: $i] :
( ~ ( relation @ SY73 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SY73 @ SY72 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY73 @ SY72 @ SV21 ) @ ( sK13_SY57 @ SY73 @ SY72 @ SV21 ) ) @ SY72 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY73 @ SY72 @ SV21 ) @ ( sK13_SY57 @ SY73 @ SY72 @ SV21 ) ) @ SY73 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SY73 @ SY72 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY73 @ SY72 @ SV21 ) @ ( sK13_SY57 @ SY73 @ SY72 @ SV21 ) ) @ SY73 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SY73 @ SY72 @ SV21 ) @ ( sK13_SY57 @ SY73 @ SY72 @ SV21 ) ) @ SY72 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY73 @ SY72 @ SV21 ) @ ( sK13_SY57 @ SY73 @ SY72 @ SV21 ) ) @ SY73 ) ) ) )
| ( SY73
= ( relation_rng_restriction @ SV21 @ SY72 ) ) )
| ~ ! [SY74: $i] :
( ~ ( relation @ SY74 )
| ( SY74
!= ( relation_rng_restriction @ SV21 @ SY72 ) )
| ~ ( ~ ! [SY75: $i,SY76: $i] :
( ~ ( in @ SY76 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY75 @ SY76 ) @ SY72 )
| ( in @ ( ordered_pair @ SY75 @ SY76 ) @ SY74 ) )
| ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( in @ ( ordered_pair @ SY77 @ SY78 ) @ SY74 )
| ( in @ SY78 @ SV21 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY74 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY72 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(172,plain,
! [SV22: $i] :
( ( ~ ( relation @ SV22 )
| ~ ( ~ ! [SY81: $i] :
( ~ ( relation @ SY81 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SY81 ) )
| ( subset @ SV22 @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( relation @ SY82 )
| ~ ( subset @ SV22 @ SY82 )
| ! [SY83: $i,SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV22 )
| ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(173,plain,
! [SV23: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV23 )
| ~ ( in @ SV23 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(174,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(175,plain,
! [SV24: $i,SV3: $i] :
( ( ( unordered_pair @ SV3 @ SV24 )
= ( unordered_pair @ SV24 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(176,plain,
! [SV25: $i,SV4: $i] :
( ( ( ordered_pair @ SV4 @ SV25 )
= ( unordered_pair @ ( unordered_pair @ SV4 @ SV25 ) @ ( singleton @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(177,plain,
! [SV5: $i,SV26: $i] :
( ( ~ ( relation @ SV26 )
| ( relation @ ( relation_rng_restriction @ SV5 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(178,plain,
! [SV7: $i] :
( ( empty @ ( powerset @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(179,plain,
! [SV27: $i,SV8: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV8 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(180,plain,
! [SV9: $i] :
( ( empty @ ( singleton @ SV9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(181,plain,
! [SV28: $i,SV10: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV10 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(182,plain,
! [SV29: $i,SV12: $i] :
( ( ~ ( in @ SV12 @ SV29 )
| ( element @ SV12 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(183,plain,
! [SV30: $i,SV13: $i] :
( ( ~ ( element @ SV13 @ SV30 )
| ( empty @ SV30 )
| ( in @ SV13 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(184,plain,
! [SV14: $i,SV31: $i] :
( ( ! [SY85: $i] :
( ~ ( element @ SV31 @ ( powerset @ SY85 ) )
| ~ ( in @ SV14 @ SV31 )
| ( element @ SV14 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(185,plain,
! [SV15: $i,SV32: $i] :
( ( ! [SY86: $i] :
( ~ ( element @ SV32 @ ( powerset @ SY86 ) )
| ~ ( in @ SV15 @ SV32 )
| ~ ( empty @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(186,plain,
! [SV16: $i] :
( ( ( ~ ( empty @ SV16 ) )
= $true )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(187,plain,
! [SV17: $i,SV33: $i] :
( ( ~ ( empty @ SV33 )
| ~ ( in @ SV17 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(188,plain,
! [SV34: $i,SV18: $i] :
( ( ( SV18 = SV34 )
| ~ ( empty @ SV18 )
| ~ ( empty @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(189,plain,
( ( ~ ~ ( empty @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(190,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(191,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(192,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(193,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(194,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(195,plain,
( ( ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(196,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(197,plain,
! [SV19: $i] :
( ( ~ ( element @ ( sK4_B @ SV19 ) @ ( powerset @ SV19 ) )
| ~ ( empty @ ( sK4_B @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(198,plain,
! [SV20: $i] :
( ( ( empty @ SV20 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK7_B @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(199,plain,
! [SV21: $i,SV35: $i] :
( ( ~ ( relation @ SV35 )
| ~ ( ~ ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) ) ) )
| ( SY87
= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
| ~ ! [SY88: $i] :
( ~ ( relation @ SY88 )
| ( SY88
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( in @ SY90 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV35 )
| ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SY88 ) )
| ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( in @ ( ordered_pair @ SY77 @ SY78 ) @ SY88 )
| ( in @ SY78 @ SV21 ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SY88 )
| ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SV35 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(200,plain,
! [SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( ~ ( ~ ! [SY81: $i] :
( ~ ( relation @ SY81 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SY81 ) )
| ( subset @ SV22 @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( relation @ SY82 )
| ~ ( subset @ SV22 @ SY82 )
| ! [SY83: $i,SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV22 )
| ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SY82 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(201,plain,
! [SV23: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV23 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(202,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( relation @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(203,plain,
! [SV5: $i,SV26: $i] :
( ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV5 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(204,plain,
! [SV27: $i,SV8: $i] :
( ( empty @ ( ordered_pair @ SV8 @ SV27 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(205,plain,
! [SV28: $i,SV10: $i] :
( ( empty @ ( unordered_pair @ SV10 @ SV28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(206,plain,
! [SV29: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV29 ) )
= $true )
| ( ( element @ SV12 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(207,plain,
! [SV30: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ SV30 ) )
= $true )
| ( ( ( empty @ SV30 )
| ( in @ SV13 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(208,plain,
! [SV14: $i,SV36: $i,SV31: $i] :
( ( ~ ( element @ SV31 @ ( powerset @ SV36 ) )
| ~ ( in @ SV14 @ SV31 )
| ( element @ SV14 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(209,plain,
! [SV15: $i,SV37: $i,SV32: $i] :
( ( ~ ( element @ SV32 @ ( powerset @ SV37 ) )
| ~ ( in @ SV15 @ SV32 )
| ~ ( empty @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(210,plain,
! [SV16: $i] :
( ( ( empty @ SV16 )
= $false )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(211,plain,
! [SV17: $i,SV33: $i] :
( ( ( ~ ( empty @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV17 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(212,plain,
! [SV34: $i,SV18: $i] :
( ( ( ( SV18 = SV34 )
| ~ ( empty @ SV18 ) )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(213,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(214,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(215,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(216,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(217,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(218,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(219,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(220,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(221,plain,
! [SV19: $i] :
( ( ~ ( element @ ( sK4_B @ SV19 ) @ ( powerset @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(222,plain,
! [SV19: $i] :
( ( ~ ( empty @ ( sK4_B @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(223,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ~ ( empty @ ( sK7_B @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(224,plain,
! [SV21: $i,SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( ~ ( ~ ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) ) ) )
| ( SY87
= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
| ~ ! [SY88: $i] :
( ~ ( relation @ SY88 )
| ( SY88
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( in @ SY90 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV35 )
| ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SY88 ) )
| ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( in @ ( ordered_pair @ SY77 @ SY78 ) @ SY88 )
| ( in @ SY78 @ SV21 ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SY88 )
| ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SV35 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(225,plain,
! [SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( ~ ( ~ ! [SY81: $i] :
( ~ ( relation @ SY81 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SY81 ) )
| ( subset @ SV22 @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( relation @ SY82 )
| ~ ( subset @ SV22 @ SY82 )
| ! [SY83: $i,SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV22 )
| ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SY82 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV23: $i,SV1: $i] :
( ( ( in @ SV1 @ SV23 )
= $false )
| ( ( ~ ( in @ SV23 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(227,plain,
! [SV5: $i,SV26: $i] :
( ( ( relation @ SV26 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV5 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(228,plain,
! [SV29: $i,SV12: $i] :
( ( ( in @ SV12 @ SV29 )
= $false )
| ( ( element @ SV12 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(229,plain,
! [SV30: $i,SV13: $i] :
( ( ( element @ SV13 @ SV30 )
= $false )
| ( ( ( empty @ SV30 )
| ( in @ SV13 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(230,plain,
! [SV14: $i,SV36: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV36 ) )
| ~ ( in @ SV14 @ SV31 ) )
= $true )
| ( ( element @ SV14 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(231,plain,
! [SV15: $i,SV37: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV37 ) )
| ~ ( in @ SV15 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(232,plain,
! [SV17: $i,SV33: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( ~ ( in @ SV17 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(233,plain,
! [SV34: $i,SV18: $i] :
( ( ( SV18 = SV34 )
= $true )
| ( ( ~ ( empty @ SV18 ) )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(234,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(235,plain,
! [SV38: $i] :
( ( ! [SY95: $i] :
( ~ ( element @ SV38 @ ( powerset @ SY95 ) )
| ( subset @ SV38 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(236,plain,
! [SV39: $i] :
( ( ! [SY96: $i] :
( ~ ( subset @ SV39 @ SY96 )
| ( element @ SV39 @ ( powerset @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(237,plain,
! [SV19: $i] :
( ( element @ ( sK4_B @ SV19 ) @ ( powerset @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(238,plain,
! [SV19: $i] :
( ( empty @ ( sK4_B @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(239,plain,
! [SV20: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(240,plain,
! [SV20: $i] :
( ( ( ~ ~ ( empty @ ( sK7_B @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[223]) ).
thf(241,plain,
! [SV21: $i,SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( ~ ( ~ ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) ) ) )
| ( SY87
= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
| ~ ! [SY88: $i] :
( ~ ( relation @ SY88 )
| ( SY88
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( in @ SY90 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV35 )
| ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SY88 ) )
| ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( in @ ( ordered_pair @ SY77 @ SY78 ) @ SY88 )
| ( in @ SY78 @ SV21 ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SY88 )
| ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SV35 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(242,plain,
! [SV22: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( relation @ SY81 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SY81 ) )
| ( subset @ SV22 @ SY81 ) )
| ~ ! [SY82: $i] :
( ~ ( relation @ SY82 )
| ~ ( subset @ SV22 @ SY82 )
| ! [SY83: $i,SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV22 )
| ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SY82 ) ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(243,plain,
! [SV1: $i,SV23: $i] :
( ( ( in @ SV23 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(244,plain,
! [SV13: $i,SV30: $i] :
( ( ( empty @ SV30 )
= $true )
| ( ( in @ SV13 @ SV30 )
= $true )
| ( ( element @ SV13 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV14: $i,SV36: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV31 ) )
= $true )
| ( ( element @ SV14 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV15: $i,SV37: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(247,plain,
! [SV33: $i,SV17: $i] :
( ( ( in @ SV17 @ SV33 )
= $false )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV34: $i,SV18: $i] :
( ( ( empty @ SV18 )
= $false )
| ( ( SV18 = SV34 )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV40: $i,SV38: $i] :
( ( ~ ( element @ SV38 @ ( powerset @ SV40 ) )
| ( subset @ SV38 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(250,plain,
! [SV41: $i,SV39: $i] :
( ( ~ ( subset @ SV39 @ SV41 )
| ( element @ SV39 @ ( powerset @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(251,plain,
! [SV20: $i] :
( ( ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(252,plain,
! [SV20: $i] :
( ( ( ~ ( empty @ ( sK7_B @ SV20 ) ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(253,plain,
! [SV21: $i,SV35: $i] :
( ( ( ~ ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) ) ) )
| ( SY87
= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
| ~ ! [SY88: $i] :
( ~ ( relation @ SY88 )
| ( SY88
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( in @ SY90 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV35 )
| ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SY88 ) )
| ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( in @ ( ordered_pair @ SY77 @ SY78 ) @ SY88 )
| ( in @ SY78 @ SV21 ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SY88 )
| ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SV35 ) ) ) ) ) )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(254,plain,
! [SV22: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( relation @ SY81 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SY81 ) )
| ( subset @ SV22 @ SY81 ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(255,plain,
! [SV22: $i] :
( ( ( ~ ! [SY82: $i] :
( ~ ( relation @ SY82 )
| ~ ( subset @ SV22 @ SY82 )
| ! [SY83: $i,SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV22 )
| ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SY82 ) ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(256,plain,
! [SV14: $i,SV36: $i,SV31: $i] :
( ( ( element @ SV31 @ ( powerset @ SV36 ) )
= $false )
| ( ( ~ ( in @ SV14 @ SV31 ) )
= $true )
| ( ( element @ SV14 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(257,plain,
! [SV15: $i,SV37: $i,SV32: $i] :
( ( ( element @ SV32 @ ( powerset @ SV37 ) )
= $false )
| ( ( ~ ( in @ SV15 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(258,plain,
! [SV18: $i,SV34: $i] :
( ( ( empty @ SV34 )
= $false )
| ( ( SV18 = SV34 )
= $true )
| ( ( empty @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(259,plain,
! [SV40: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( powerset @ SV40 ) ) )
= $true )
| ( ( subset @ SV38 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(260,plain,
! [SV41: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV41 ) )
= $true )
| ( ( element @ SV39 @ ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(261,plain,
! [SV20: $i] :
( ( ( empty @ ( sK7_B @ SV20 ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(262,plain,
! [SV21: $i,SV35: $i] :
( ( ( ~ ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) ) ) )
| ( SY87
= ( relation_rng_restriction @ SV21 @ SV35 ) ) ) )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(263,plain,
! [SV35: $i,SV21: $i] :
( ( ( ~ ! [SY88: $i] :
( ~ ( relation @ SY88 )
| ( SY88
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( in @ SY90 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV35 )
| ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SY88 ) )
| ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( in @ ( ordered_pair @ SY77 @ SY78 ) @ SY88 )
| ( in @ SY78 @ SV21 ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SY88 )
| ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SV35 ) ) ) ) ) )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(264,plain,
! [SV22: $i] :
( ( ( ! [SY81: $i] :
( ~ ( relation @ SY81 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY81 @ SV22 ) @ ( sK11_SY56 @ SY81 @ SV22 ) ) @ SY81 ) )
| ( subset @ SV22 @ SY81 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(265,plain,
! [SV22: $i] :
( ( ( ! [SY82: $i] :
( ~ ( relation @ SY82 )
| ~ ( subset @ SV22 @ SY82 )
| ! [SY83: $i,SY84: $i] :
( ~ ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SV22 )
| ( in @ ( ordered_pair @ SY83 @ SY84 ) @ SY82 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(266,plain,
! [SV36: $i,SV31: $i,SV14: $i] :
( ( ( in @ SV14 @ SV31 )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV36 ) )
= $false )
| ( ( element @ SV14 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(267,plain,
! [SV37: $i,SV32: $i,SV15: $i] :
( ( ( in @ SV15 @ SV32 )
= $false )
| ( ( element @ SV32 @ ( powerset @ SV37 ) )
= $false )
| ( ( ~ ( empty @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(268,plain,
! [SV40: $i,SV38: $i] :
( ( ( element @ SV38 @ ( powerset @ SV40 ) )
= $false )
| ( ( subset @ SV38 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV41: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV41 )
= $false )
| ( ( element @ SV39 @ ( powerset @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(270,plain,
! [SV21: $i,SV35: $i] :
( ( ( ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SY87 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SY87 @ SV35 @ SV21 ) ) @ SY87 ) ) ) )
| ( SY87
= ( relation_rng_restriction @ SV21 @ SV35 ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(271,plain,
! [SV35: $i,SV21: $i] :
( ( ( ! [SY88: $i] :
( ~ ( relation @ SY88 )
| ( SY88
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY89: $i,SY90: $i] :
( ~ ( in @ SY90 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SV35 )
| ( in @ ( ordered_pair @ SY89 @ SY90 ) @ SY88 ) )
| ~ ~ ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( in @ ( ordered_pair @ SY77 @ SY78 ) @ SY88 )
| ( in @ SY78 @ SV21 ) )
| ~ ! [SY93: $i,SY94: $i] :
( ~ ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SY88 )
| ( in @ ( ordered_pair @ SY93 @ SY94 ) @ SV35 ) ) ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(272,plain,
! [SV22: $i,SV42: $i] :
( ( ( ~ ( relation @ SV42 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 ) )
| ( subset @ SV22 @ SV42 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV22: $i,SV43: $i] :
( ( ( ~ ( relation @ SV43 )
| ~ ( subset @ SV22 @ SV43 )
| ! [SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV22 )
| ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV43 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV15: $i,SV32: $i,SV37: $i] :
( ( ( empty @ SV37 )
= $false )
| ( ( element @ SV32 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV15 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(275,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 )
| ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) ) )
| ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(276,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ~ ( relation @ SV45 )
| ( SV45
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) )
| ~ ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(277,plain,
! [SV22: $i,SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 ) )
| ( subset @ SV22 @ SV42 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(278,plain,
! [SV22: $i,SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ~ ( subset @ SV22 @ SV43 )
| ! [SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV22 )
| ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV43 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(279,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) ) )
| ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(280,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ( SV45
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) )
| ~ ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(281,plain,
! [SV22: $i,SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 ) )
| ( subset @ SV22 @ SV42 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(282,plain,
! [SV22: $i,SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ~ ( subset @ SV22 @ SV43 )
| ! [SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV22 )
| ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV43 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) ) )
| ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(284,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ( SV45
!= ( relation_rng_restriction @ SV21 @ SV35 ) )
| ~ ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) )
| ~ ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(285,plain,
! [SV22: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 ) ) )
= $true )
| ( ( subset @ SV22 @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(286,plain,
! [SV43: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV43 ) )
= $true )
| ( ( ! [SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV22 )
| ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV43 ) ) )
= $true )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(287,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) ) ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(288,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ( SV45
!= ( relation_rng_restriction @ SV21 @ SV35 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) )
| ~ ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(289,plain,
! [SV22: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV22 )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 ) )
= $false )
| ( ( subset @ SV22 @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(290,plain,
! [SV43: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV43 )
= $false )
| ( ( ! [SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV22 )
| ( in @ ( ordered_pair @ SY97 @ SY98 ) @ SV43 ) ) )
= $true )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(291,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) ) )
= $false )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(292,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( ~ ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) )
| ~ ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(293,plain,
! [SV22: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV22 ) )
= $false )
| ( ( subset @ SV22 @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(294,plain,
! [SV22: $i,SV42: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 ) )
= $false )
| ( ( subset @ SV22 @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(295,plain,
! [SV43: $i,SV22: $i,SV46: $i] :
( ( ( ! [SY105: $i] :
( ~ ( in @ ( ordered_pair @ SV46 @ SY105 ) @ SV22 )
| ( in @ ( ordered_pair @ SV46 @ SY105 ) @ SV43 ) ) )
= $true )
| ( ( subset @ SV22 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(296,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) )
= $false )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(297,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) ) )
= $false )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(298,plain,
! [SV45: $i,SV35: $i,SV21: $i] :
( ( ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) )
| ~ ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) )
= $false )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(299,plain,
! [SV22: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV22 )
= $true )
| ( ( subset @ SV22 @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(300,plain,
! [SV22: $i,SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 ) )
= $true )
| ( ( subset @ SV22 @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(301,plain,
! [SV43: $i,SV22: $i,SV47: $i,SV46: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV47 ) @ SV22 )
| ( in @ ( ordered_pair @ SV46 @ SV47 ) @ SV43 ) )
= $true )
| ( ( subset @ SV22 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(302,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(303,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(304,plain,
! [SV45: $i,SV35: $i,SV21: $i] :
( ( ( ~ ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) ) )
= $false )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(305,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) )
= $false )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(306,plain,
! [SV22: $i,SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV42 @ SV22 ) @ ( sK11_SY56 @ SV42 @ SV22 ) ) @ SV42 )
= $false )
| ( ( subset @ SV22 @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(307,plain,
! [SV43: $i,SV22: $i,SV47: $i,SV46: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV46 @ SV47 ) @ SV22 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV46 @ SV47 ) @ SV43 )
= $true )
| ( ( subset @ SV22 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(308,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(309,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) )
= $false )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(310,plain,
! [SV45: $i,SV35: $i,SV21: $i] :
( ( ( ! [SY99: $i,SY100: $i] :
( ~ ( in @ SY100 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV35 )
| ( in @ ( ordered_pair @ SY99 @ SY100 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(311,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ~ ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(312,plain,
! [SV43: $i,SV22: $i,SV47: $i,SV46: $i] :
( ( ( in @ ( ordered_pair @ SV46 @ SV47 ) @ SV22 )
= $false )
| ( ( in @ ( ordered_pair @ SV46 @ SV47 ) @ SV43 )
= $true )
| ( ( subset @ SV22 @ SV43 )
= $false )
| ( ( relation @ SV43 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(313,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(314,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) )
= $false )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(315,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) ) )
= $false )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(316,plain,
! [SV45: $i,SV35: $i,SV48: $i,SV21: $i] :
( ( ( ! [SY106: $i] :
( ~ ( in @ SY106 @ SV21 )
| ~ ( in @ ( ordered_pair @ SV48 @ SY106 ) @ SV35 )
| ( in @ ( ordered_pair @ SV48 @ SY106 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(317,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) )
| ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) )
= $false )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(318,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(319,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(320,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
| ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(321,plain,
! [SV45: $i,SV35: $i,SV48: $i,SV21: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV21 )
| ~ ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV35 )
| ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV45 ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(322,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ~ ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) ) )
= $false )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(323,plain,
! [SV21: $i,SV35: $i,SV45: $i] :
( ( ( ~ ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) )
= $false )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(324,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
= $false )
| ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 ) )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(325,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(326,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 )
= $true )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(327,plain,
! [SV45: $i,SV35: $i,SV48: $i,SV21: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV21 )
| ~ ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV35 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(328,plain,
! [SV35: $i,SV21: $i,SV45: $i] :
( ( ( ! [SY101: $i,SY102: $i] :
( ~ ( in @ ( ordered_pair @ SY101 @ SY102 ) @ SV45 )
| ( in @ SY102 @ SV21 ) ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(329,plain,
! [SV21: $i,SV35: $i,SV45: $i] :
( ( ( ! [SY103: $i,SY104: $i] :
( ~ ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV45 )
| ( in @ ( ordered_pair @ SY103 @ SY104 ) @ SV35 ) ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(330,plain,
! [SV21: $i,SV35: $i,SV44: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV44 )
= $false )
| ( ( in @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) @ SV21 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_D @ SV44 @ SV35 @ SV21 ) @ ( sK13_SY57 @ SV44 @ SV35 @ SV21 ) ) @ SV35 )
= $false )
| ( ( SV44
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(331,plain,
! [SV45: $i,SV35: $i,SV48: $i,SV21: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV21 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV35 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(332,plain,
! [SV35: $i,SV21: $i,SV45: $i,SV50: $i] :
( ( ( ! [SY107: $i] :
( ~ ( in @ ( ordered_pair @ SV50 @ SY107 ) @ SV45 )
| ( in @ SY107 @ SV21 ) ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(333,plain,
! [SV21: $i,SV35: $i,SV45: $i,SV51: $i] :
( ( ( ! [SY108: $i] :
( ~ ( in @ ( ordered_pair @ SV51 @ SY108 ) @ SV45 )
| ( in @ ( ordered_pair @ SV51 @ SY108 ) @ SV35 ) ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(334,plain,
! [SV45: $i,SV35: $i,SV48: $i,SV21: $i,SV49: $i] :
( ( ( in @ SV49 @ SV21 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV35 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(335,plain,
! [SV35: $i,SV21: $i,SV45: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV50 @ SV52 ) @ SV45 )
| ( in @ SV52 @ SV21 ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(336,plain,
! [SV21: $i,SV35: $i,SV45: $i,SV53: $i,SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV51 @ SV53 ) @ SV45 )
| ( in @ ( ordered_pair @ SV51 @ SV53 ) @ SV35 ) )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(337,plain,
! [SV45: $i,SV21: $i,SV35: $i,SV49: $i,SV48: $i] :
( ( ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV35 )
= $false )
| ( ( in @ SV49 @ SV21 )
= $false )
| ( ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV45 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(338,plain,
! [SV35: $i,SV21: $i,SV45: $i,SV52: $i,SV50: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV50 @ SV52 ) @ SV45 ) )
= $true )
| ( ( in @ SV52 @ SV21 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(339,plain,
! [SV21: $i,SV35: $i,SV45: $i,SV53: $i,SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV51 @ SV53 ) @ SV45 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV51 @ SV53 ) @ SV35 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(340,plain,
! [SV35: $i,SV21: $i,SV45: $i,SV52: $i,SV50: $i] :
( ( ( in @ ( ordered_pair @ SV50 @ SV52 ) @ SV45 )
= $false )
| ( ( in @ SV52 @ SV21 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(341,plain,
! [SV21: $i,SV35: $i,SV45: $i,SV53: $i,SV51: $i] :
( ( ( in @ ( ordered_pair @ SV51 @ SV53 ) @ SV45 )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ SV53 ) @ SV35 )
= $true )
| ( ( SV45
= ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(342,plain,
! [SV1: $i,SV23: $i] :
( ( ( in @ SV1 @ SV23 )
= $false )
| ( ( ( in @ SV23 @ SV1 )
= ( in @ SV1 @ SV23 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[243]) ).
thf(343,plain,
! [SV33: $i,SV17: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( ( in @ SV17 @ SV33 )
= ( empty @ SV33 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[247]) ).
thf(344,plain,
! [SV20: $i] :
( ( ( empty @ SV20 )
= $true )
| ( ( ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
= ( empty @ SV20 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[251]) ).
thf(345,plain,
! [SV1: $i,SV23: $i] :
( ( ( ~ ( ( in @ SV23 @ SV1 )
| ( in @ SV1 @ SV23 ) )
| ~ ( ~ ( in @ SV23 @ SV1 )
| ~ ( in @ SV1 @ SV23 ) ) )
= $false )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[342]) ).
thf(346,plain,
! [SV1: $i,SV23: $i] :
( ( ( ( in @ SV23 @ SV1 )
= ( in @ SV1 @ SV23 ) )
= $false )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[342]) ).
thf(347,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ( ( in @ SV17 @ SV33 )
| ( empty @ SV33 ) )
| ~ ( ~ ( in @ SV17 @ SV33 )
| ~ ( empty @ SV33 ) ) )
= $false )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[343]) ).
thf(349,plain,
! [SV20: $i] :
( ( ( ~ ( ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
| ( empty @ SV20 ) )
| ~ ( ~ ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
| ~ ( empty @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[344]) ).
thf(352,plain,
! [SV1: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ SV1 )
| ~ ( in @ SV1 @ SV23 ) ) )
= $false )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(354,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ SV33 )
| ~ ( empty @ SV33 ) ) )
= $false )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(355,plain,
! [SV20: $i] :
( ( ( ~ ( ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
| ( empty @ SV20 ) ) )
= $false )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(358,plain,
! [SV1: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV1 )
| ~ ( in @ SV1 @ SV23 ) )
= $true )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(360,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV33 )
| ~ ( empty @ SV33 ) )
= $true )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(361,plain,
! [SV20: $i] :
( ( ( ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
| ( empty @ SV20 ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(364,plain,
! [SV1: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV1 @ SV23 ) )
= $true )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(366,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV33 ) )
= $true )
| ( ( ~ ( empty @ SV33 ) )
= $true )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(367,plain,
! [SV20: $i] :
( ( ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
= $true )
| ( ( empty @ SV20 )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(369,plain,
! [SV1: $i,SV23: $i] :
( ( ( in @ SV23 @ SV1 )
= $false )
| ( ( ~ ( in @ SV1 @ SV23 ) )
= $true )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(370,plain,
! [SV33: $i,SV17: $i] :
( ( ( in @ SV17 @ SV33 )
= $false )
| ( ( ~ ( empty @ SV33 ) )
= $true )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(372,plain,
! [SV23: $i,SV1: $i] :
( ( ( in @ SV1 @ SV23 )
= $false )
| ( ( in @ SV23 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(373,plain,
! [SV17: $i,SV33: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( in @ SV17 @ SV33 )
= $false )
| ( ( empty @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(375,plain,
! [SV1: $i] :
( ( in @ SV1 @ SV1 )
= $false ),
inference(extuni,[status(esa)],[346:[bind(SV23,$thf( SV1 ))]]) ).
thf(376,plain,
! [SV49: $i,SV48: $i,SV21: $i,SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV48 @ SV49 ) @ ( relation_rng_restriction @ SV21 @ SV35 ) )
= $true )
| ( ( in @ SV49 @ SV21 )
= $false )
| ( ( in @ ( ordered_pair @ SV48 @ SV49 ) @ SV35 )
= $false ) ),
inference(extuni,[status(esa)],[337:[bind(SV45,$thf( relation_rng_restriction @ SV21 @ SV35 ))]]) ).
thf(377,plain,
! [SV50: $i,SV52: $i,SV21: $i,SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( in @ SV52 @ SV21 )
= $true )
| ( ( in @ ( ordered_pair @ SV50 @ SV52 ) @ ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false ) ),
inference(extuni,[status(esa)],[340:[bind(SV45,$thf( relation_rng_restriction @ SV21 @ SV35 ))]]) ).
thf(378,plain,
! [SV53: $i,SV51: $i,SV21: $i,SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV51 @ SV53 ) @ SV35 )
= $true )
| ( ( in @ ( ordered_pair @ SV51 @ SV53 ) @ ( relation_rng_restriction @ SV21 @ SV35 ) )
= $false ) ),
inference(extuni,[status(esa)],[341:[bind(SV45,$thf( relation_rng_restriction @ SV21 @ SV35 ))]]) ).
thf(379,plain,
! [SV23: $i,SV1: $i] :
( ( ( in @ SV1 @ SV23 )
= $false )
| ( ( in @ SV23 @ SV1 )
= $false ) ),
inference(sim,[status(thm)],[372]) ).
thf(380,plain,
! [SV17: $i,SV33: $i] :
( ( ( empty @ SV33 )
= $false )
| ( ( in @ SV17 @ SV33 )
= $false ) ),
inference(sim,[status(thm)],[373]) ).
thf(381,plain,
! [SV20: $i] :
( ( ( element @ ( sK7_B @ SV20 ) @ ( powerset @ SV20 ) )
= $true )
| ( ( empty @ SV20 )
= $true ) ),
inference(sim,[status(thm)],[367]) ).
thf(382,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[115,381,380,379,378,377,376,375,341,340,337,330,326,325,312,306,299,274,269,268,266,261,258,251,247,244,243,238,237,234,228,227,220,219,218,217,214,210,205,204,202,180,178,176,175,164,156,155,150,135,122]) ).
thf(383,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU199+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 01:27:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 35
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.37 .
% 0.13/0.38 (rf:0,axioms:35,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:0,translation:fof_full)...................eprover: CPU time limit exceeded, terminating
% 74.36/74.63 ...
% 80.76/81.06
% 80.76/81.06 ********************************
% 80.76/81.06 * All subproblems solved! *
% 80.76/81.06 ********************************
% 80.76/81.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:36,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:382,loop_count:0,foatp_calls:2,translation:fof_full)
% 80.85/81.14
% 80.85/81.14 %**** Beginning of derivation protocol ****
% 80.85/81.14 % SZS output start CNFRefutation
% See solution above
% 80.85/81.14
% 80.85/81.14 %**** End of derivation protocol ****
% 80.85/81.14 %**** no. of clauses in derivation: 352 ****
% 80.85/81.14 %**** clause counter: 382 ****
% 80.85/81.14
% 80.85/81.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:36,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:382,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------