TSTP Solution File: SET988+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.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 03:06:47 EDT 2022
% Result : Theorem 0.43s 0.84s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 63
% Syntax : Number of formulae : 603 ( 387 unt; 30 typ; 0 def)
% Number of atoms : 2810 ( 937 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 4346 ( 845 ~; 611 |; 95 &;2762 @)
% ( 6 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 10 con; 0-2 aty)
% Number of variables : 948 ( 0 ^ 930 !; 18 ?; 948 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_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_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_A,type,
sK12_A: $i ).
thf(tp_sK13_A,type,
sK13_A: $i ).
thf(tp_sK14_A,type,
sK14_A: $i ).
thf(tp_sK15_B,type,
sK15_B: $i > $i ).
thf(tp_sK16_B,type,
sK16_B: $i > $i ).
thf(tp_sK17_A,type,
sK17_A: $i ).
thf(tp_sK18_B,type,
sK18_B: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_C,type,
sK2_C: $i > $i ).
thf(tp_sK3_SY66,type,
sK3_SY66: $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_sK5_SY67,type,
sK5_SY67: $i > $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_SY70,type,
sK8_SY70: $i > $i ).
thf(tp_sK9_SY72,type,
sK9_SY72: $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] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(2,axiom,
! [A: $i] :
( ( function @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(7,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(9,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(10,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(11,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(13,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(14,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(17,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(22,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(24,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(25,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(26,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(27,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(29,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(30,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(31,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(32,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(33,conjecture,
! [A: $i] :
( ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( relation @ A )
& ( function @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
thf(34,negated_conjecture,
( ( ! [A: $i] :
( ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( relation @ A )
& ( function @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) )
=> ( ( relation @ A )
& ( function @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( function @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ B @ D ) @ A ) )
=> ( C = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(41,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(42,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(44,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(45,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(46,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(47,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(48,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(49,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(59,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(60,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(62,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(64,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(65,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(66,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(68,plain,
( ( ( ! [SY60: $i] :
~ ( ( in @ SY60 @ sK1_A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= SY60 ) )
& ! [SY63: $i,SY64: $i,SY65: $i] :
( ( ( in @ ( ordered_pair @ SY63 @ SY64 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY63 @ SY65 ) @ sK1_A ) )
=> ( SY64 = SY65 ) ) )
=> ( ( relation @ sK1_A )
& ( function @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(69,plain,
( ( ! [SY60: $i] :
~ ( ( in @ SY60 @ sK1_A )
& ! [C: $i,D: $i] :
( ( ordered_pair @ C @ D )
!= SY60 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[68]) ).
thf(70,plain,
( ( ! [SY63: $i,SY64: $i,SY65: $i] :
( ( ( in @ ( ordered_pair @ SY63 @ SY64 ) @ sK1_A )
& ( in @ ( ordered_pair @ SY63 @ SY65 ) @ sK1_A ) )
=> ( SY64 = SY65 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[68]) ).
thf(71,plain,
( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[68]) ).
thf(72,plain,
( ( relation @ sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[71]) ).
thf(73,plain,
( ( function @ sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[71]) ).
thf(74,plain,
( ( ~ ( relation @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[72]) ).
thf(75,plain,
( ( ~ ( function @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[73]) ).
thf(76,plain,
( ( ! [SY60: $i] :
( ( ( ordered_pair @ ( sK2_C @ SY60 ) @ ( sK3_SY66 @ SY60 ) )
= SY60 )
| ~ ( in @ SY60 @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(77,plain,
( ( ! [SY63: $i,SY64: $i,SY65: $i] :
( ~ ( in @ ( ordered_pair @ SY63 @ SY64 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SY63 @ SY65 ) @ sK1_A )
| ( SY64 = SY65 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( sK6_B @ A )
!= ( ordered_pair @ SY68 @ SY69 ) )
& ( in @ ( sK6_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK4_C @ B @ A ) @ ( sK5_SY67 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(79,plain,
( ( ! [A: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_B @ A ) @ ( sK8_SY70 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_B @ A ) @ ( sK9_SY72 @ A ) ) @ A )
& ( ( sK8_SY70 @ A )
!= ( sK9_SY72 @ A ) ) )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ B @ D ) @ A )
| ( C = D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(82,plain,
( ( ~ ( empty @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(83,plain,
( ( empty @ sK11_A )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(84,plain,
( ( ( relation @ sK12_A )
& ( relation_empty_yielding @ sK12_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(85,plain,
( ( ~ ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(86,plain,
( ( ( empty @ sK14_A )
& ( relation @ sK14_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( element @ ( sK15_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK15_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(88,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK16_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK16_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(89,plain,
( ( ( function @ sK17_A )
& ( relation @ sK17_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(92,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(93,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(94,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(95,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)],[55]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(97,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(98,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(99,plain,
( ( ! [A: $i] : ( element @ ( sK18_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(100,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(101,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(102,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(103,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(104,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(106,plain,
( ( ! [A: $i] : ( element @ ( sK18_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(107,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(108,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(109,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(111,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(113,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)],[95]) ).
thf(114,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(116,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(119,plain,
( ( ( function @ sK17_A )
& ( relation @ sK17_A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(120,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK16_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK16_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( element @ ( sK15_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK15_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(122,plain,
( ( ( empty @ sK14_A )
& ( relation @ sK14_A ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(123,plain,
( ( ~ ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(124,plain,
( ( ( relation @ sK12_A )
& ( relation_empty_yielding @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(126,plain,
( ( empty @ sK11_A )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(127,plain,
( ( ~ ( empty @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(128,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(131,plain,
( ( ! [A: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_B @ A ) @ ( sK8_SY70 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_B @ A ) @ ( sK9_SY72 @ A ) ) @ A )
& ( ( sK8_SY70 @ A )
!= ( sK9_SY72 @ A ) ) )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ B @ D ) @ A )
| ( C = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(132,plain,
( ( ! [A: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( sK6_B @ A )
!= ( ordered_pair @ SY68 @ SY69 ) )
& ( in @ ( sK6_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK4_C @ B @ A ) @ ( sK5_SY67 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(133,plain,
( ( ! [SY63: $i,SY64: $i,SY65: $i] :
( ~ ( in @ ( ordered_pair @ SY63 @ SY64 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SY63 @ SY65 ) @ sK1_A )
| ( SY64 = SY65 ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(134,plain,
( ( ! [SY60: $i] :
( ( ( ordered_pair @ ( sK2_C @ SY60 ) @ ( sK3_SY66 @ SY60 ) )
= SY60 )
| ~ ( in @ SY60 @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(135,plain,
( ( ~ ( relation @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(136,plain,
( ( ~ ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(137,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)],[113]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(139,plain,
( ( ~ ( ~ ( function @ sK17_A )
| ~ ( relation @ sK17_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(140,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK16_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK16_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(141,plain,
( ( ~ ( ~ ( empty @ sK14_A )
| ~ ( relation @ sK14_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(142,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(143,plain,
( ( ~ ( ~ ( relation @ sK12_A )
| ~ ( relation_empty_yielding @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(144,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK15_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK15_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(145,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(146,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(147,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(148,plain,
! [SV2: $i] :
( ( ! [SY73: $i] :
( ( unordered_pair @ SV2 @ SY73 )
= ( unordered_pair @ SY73 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(149,plain,
! [SV3: $i] :
( ( element @ ( sK18_B @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(150,plain,
! [SV4: $i] :
( ( ~ ( empty @ SV4 )
| ( function @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(151,plain,
! [SV5: $i] :
( ( ~ ( empty @ ( powerset @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(152,plain,
! [SV6: $i] :
( ( ~ ( empty @ ( singleton @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(153,plain,
! [SV7: $i] :
( ( ! [SY74: $i] :
~ ( empty @ ( unordered_pair @ SV7 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(154,plain,
! [SV8: $i] :
( ( ~ ( empty @ SV8 )
| ( relation @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(155,plain,
! [SV9: $i] :
( ( ! [SY75: $i] :
( ~ ( element @ SV9 @ SY75 )
| ( empty @ SY75 )
| ( in @ SV9 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(156,plain,
! [SV10: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( element @ SY76 @ ( powerset @ SY77 ) )
| ~ ( in @ SV10 @ SY76 )
| ( element @ SV10 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(157,plain,
! [SV11: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( element @ SY78 @ ( powerset @ SY79 ) )
| ~ ( in @ SV11 @ SY78 )
| ~ ( empty @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(158,plain,
! [SV12: $i] :
( ( ~ ( empty @ SV12 )
| ( SV12 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(159,plain,
! [SV13: $i] :
( ( ! [SY80: $i] :
( ( SV13 = SY80 )
| ~ ( empty @ SV13 )
| ~ ( empty @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(160,plain,
! [SV14: $i] :
( ( ! [SY81: $i] :
( ~ ( in @ SV14 @ SY81 )
| ~ ( in @ SY81 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(161,plain,
! [SV15: $i] :
( ( ! [SY82: $i] :
~ ( empty @ ( ordered_pair @ SV15 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(162,plain,
( ( empty @ sK10_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(163,plain,
! [SV16: $i] :
( ( ! [SY83: $i] :
( ~ ( in @ SV16 @ SY83 )
| ( element @ SV16 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(164,plain,
! [SV17: $i] :
( ( ! [SY84: $i] :
( ~ ( empty @ SY84 )
| ~ ( in @ SV17 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(165,plain,
! [SV18: $i] :
( ( ! [SY85: $i] :
( ( ordered_pair @ SV18 @ SY85 )
= ( unordered_pair @ ( unordered_pair @ SV18 @ SY85 ) @ ( singleton @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(166,plain,
! [SV19: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( in @ ( ordered_pair @ SV19 @ SY86 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV19 @ SY87 ) @ sK1_A )
| ( SY86 = SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(167,plain,
! [SV20: $i] :
( ( ( ( ordered_pair @ ( sK2_C @ SV20 ) @ ( sK3_SY66 @ SV20 ) )
= SV20 )
| ~ ( in @ SV20 @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(168,plain,
( ( relation @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(169,plain,
( ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(170,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)],[137]) ).
thf(171,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(172,plain,
( ( ~ ( function @ sK17_A )
| ~ ( relation @ sK17_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(173,plain,
! [SV21: $i] :
( ( ( empty @ SV21 )
| ~ ( ~ ( element @ ( sK16_B @ SV21 ) @ ( powerset @ SV21 ) )
| ~ ~ ( empty @ ( sK16_B @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(174,plain,
( ( ~ ( empty @ sK14_A )
| ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(175,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(176,plain,
( ( ~ ( relation @ sK12_A )
| ~ ( relation_empty_yielding @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(177,plain,
! [SV22: $i] :
( ( ~ ( ~ ( element @ ( sK15_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ( empty @ ( sK15_B @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(178,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(179,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(180,plain,
! [SV23: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV23 )
= ( unordered_pair @ SV23 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(181,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $true )
| ( ( function @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(182,plain,
! [SV5: $i] :
( ( empty @ ( powerset @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(183,plain,
! [SV6: $i] :
( ( empty @ ( singleton @ SV6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(184,plain,
! [SV24: $i,SV7: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV7 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(185,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(186,plain,
! [SV25: $i,SV9: $i] :
( ( ~ ( element @ SV9 @ SV25 )
| ( empty @ SV25 )
| ( in @ SV9 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(187,plain,
! [SV10: $i,SV26: $i] :
( ( ! [SY88: $i] :
( ~ ( element @ SV26 @ ( powerset @ SY88 ) )
| ~ ( in @ SV10 @ SV26 )
| ( element @ SV10 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(188,plain,
! [SV11: $i,SV27: $i] :
( ( ! [SY89: $i] :
( ~ ( element @ SV27 @ ( powerset @ SY89 ) )
| ~ ( in @ SV11 @ SV27 )
| ~ ( empty @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(189,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $true )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(190,plain,
! [SV28: $i,SV13: $i] :
( ( ( SV13 = SV28 )
| ~ ( empty @ SV13 )
| ~ ( empty @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(191,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( in @ SV14 @ SV29 )
| ~ ( in @ SV29 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(192,plain,
! [SV30: $i,SV15: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV15 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(193,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( in @ SV16 @ SV31 )
| ( element @ SV16 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(194,plain,
! [SV17: $i,SV32: $i] :
( ( ~ ( empty @ SV32 )
| ~ ( in @ SV17 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(195,plain,
! [SV33: $i,SV18: $i] :
( ( ( ordered_pair @ SV18 @ SV33 )
= ( unordered_pair @ ( unordered_pair @ SV18 @ SV33 ) @ ( singleton @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(196,plain,
! [SV34: $i,SV19: $i] :
( ( ! [SY90: $i] :
( ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV19 @ SY90 ) @ sK1_A )
| ( SV34 = SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(197,plain,
! [SV20: $i] :
( ( ( ( ordered_pair @ ( sK2_C @ SV20 ) @ ( sK3_SY66 @ SV20 ) )
= SV20 )
= $true )
| ( ( ~ ( in @ SV20 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(198,plain,
( ( ~ ~ ( empty @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(199,plain,
( ( ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(200,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(201,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(202,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(203,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(204,plain,
( ( ~ ( function @ sK17_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(205,plain,
( ( ~ ( relation @ sK17_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(206,plain,
! [SV21: $i] :
( ( ( empty @ SV21 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK16_B @ SV21 ) @ ( powerset @ SV21 ) )
| ~ ~ ( empty @ ( sK16_B @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(207,plain,
( ( ~ ( empty @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(208,plain,
( ( ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(209,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(210,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(211,plain,
( ( ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(212,plain,
( ( ~ ( relation_empty_yielding @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(213,plain,
! [SV22: $i] :
( ( ~ ( element @ ( sK15_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ( empty @ ( sK15_B @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(214,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(215,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(216,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(217,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(218,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $false )
| ( ( function @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(219,plain,
! [SV24: $i,SV7: $i] :
( ( empty @ ( unordered_pair @ SV7 @ SV24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(220,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(221,plain,
! [SV25: $i,SV9: $i] :
( ( ( ~ ( element @ SV9 @ SV25 ) )
= $true )
| ( ( ( empty @ SV25 )
| ( in @ SV9 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(222,plain,
! [SV10: $i,SV35: $i,SV26: $i] :
( ( ~ ( element @ SV26 @ ( powerset @ SV35 ) )
| ~ ( in @ SV10 @ SV26 )
| ( element @ SV10 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(223,plain,
! [SV11: $i,SV36: $i,SV27: $i] :
( ( ~ ( element @ SV27 @ ( powerset @ SV36 ) )
| ~ ( in @ SV11 @ SV27 )
| ~ ( empty @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(224,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(225,plain,
! [SV28: $i,SV13: $i] :
( ( ( ( SV13 = SV28 )
| ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(226,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV29 ) )
= $true )
| ( ( ~ ( in @ SV29 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(227,plain,
! [SV30: $i,SV15: $i] :
( ( empty @ ( ordered_pair @ SV15 @ SV30 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(228,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV31 ) )
= $true )
| ( ( element @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(229,plain,
! [SV17: $i,SV32: $i] :
( ( ( ~ ( empty @ SV32 ) )
= $true )
| ( ( ~ ( in @ SV17 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(230,plain,
! [SV37: $i,SV34: $i,SV19: $i] :
( ( ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV19 @ SV37 ) @ sK1_A )
| ( SV34 = SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(231,plain,
! [SV20: $i] :
( ( ( in @ SV20 @ sK1_A )
= $false )
| ( ( ( ordered_pair @ ( sK2_C @ SV20 ) @ ( sK3_SY66 @ SV20 ) )
= SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(232,plain,
( ( ~ ( empty @ sK13_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(233,plain,
( ( relation @ sK13_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(234,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(235,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(236,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(237,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(238,plain,
( ( function @ sK17_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(239,plain,
( ( relation @ sK17_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(240,plain,
! [SV21: $i] :
( ( ( ~ ( element @ ( sK16_B @ SV21 ) @ ( powerset @ SV21 ) )
| ~ ~ ( empty @ ( sK16_B @ SV21 ) ) )
= $false )
| ( ( empty @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(241,plain,
( ( empty @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(242,plain,
( ( relation @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(243,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(244,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(245,plain,
( ( relation @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(246,plain,
( ( relation_empty_yielding @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(247,plain,
! [SV22: $i] :
( ( ~ ( element @ ( sK15_B @ SV22 ) @ ( powerset @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(248,plain,
! [SV22: $i] :
( ( ~ ( empty @ ( sK15_B @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(249,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(250,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(251,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(252,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(253,plain,
! [SV25: $i,SV9: $i] :
( ( ( element @ SV9 @ SV25 )
= $false )
| ( ( ( empty @ SV25 )
| ( in @ SV9 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(254,plain,
! [SV10: $i,SV35: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( powerset @ SV35 ) )
| ~ ( in @ SV10 @ SV26 ) )
= $true )
| ( ( element @ SV10 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(255,plain,
! [SV11: $i,SV36: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( powerset @ SV36 ) )
| ~ ( in @ SV11 @ SV27 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(256,plain,
! [SV28: $i,SV13: $i] :
( ( ( SV13 = SV28 )
= $true )
| ( ( ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(257,plain,
! [SV29: $i,SV14: $i] :
( ( ( in @ SV14 @ SV29 )
= $false )
| ( ( ~ ( in @ SV29 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(258,plain,
! [SV31: $i,SV16: $i] :
( ( ( in @ SV16 @ SV31 )
= $false )
| ( ( element @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(259,plain,
! [SV17: $i,SV32: $i] :
( ( ( empty @ SV32 )
= $false )
| ( ( ~ ( in @ SV17 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(260,plain,
! [SV37: $i,SV34: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV19 @ SV37 ) @ sK1_A ) )
= $true )
| ( ( SV34 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(261,plain,
( ( empty @ sK13_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(262,plain,
! [SV38: $i] :
( ( ! [SY91: $i] :
( ~ ( element @ SV38 @ ( powerset @ SY91 ) )
| ( subset @ SV38 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(263,plain,
! [SV39: $i] :
( ( ! [SY92: $i] :
( ~ ( subset @ SV39 @ SY92 )
| ( element @ SV39 @ ( powerset @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(264,plain,
! [SV40: $i] :
( ( ~ ( ~ ! [SY93: $i,SY94: $i] :
( ( sK6_B @ SV40 )
!= ( ordered_pair @ SY93 @ SY94 ) )
| ~ ( in @ ( sK6_B @ SV40 ) @ SV40 ) )
| ( relation @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(265,plain,
! [SV41: $i] :
( ( ~ ( relation @ SV41 )
| ! [SY95: $i] :
( ( SY95
= ( ordered_pair @ ( sK4_C @ SY95 @ SV41 ) @ ( sK5_SY67 @ SY95 @ SV41 ) ) )
| ~ ( in @ SY95 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(266,plain,
! [SV21: $i] :
( ( ( ~ ( element @ ( sK16_B @ SV21 ) @ ( powerset @ SV21 ) ) )
= $false )
| ( ( empty @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(267,plain,
! [SV21: $i] :
( ( ( ~ ~ ( empty @ ( sK16_B @ SV21 ) ) )
= $false )
| ( ( empty @ SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(268,plain,
! [SV42: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 ) )
| ~ ( ( ( sK8_SY70 @ SV42 )
!= ( sK9_SY72 @ SV42 ) ) ) )
| ( function @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(269,plain,
! [SV43: $i] :
( ( ~ ( function @ SV43 )
| ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY96 @ SY98 ) @ SV43 )
| ( SY97 = SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(270,plain,
! [SV22: $i] :
( ( element @ ( sK15_B @ SV22 ) @ ( powerset @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(271,plain,
! [SV22: $i] :
( ( empty @ ( sK15_B @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(272,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(273,plain,
! [SV9: $i,SV25: $i] :
( ( ( empty @ SV25 )
= $true )
| ( ( in @ SV9 @ SV25 )
= $true )
| ( ( element @ SV9 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(274,plain,
! [SV10: $i,SV35: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV26 ) )
= $true )
| ( ( element @ SV10 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(275,plain,
! [SV11: $i,SV36: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( ~ ( in @ SV11 @ SV27 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(276,plain,
! [SV28: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( SV13 = SV28 )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(277,plain,
! [SV14: $i,SV29: $i] :
( ( ( in @ SV29 @ SV14 )
= $false )
| ( ( in @ SV14 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(278,plain,
! [SV32: $i,SV17: $i] :
( ( ( in @ SV17 @ SV32 )
= $false )
| ( ( empty @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(279,plain,
! [SV37: $i,SV34: $i,SV19: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV34 ) @ sK1_A ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV37 ) @ sK1_A ) )
= $true )
| ( ( SV34 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(280,plain,
! [SV44: $i,SV38: $i] :
( ( ~ ( element @ SV38 @ ( powerset @ SV44 ) )
| ( subset @ SV38 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(281,plain,
! [SV45: $i,SV39: $i] :
( ( ~ ( subset @ SV39 @ SV45 )
| ( element @ SV39 @ ( powerset @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(282,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ! [SY93: $i,SY94: $i] :
( ( sK6_B @ SV40 )
!= ( ordered_pair @ SY93 @ SY94 ) )
| ~ ( in @ ( sK6_B @ SV40 ) @ SV40 ) ) )
= $true )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(283,plain,
! [SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ! [SY95: $i] :
( ( SY95
= ( ordered_pair @ ( sK4_C @ SY95 @ SV41 ) @ ( sK5_SY67 @ SY95 @ SV41 ) ) )
| ~ ( in @ SY95 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(284,plain,
! [SV21: $i] :
( ( ( element @ ( sK16_B @ SV21 ) @ ( powerset @ SV21 ) )
= $true )
| ( ( empty @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(285,plain,
! [SV21: $i] :
( ( ( ~ ( empty @ ( sK16_B @ SV21 ) ) )
= $true )
| ( ( empty @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(286,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 ) )
| ~ ( ( ( sK8_SY70 @ SV42 )
!= ( sK9_SY72 @ SV42 ) ) ) ) )
= $true )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(287,plain,
! [SV43: $i] :
( ( ( ~ ( function @ SV43 ) )
= $true )
| ( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY96 @ SY98 ) @ SV43 )
| ( SY97 = SY98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(288,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(289,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(290,plain,
! [SV10: $i,SV35: $i,SV26: $i] :
( ( ( element @ SV26 @ ( powerset @ SV35 ) )
= $false )
| ( ( ~ ( in @ SV10 @ SV26 ) )
= $true )
| ( ( element @ SV10 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(291,plain,
! [SV11: $i,SV36: $i,SV27: $i] :
( ( ( element @ SV27 @ ( powerset @ SV36 ) )
= $false )
| ( ( ~ ( in @ SV11 @ SV27 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(292,plain,
! [SV13: $i,SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( SV13 = SV28 )
= $true )
| ( ( empty @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(293,plain,
! [SV37: $i,SV34: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ SV34 ) @ sK1_A )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV19 @ SV37 ) @ sK1_A ) )
= $true )
| ( ( SV34 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(294,plain,
! [SV44: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( powerset @ SV44 ) ) )
= $true )
| ( ( subset @ SV38 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(295,plain,
! [SV45: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV45 ) )
= $true )
| ( ( element @ SV39 @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(296,plain,
! [SV40: $i] :
( ( ( ~ ! [SY93: $i,SY94: $i] :
( ( sK6_B @ SV40 )
!= ( ordered_pair @ SY93 @ SY94 ) )
| ~ ( in @ ( sK6_B @ SV40 ) @ SV40 ) )
= $false )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(297,plain,
! [SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ! [SY95: $i] :
( ( SY95
= ( ordered_pair @ ( sK4_C @ SY95 @ SV41 ) @ ( sK5_SY67 @ SY95 @ SV41 ) ) )
| ~ ( in @ SY95 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(298,plain,
! [SV21: $i] :
( ( ( empty @ ( sK16_B @ SV21 ) )
= $false )
| ( ( empty @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(299,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 ) )
| ~ ( ( ( sK8_SY70 @ SV42 )
!= ( sK9_SY72 @ SV42 ) ) ) )
= $false )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(300,plain,
! [SV43: $i] :
( ( ( function @ SV43 )
= $false )
| ( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SY96 @ SY98 ) @ SV43 )
| ( SY97 = SY98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(301,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(302,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(303,plain,
! [SV35: $i,SV26: $i,SV10: $i] :
( ( ( in @ SV10 @ SV26 )
= $false )
| ( ( element @ SV26 @ ( powerset @ SV35 ) )
= $false )
| ( ( element @ SV10 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(304,plain,
! [SV36: $i,SV27: $i,SV11: $i] :
( ( ( in @ SV11 @ SV27 )
= $false )
| ( ( element @ SV27 @ ( powerset @ SV36 ) )
= $false )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(305,plain,
! [SV34: $i,SV37: $i,SV19: $i] :
( ( ( in @ ( ordered_pair @ SV19 @ SV37 ) @ sK1_A )
= $false )
| ( ( in @ ( ordered_pair @ SV19 @ SV34 ) @ sK1_A )
= $false )
| ( ( SV34 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV44: $i,SV38: $i] :
( ( ( element @ SV38 @ ( powerset @ SV44 ) )
= $false )
| ( ( subset @ SV38 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV45: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV45 )
= $false )
| ( ( element @ SV39 @ ( powerset @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV40: $i] :
( ( ( ~ ! [SY93: $i,SY94: $i] :
( ( sK6_B @ SV40 )
!= ( ordered_pair @ SY93 @ SY94 ) ) )
= $false )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(309,plain,
! [SV40: $i] :
( ( ( ~ ( in @ ( sK6_B @ SV40 ) @ SV40 ) )
= $false )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(310,plain,
! [SV41: $i,SV46: $i] :
( ( ( ( SV46
= ( ordered_pair @ ( sK4_C @ SV46 @ SV41 ) @ ( sK5_SY67 @ SV46 @ SV41 ) ) )
| ~ ( in @ SV46 @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(311,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 ) ) )
= $false )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(312,plain,
! [SV42: $i] :
( ( ( ~ ( ( ( sK8_SY70 @ SV42 )
!= ( sK9_SY72 @ SV42 ) ) ) )
= $false )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(313,plain,
! [SV43: $i,SV47: $i] :
( ( ( ! [SY99: $i,SY100: $i] :
( ~ ( in @ ( ordered_pair @ SV47 @ SY99 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY100 ) @ SV43 )
| ( SY99 = SY100 ) ) )
= $true )
| ( ( function @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(314,plain,
! [SV11: $i,SV27: $i,SV36: $i] :
( ( ( empty @ SV36 )
= $false )
| ( ( element @ SV27 @ ( powerset @ SV36 ) )
= $false )
| ( ( in @ SV11 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(315,plain,
! [SV40: $i] :
( ( ( ! [SY93: $i,SY94: $i] :
( ( sK6_B @ SV40 )
!= ( ordered_pair @ SY93 @ SY94 ) ) )
= $true )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(316,plain,
! [SV40: $i] :
( ( ( in @ ( sK6_B @ SV40 ) @ SV40 )
= $true )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(317,plain,
! [SV41: $i,SV46: $i] :
( ( ( SV46
= ( ordered_pair @ ( sK4_C @ SV46 @ SV41 ) @ ( sK5_SY67 @ SV46 @ SV41 ) ) )
= $true )
| ( ( ~ ( in @ SV46 @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(318,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 ) ) )
= $true )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(319,plain,
! [SV42: $i] :
( ( ( ( ( sK8_SY70 @ SV42 )
!= ( sK9_SY72 @ SV42 ) ) )
= $true )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(320,plain,
! [SV43: $i,SV48: $i,SV47: $i] :
( ( ( ! [SY101: $i] :
( ~ ( in @ ( ordered_pair @ SV47 @ SV48 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY101 ) @ SV43 )
| ( SV48 = SY101 ) ) )
= $true )
| ( ( function @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(321,plain,
! [SV49: $i,SV40: $i] :
( ( ( ! [SY102: $i] :
( ( sK6_B @ SV40 )
!= ( ordered_pair @ SV49 @ SY102 ) ) )
= $true )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(322,plain,
! [SV41: $i,SV46: $i] :
( ( ( in @ SV46 @ SV41 )
= $false )
| ( ( SV46
= ( ordered_pair @ ( sK4_C @ SV46 @ SV41 ) @ ( sK5_SY67 @ SV46 @ SV41 ) ) )
= $true )
| ( ( relation @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(323,plain,
! [SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 ) )
= $false )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(324,plain,
! [SV42: $i] :
( ( ( ( sK8_SY70 @ SV42 )
= ( sK9_SY72 @ SV42 ) )
= $false )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(325,plain,
! [SV50: $i,SV43: $i,SV48: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV48 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV50 ) @ SV43 )
| ( SV48 = SV50 ) )
= $true )
| ( ( function @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(326,plain,
! [SV51: $i,SV49: $i,SV40: $i] :
( ( ( ( ( sK6_B @ SV40 )
!= ( ordered_pair @ SV49 @ SV51 ) ) )
= $true )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(327,plain,
! [SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 ) )
= $false )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(328,plain,
! [SV42: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 ) )
= $false )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(329,plain,
! [SV50: $i,SV43: $i,SV48: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV48 ) @ SV43 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV50 ) @ SV43 ) )
= $true )
| ( ( SV48 = SV50 )
= $true )
| ( ( function @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(330,plain,
! [SV51: $i,SV49: $i,SV40: $i] :
( ( ( ( sK6_B @ SV40 )
= ( ordered_pair @ SV49 @ SV51 ) )
= $false )
| ( ( relation @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(331,plain,
! [SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK8_SY70 @ SV42 ) ) @ SV42 )
= $true )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(332,plain,
! [SV42: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_B @ SV42 ) @ ( sK9_SY72 @ SV42 ) ) @ SV42 )
= $true )
| ( ( function @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(333,plain,
! [SV50: $i,SV43: $i,SV48: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV48 ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV50 ) @ SV43 ) )
= $true )
| ( ( SV48 = SV50 )
= $true )
| ( ( function @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(334,plain,
! [SV50: $i,SV43: $i,SV48: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV48 ) @ SV43 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV50 ) @ SV43 ) )
= $true )
| ( ( SV48 = SV50 )
= $true )
| ( ( function @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(335,plain,
! [SV48: $i,SV43: $i,SV50: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV50 ) @ SV43 )
= $false )
| ( ( in @ ( ordered_pair @ SV47 @ SV48 ) @ SV43 )
= $false )
| ( ( SV48 = SV50 )
= $true )
| ( ( function @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(336,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[104,335,332,331,330,324,322,316,314,307,306,305,303,302,301,298,292,284,278,277,273,271,270,261,258,252,250,249,246,245,242,241,239,238,233,231,227,224,220,219,218,195,183,182,180,168,162,149,147,126]) ).
thf(337,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(338,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(339,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(340,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(342,plain,
( ( ! [A: $i] : ( element @ ( sK18_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(343,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(344,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(345,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(346,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(347,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(349,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)],[95]) ).
thf(350,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(351,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(352,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(355,plain,
( ( ( function @ sK17_A )
& ( relation @ sK17_A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(356,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK16_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK16_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(357,plain,
( ( ! [A: $i] :
( ( element @ ( sK15_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK15_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(358,plain,
( ( ( empty @ sK14_A )
& ( relation @ sK14_A ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(359,plain,
( ( ~ ( empty @ sK13_A )
& ( relation @ sK13_A ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(360,plain,
( ( ( relation @ sK12_A )
& ( relation_empty_yielding @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(361,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(362,plain,
( ( empty @ sK11_A )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(363,plain,
( ( ~ ( empty @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(364,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_B @ A ) @ ( sK8_SY70 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK7_B @ A ) @ ( sK9_SY72 @ A ) ) @ A )
& ( ( sK8_SY70 @ A )
!= ( sK9_SY72 @ A ) ) )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ B @ D ) @ A )
| ( C = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(368,plain,
( ( ! [A: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( sK6_B @ A )
!= ( ordered_pair @ SY68 @ SY69 ) )
& ( in @ ( sK6_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK4_C @ B @ A ) @ ( sK5_SY67 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(369,plain,
( ( ! [SY63: $i,SY64: $i,SY65: $i] :
( ~ ( in @ ( ordered_pair @ SY63 @ SY64 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SY63 @ SY65 ) @ sK1_A )
| ( SY64 = SY65 ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(370,plain,
( ( ! [SY60: $i] :
( ( ( ordered_pair @ ( sK2_C @ SY60 ) @ ( sK3_SY66 @ SY60 ) )
= SY60 )
| ~ ( in @ SY60 @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(371,plain,
( ( ~ ( function @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(372,plain,
( ( ~ ( ~ ( relation @ sK12_A )
| ~ ( relation_empty_yielding @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(373,plain,
( ( ~ ( ~ ( empty @ sK14_A )
| ~ ( relation @ sK14_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(374,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(375,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(376,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(377,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(378,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK16_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK16_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(379,plain,
( ( ~ ( ~ ( function @ sK17_A )
| ~ ( relation @ sK17_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(380,plain,
( ( ~ ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(381,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)],[349]) ).
thf(382,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK15_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK15_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(383,plain,
! [SV52: $i] :
( ( subset @ SV52 @ SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(384,plain,
! [SV53: $i] :
( ( ! [SY103: $i] :
( ( unordered_pair @ SV53 @ SY103 )
= ( unordered_pair @ SY103 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(385,plain,
! [SV54: $i] :
( ( element @ ( sK18_B @ SV54 ) @ SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(386,plain,
! [SV55: $i] :
( ( ~ ( empty @ SV55 )
| ( function @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(387,plain,
! [SV56: $i] :
( ( ~ ( empty @ ( powerset @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(388,plain,
! [SV57: $i] :
( ( ~ ( empty @ ( singleton @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(389,plain,
! [SV58: $i] :
( ( ! [SY104: $i] :
~ ( empty @ ( unordered_pair @ SV58 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(390,plain,
! [SV59: $i] :
( ( ~ ( empty @ SV59 )
| ( relation @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(391,plain,
! [SV60: $i] :
( ( ! [SY105: $i] :
( ~ ( element @ SV60 @ SY105 )
| ( empty @ SY105 )
| ( in @ SV60 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(392,plain,
! [SV61: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ~ ( element @ SY106 @ ( powerset @ SY107 ) )
| ~ ( in @ SV61 @ SY106 )
| ( element @ SV61 @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(393,plain,
! [SV62: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( element @ SY108 @ ( powerset @ SY109 ) )
| ~ ( in @ SV62 @ SY108 )
| ~ ( empty @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(394,plain,
! [SV63: $i] :
( ( ~ ( empty @ SV63 )
| ( SV63 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(395,plain,
! [SV64: $i] :
( ( ! [SY110: $i] :
( ( SV64 = SY110 )
| ~ ( empty @ SV64 )
| ~ ( empty @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(396,plain,
! [SV65: $i] :
( ( ! [SY111: $i] :
( ~ ( in @ SV65 @ SY111 )
| ~ ( in @ SY111 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(397,plain,
! [SV66: $i] :
( ( ! [SY112: $i] :
~ ( empty @ ( ordered_pair @ SV66 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(398,plain,
( ( empty @ sK10_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(399,plain,
! [SV67: $i] :
( ( ! [SY113: $i] :
( ~ ( in @ SV67 @ SY113 )
| ( element @ SV67 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(400,plain,
! [SV68: $i] :
( ( ! [SY114: $i] :
( ~ ( empty @ SY114 )
| ~ ( in @ SV68 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(401,plain,
! [SV69: $i] :
( ( ! [SY115: $i] :
( ( ordered_pair @ SV69 @ SY115 )
= ( unordered_pair @ ( unordered_pair @ SV69 @ SY115 ) @ ( singleton @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(402,plain,
! [SV70: $i] :
( ( ! [SY116: $i,SY117: $i] :
( ~ ( in @ ( ordered_pair @ SV70 @ SY116 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV70 @ SY117 ) @ sK1_A )
| ( SY116 = SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(403,plain,
! [SV71: $i] :
( ( ( ( ordered_pair @ ( sK2_C @ SV71 ) @ ( sK3_SY66 @ SV71 ) )
= SV71 )
| ~ ( in @ SV71 @ sK1_A ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(404,plain,
( ( function @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(405,plain,
( ( ~ ( relation @ sK12_A )
| ~ ( relation_empty_yielding @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(406,plain,
( ( ~ ( empty @ sK14_A )
| ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(407,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(408,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(409,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(410,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(411,plain,
! [SV72: $i] :
( ( ( empty @ SV72 )
| ~ ( ~ ( element @ ( sK16_B @ SV72 ) @ ( powerset @ SV72 ) )
| ~ ~ ( empty @ ( sK16_B @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(412,plain,
( ( ~ ( function @ sK17_A )
| ~ ( relation @ sK17_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(413,plain,
( ( ~ ~ ( empty @ sK13_A )
| ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(414,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)],[381]) ).
thf(415,plain,
! [SV73: $i] :
( ( ~ ( ~ ( element @ ( sK15_B @ SV73 ) @ ( powerset @ SV73 ) )
| ~ ( empty @ ( sK15_B @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(416,plain,
! [SV74: $i,SV53: $i] :
( ( ( unordered_pair @ SV53 @ SV74 )
= ( unordered_pair @ SV74 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(417,plain,
! [SV55: $i] :
( ( ( ~ ( empty @ SV55 ) )
= $true )
| ( ( function @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(418,plain,
! [SV56: $i] :
( ( empty @ ( powerset @ SV56 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(419,plain,
! [SV57: $i] :
( ( empty @ ( singleton @ SV57 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(420,plain,
! [SV75: $i,SV58: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV58 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(421,plain,
! [SV59: $i] :
( ( ( ~ ( empty @ SV59 ) )
= $true )
| ( ( relation @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(422,plain,
! [SV76: $i,SV60: $i] :
( ( ~ ( element @ SV60 @ SV76 )
| ( empty @ SV76 )
| ( in @ SV60 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(423,plain,
! [SV61: $i,SV77: $i] :
( ( ! [SY118: $i] :
( ~ ( element @ SV77 @ ( powerset @ SY118 ) )
| ~ ( in @ SV61 @ SV77 )
| ( element @ SV61 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(424,plain,
! [SV62: $i,SV78: $i] :
( ( ! [SY119: $i] :
( ~ ( element @ SV78 @ ( powerset @ SY119 ) )
| ~ ( in @ SV62 @ SV78 )
| ~ ( empty @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(425,plain,
! [SV63: $i] :
( ( ( ~ ( empty @ SV63 ) )
= $true )
| ( ( SV63 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(426,plain,
! [SV79: $i,SV64: $i] :
( ( ( SV64 = SV79 )
| ~ ( empty @ SV64 )
| ~ ( empty @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(427,plain,
! [SV80: $i,SV65: $i] :
( ( ~ ( in @ SV65 @ SV80 )
| ~ ( in @ SV80 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(428,plain,
! [SV81: $i,SV66: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV66 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(429,plain,
! [SV82: $i,SV67: $i] :
( ( ~ ( in @ SV67 @ SV82 )
| ( element @ SV67 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(430,plain,
! [SV68: $i,SV83: $i] :
( ( ~ ( empty @ SV83 )
| ~ ( in @ SV68 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(431,plain,
! [SV84: $i,SV69: $i] :
( ( ( ordered_pair @ SV69 @ SV84 )
= ( unordered_pair @ ( unordered_pair @ SV69 @ SV84 ) @ ( singleton @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(432,plain,
! [SV85: $i,SV70: $i] :
( ( ! [SY120: $i] :
( ~ ( in @ ( ordered_pair @ SV70 @ SV85 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV70 @ SY120 ) @ sK1_A )
| ( SV85 = SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(433,plain,
! [SV71: $i] :
( ( ( ( ordered_pair @ ( sK2_C @ SV71 ) @ ( sK3_SY66 @ SV71 ) )
= SV71 )
= $true )
| ( ( ~ ( in @ SV71 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(434,plain,
( ( ~ ( relation @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(435,plain,
( ( ~ ( relation_empty_yielding @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(436,plain,
( ( ~ ( empty @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(437,plain,
( ( ~ ( relation @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(438,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(439,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(440,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(441,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(442,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(443,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(444,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(445,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(446,plain,
! [SV72: $i] :
( ( ( empty @ SV72 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK16_B @ SV72 ) @ ( powerset @ SV72 ) )
| ~ ~ ( empty @ ( sK16_B @ SV72 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(447,plain,
( ( ~ ( function @ sK17_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(448,plain,
( ( ~ ( relation @ sK17_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(449,plain,
( ( ~ ~ ( empty @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(450,plain,
( ( ~ ( relation @ sK13_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(451,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(452,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(453,plain,
! [SV73: $i] :
( ( ~ ( element @ ( sK15_B @ SV73 ) @ ( powerset @ SV73 ) )
| ~ ( empty @ ( sK15_B @ SV73 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(454,plain,
! [SV55: $i] :
( ( ( empty @ SV55 )
= $false )
| ( ( function @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(455,plain,
! [SV75: $i,SV58: $i] :
( ( empty @ ( unordered_pair @ SV58 @ SV75 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(456,plain,
! [SV59: $i] :
( ( ( empty @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(457,plain,
! [SV76: $i,SV60: $i] :
( ( ( ~ ( element @ SV60 @ SV76 ) )
= $true )
| ( ( ( empty @ SV76 )
| ( in @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(458,plain,
! [SV61: $i,SV86: $i,SV77: $i] :
( ( ~ ( element @ SV77 @ ( powerset @ SV86 ) )
| ~ ( in @ SV61 @ SV77 )
| ( element @ SV61 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(459,plain,
! [SV62: $i,SV87: $i,SV78: $i] :
( ( ~ ( element @ SV78 @ ( powerset @ SV87 ) )
| ~ ( in @ SV62 @ SV78 )
| ~ ( empty @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(460,plain,
! [SV63: $i] :
( ( ( empty @ SV63 )
= $false )
| ( ( SV63 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(461,plain,
! [SV79: $i,SV64: $i] :
( ( ( ( SV64 = SV79 )
| ~ ( empty @ SV64 ) )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(462,plain,
! [SV80: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV80 ) )
= $true )
| ( ( ~ ( in @ SV80 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(463,plain,
! [SV81: $i,SV66: $i] :
( ( empty @ ( ordered_pair @ SV66 @ SV81 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(464,plain,
! [SV82: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV82 ) )
= $true )
| ( ( element @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(465,plain,
! [SV68: $i,SV83: $i] :
( ( ( ~ ( empty @ SV83 ) )
= $true )
| ( ( ~ ( in @ SV68 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(466,plain,
! [SV88: $i,SV85: $i,SV70: $i] :
( ( ~ ( in @ ( ordered_pair @ SV70 @ SV85 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV70 @ SV88 ) @ sK1_A )
| ( SV85 = SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(467,plain,
! [SV71: $i] :
( ( ( in @ SV71 @ sK1_A )
= $false )
| ( ( ( ordered_pair @ ( sK2_C @ SV71 ) @ ( sK3_SY66 @ SV71 ) )
= SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(468,plain,
( ( relation @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(469,plain,
( ( relation_empty_yielding @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(470,plain,
( ( empty @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(471,plain,
( ( relation @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(472,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK8_SY70 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SX0 ) @ ( sK9_SY72 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK8_SY70 @ SX0 )
!= ( sK9_SY72 @ SX0 ) ) ) )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(473,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(474,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(475,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(476,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK6_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK6_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(477,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK4_C @ SX1 @ SX0 ) @ ( sK5_SY67 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(478,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(479,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(480,plain,
! [SV72: $i] :
( ( ( ~ ( element @ ( sK16_B @ SV72 ) @ ( powerset @ SV72 ) )
| ~ ~ ( empty @ ( sK16_B @ SV72 ) ) )
= $false )
| ( ( empty @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(481,plain,
( ( function @ sK17_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(482,plain,
( ( relation @ sK17_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(483,plain,
( ( ~ ( empty @ sK13_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(484,plain,
( ( relation @ sK13_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(485,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(486,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(487,plain,
! [SV73: $i] :
( ( ~ ( element @ ( sK15_B @ SV73 ) @ ( powerset @ SV73 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(488,plain,
! [SV73: $i] :
( ( ~ ( empty @ ( sK15_B @ SV73 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(489,plain,
! [SV76: $i,SV60: $i] :
( ( ( element @ SV60 @ SV76 )
= $false )
| ( ( ( empty @ SV76 )
| ( in @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(490,plain,
! [SV61: $i,SV86: $i,SV77: $i] :
( ( ( ~ ( element @ SV77 @ ( powerset @ SV86 ) )
| ~ ( in @ SV61 @ SV77 ) )
= $true )
| ( ( element @ SV61 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(491,plain,
! [SV62: $i,SV87: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ SV87 ) )
| ~ ( in @ SV62 @ SV78 ) )
= $true )
| ( ( ~ ( empty @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(492,plain,
! [SV79: $i,SV64: $i] :
( ( ( SV64 = SV79 )
= $true )
| ( ( ~ ( empty @ SV64 ) )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(493,plain,
! [SV80: $i,SV65: $i] :
( ( ( in @ SV65 @ SV80 )
= $false )
| ( ( ~ ( in @ SV80 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(494,plain,
! [SV82: $i,SV67: $i] :
( ( ( in @ SV67 @ SV82 )
= $false )
| ( ( element @ SV67 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(495,plain,
! [SV68: $i,SV83: $i] :
( ( ( empty @ SV83 )
= $false )
| ( ( ~ ( in @ SV68 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(496,plain,
! [SV88: $i,SV85: $i,SV70: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV70 @ SV85 ) @ sK1_A )
| ~ ( in @ ( ordered_pair @ SV70 @ SV88 ) @ sK1_A ) )
= $true )
| ( ( SV85 = SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(497,plain,
! [SV89: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 ) )
| ~ ( ( ( sK8_SY70 @ SV89 )
!= ( sK9_SY72 @ SV89 ) ) ) )
| ( function @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(498,plain,
! [SV90: $i] :
( ( ~ ( function @ SV90 )
| ! [SY121: $i,SY122: $i,SY123: $i] :
( ~ ( in @ ( ordered_pair @ SY121 @ SY122 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY121 @ SY123 ) @ SV90 )
| ( SY122 = SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(499,plain,
! [SV91: $i] :
( ( ~ ( ~ ! [SY124: $i,SY125: $i] :
( ( sK6_B @ SV91 )
!= ( ordered_pair @ SY124 @ SY125 ) )
| ~ ( in @ ( sK6_B @ SV91 ) @ SV91 ) )
| ( relation @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(500,plain,
! [SV92: $i] :
( ( ~ ( relation @ SV92 )
| ! [SY126: $i] :
( ( SY126
= ( ordered_pair @ ( sK4_C @ SY126 @ SV92 ) @ ( sK5_SY67 @ SY126 @ SV92 ) ) )
| ~ ( in @ SY126 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(501,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(502,plain,
! [SV72: $i] :
( ( ( ~ ( element @ ( sK16_B @ SV72 ) @ ( powerset @ SV72 ) ) )
= $false )
| ( ( empty @ SV72 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(503,plain,
! [SV72: $i] :
( ( ( ~ ~ ( empty @ ( sK16_B @ SV72 ) ) )
= $false )
| ( ( empty @ SV72 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(504,plain,
( ( empty @ sK13_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(505,plain,
! [SV93: $i] :
( ( ! [SY127: $i] :
( ~ ( element @ SV93 @ ( powerset @ SY127 ) )
| ( subset @ SV93 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(506,plain,
! [SV94: $i] :
( ( ! [SY128: $i] :
( ~ ( subset @ SV94 @ SY128 )
| ( element @ SV94 @ ( powerset @ SY128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(507,plain,
! [SV73: $i] :
( ( element @ ( sK15_B @ SV73 ) @ ( powerset @ SV73 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(508,plain,
! [SV73: $i] :
( ( empty @ ( sK15_B @ SV73 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(509,plain,
! [SV60: $i,SV76: $i] :
( ( ( empty @ SV76 )
= $true )
| ( ( in @ SV60 @ SV76 )
= $true )
| ( ( element @ SV60 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(510,plain,
! [SV61: $i,SV86: $i,SV77: $i] :
( ( ( ~ ( element @ SV77 @ ( powerset @ SV86 ) ) )
= $true )
| ( ( ~ ( in @ SV61 @ SV77 ) )
= $true )
| ( ( element @ SV61 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(511,plain,
! [SV62: $i,SV87: $i,SV78: $i] :
( ( ( ~ ( element @ SV78 @ ( powerset @ SV87 ) ) )
= $true )
| ( ( ~ ( in @ SV62 @ SV78 ) )
= $true )
| ( ( ~ ( empty @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(512,plain,
! [SV79: $i,SV64: $i] :
( ( ( empty @ SV64 )
= $false )
| ( ( SV64 = SV79 )
= $true )
| ( ( ~ ( empty @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(513,plain,
! [SV65: $i,SV80: $i] :
( ( ( in @ SV80 @ SV65 )
= $false )
| ( ( in @ SV65 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(514,plain,
! [SV83: $i,SV68: $i] :
( ( ( in @ SV68 @ SV83 )
= $false )
| ( ( empty @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(515,plain,
! [SV88: $i,SV85: $i,SV70: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV70 @ SV85 ) @ sK1_A ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV70 @ SV88 ) @ sK1_A ) )
= $true )
| ( ( SV85 = SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(516,plain,
! [SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 ) )
| ~ ( ( ( sK8_SY70 @ SV89 )
!= ( sK9_SY72 @ SV89 ) ) ) ) )
= $true )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(517,plain,
! [SV90: $i] :
( ( ( ~ ( function @ SV90 ) )
= $true )
| ( ( ! [SY121: $i,SY122: $i,SY123: $i] :
( ~ ( in @ ( ordered_pair @ SY121 @ SY122 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY121 @ SY123 ) @ SV90 )
| ( SY122 = SY123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(518,plain,
! [SV91: $i] :
( ( ( ~ ( ~ ! [SY124: $i,SY125: $i] :
( ( sK6_B @ SV91 )
!= ( ordered_pair @ SY124 @ SY125 ) )
| ~ ( in @ ( sK6_B @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(519,plain,
! [SV92: $i] :
( ( ( ~ ( relation @ SV92 ) )
= $true )
| ( ( ! [SY126: $i] :
( ( SY126
= ( ordered_pair @ ( sK4_C @ SY126 @ SV92 ) @ ( sK5_SY67 @ SY126 @ SV92 ) ) )
| ~ ( in @ SY126 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(520,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(521,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(522,plain,
! [SV72: $i] :
( ( ( element @ ( sK16_B @ SV72 ) @ ( powerset @ SV72 ) )
= $true )
| ( ( empty @ SV72 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(523,plain,
! [SV72: $i] :
( ( ( ~ ( empty @ ( sK16_B @ SV72 ) ) )
= $true )
| ( ( empty @ SV72 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(524,plain,
! [SV95: $i,SV93: $i] :
( ( ~ ( element @ SV93 @ ( powerset @ SV95 ) )
| ( subset @ SV93 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(525,plain,
! [SV96: $i,SV94: $i] :
( ( ~ ( subset @ SV94 @ SV96 )
| ( element @ SV94 @ ( powerset @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(526,plain,
! [SV61: $i,SV86: $i,SV77: $i] :
( ( ( element @ SV77 @ ( powerset @ SV86 ) )
= $false )
| ( ( ~ ( in @ SV61 @ SV77 ) )
= $true )
| ( ( element @ SV61 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(527,plain,
! [SV62: $i,SV87: $i,SV78: $i] :
( ( ( element @ SV78 @ ( powerset @ SV87 ) )
= $false )
| ( ( ~ ( in @ SV62 @ SV78 ) )
= $true )
| ( ( ~ ( empty @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(528,plain,
! [SV64: $i,SV79: $i] :
( ( ( empty @ SV79 )
= $false )
| ( ( SV64 = SV79 )
= $true )
| ( ( empty @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(529,plain,
! [SV88: $i,SV85: $i,SV70: $i] :
( ( ( in @ ( ordered_pair @ SV70 @ SV85 ) @ sK1_A )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV70 @ SV88 ) @ sK1_A ) )
= $true )
| ( ( SV85 = SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(530,plain,
! [SV89: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 ) )
| ~ ( ( ( sK8_SY70 @ SV89 )
!= ( sK9_SY72 @ SV89 ) ) ) )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(531,plain,
! [SV90: $i] :
( ( ( function @ SV90 )
= $false )
| ( ( ! [SY121: $i,SY122: $i,SY123: $i] :
( ~ ( in @ ( ordered_pair @ SY121 @ SY122 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SY121 @ SY123 ) @ SV90 )
| ( SY122 = SY123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(532,plain,
! [SV91: $i] :
( ( ( ~ ! [SY124: $i,SY125: $i] :
( ( sK6_B @ SV91 )
!= ( ordered_pair @ SY124 @ SY125 ) )
| ~ ( in @ ( sK6_B @ SV91 ) @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(533,plain,
! [SV92: $i] :
( ( ( relation @ SV92 )
= $false )
| ( ( ! [SY126: $i] :
( ( SY126
= ( ordered_pair @ ( sK4_C @ SY126 @ SV92 ) @ ( sK5_SY67 @ SY126 @ SV92 ) ) )
| ~ ( in @ SY126 @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(534,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(535,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(536,plain,
! [SV72: $i] :
( ( ( empty @ ( sK16_B @ SV72 ) )
= $false )
| ( ( empty @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(537,plain,
! [SV95: $i,SV93: $i] :
( ( ( ~ ( element @ SV93 @ ( powerset @ SV95 ) ) )
= $true )
| ( ( subset @ SV93 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(538,plain,
! [SV96: $i,SV94: $i] :
( ( ( ~ ( subset @ SV94 @ SV96 ) )
= $true )
| ( ( element @ SV94 @ ( powerset @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(539,plain,
! [SV86: $i,SV77: $i,SV61: $i] :
( ( ( in @ SV61 @ SV77 )
= $false )
| ( ( element @ SV77 @ ( powerset @ SV86 ) )
= $false )
| ( ( element @ SV61 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(540,plain,
! [SV87: $i,SV78: $i,SV62: $i] :
( ( ( in @ SV62 @ SV78 )
= $false )
| ( ( element @ SV78 @ ( powerset @ SV87 ) )
= $false )
| ( ( ~ ( empty @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(541,plain,
! [SV85: $i,SV88: $i,SV70: $i] :
( ( ( in @ ( ordered_pair @ SV70 @ SV88 ) @ sK1_A )
= $false )
| ( ( in @ ( ordered_pair @ SV70 @ SV85 ) @ sK1_A )
= $false )
| ( ( SV85 = SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(542,plain,
! [SV89: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 ) ) )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(543,plain,
! [SV89: $i] :
( ( ( ~ ( ( ( sK8_SY70 @ SV89 )
!= ( sK9_SY72 @ SV89 ) ) ) )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(544,plain,
! [SV90: $i,SV97: $i] :
( ( ( ! [SY129: $i,SY130: $i] :
( ~ ( in @ ( ordered_pair @ SV97 @ SY129 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SV97 @ SY130 ) @ SV90 )
| ( SY129 = SY130 ) ) )
= $true )
| ( ( function @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(545,plain,
! [SV91: $i] :
( ( ( ~ ! [SY124: $i,SY125: $i] :
( ( sK6_B @ SV91 )
!= ( ordered_pair @ SY124 @ SY125 ) ) )
= $false )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[532]) ).
thf(546,plain,
! [SV91: $i] :
( ( ( ~ ( in @ ( sK6_B @ SV91 ) @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[532]) ).
thf(547,plain,
! [SV92: $i,SV98: $i] :
( ( ( ( SV98
= ( ordered_pair @ ( sK4_C @ SV98 @ SV92 ) @ ( sK5_SY67 @ SV98 @ SV92 ) ) )
| ~ ( in @ SV98 @ SV92 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(548,plain,
! [SV95: $i,SV93: $i] :
( ( ( element @ SV93 @ ( powerset @ SV95 ) )
= $false )
| ( ( subset @ SV93 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(549,plain,
! [SV96: $i,SV94: $i] :
( ( ( subset @ SV94 @ SV96 )
= $false )
| ( ( element @ SV94 @ ( powerset @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(550,plain,
! [SV62: $i,SV78: $i,SV87: $i] :
( ( ( empty @ SV87 )
= $false )
| ( ( element @ SV78 @ ( powerset @ SV87 ) )
= $false )
| ( ( in @ SV62 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(551,plain,
! [SV89: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 ) ) )
= $true )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(552,plain,
! [SV89: $i] :
( ( ( ( ( sK8_SY70 @ SV89 )
!= ( sK9_SY72 @ SV89 ) ) )
= $true )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(553,plain,
! [SV90: $i,SV99: $i,SV97: $i] :
( ( ( ! [SY131: $i] :
( ~ ( in @ ( ordered_pair @ SV97 @ SV99 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SV97 @ SY131 ) @ SV90 )
| ( SV99 = SY131 ) ) )
= $true )
| ( ( function @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(554,plain,
! [SV91: $i] :
( ( ( ! [SY124: $i,SY125: $i] :
( ( sK6_B @ SV91 )
!= ( ordered_pair @ SY124 @ SY125 ) ) )
= $true )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(555,plain,
! [SV91: $i] :
( ( ( in @ ( sK6_B @ SV91 ) @ SV91 )
= $true )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(556,plain,
! [SV92: $i,SV98: $i] :
( ( ( SV98
= ( ordered_pair @ ( sK4_C @ SV98 @ SV92 ) @ ( sK5_SY67 @ SV98 @ SV92 ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV92 ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(557,plain,
! [SV89: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 )
| ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 ) )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(558,plain,
! [SV89: $i] :
( ( ( ( sK8_SY70 @ SV89 )
= ( sK9_SY72 @ SV89 ) )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(559,plain,
! [SV100: $i,SV90: $i,SV99: $i,SV97: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV97 @ SV99 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SV97 @ SV100 ) @ SV90 )
| ( SV99 = SV100 ) )
= $true )
| ( ( function @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(560,plain,
! [SV101: $i,SV91: $i] :
( ( ( ! [SY132: $i] :
( ( sK6_B @ SV91 )
!= ( ordered_pair @ SV101 @ SY132 ) ) )
= $true )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(561,plain,
! [SV92: $i,SV98: $i] :
( ( ( in @ SV98 @ SV92 )
= $false )
| ( ( SV98
= ( ordered_pair @ ( sK4_C @ SV98 @ SV92 ) @ ( sK5_SY67 @ SV98 @ SV92 ) ) )
= $true )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(562,plain,
! [SV89: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 ) )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(563,plain,
! [SV89: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 ) )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(564,plain,
! [SV100: $i,SV90: $i,SV99: $i,SV97: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV97 @ SV99 ) @ SV90 )
| ~ ( in @ ( ordered_pair @ SV97 @ SV100 ) @ SV90 ) )
= $true )
| ( ( SV99 = SV100 )
= $true )
| ( ( function @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(565,plain,
! [SV102: $i,SV101: $i,SV91: $i] :
( ( ( ( ( sK6_B @ SV91 )
!= ( ordered_pair @ SV101 @ SV102 ) ) )
= $true )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(566,plain,
! [SV89: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK8_SY70 @ SV89 ) ) @ SV89 )
= $true )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(567,plain,
! [SV89: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_B @ SV89 ) @ ( sK9_SY72 @ SV89 ) ) @ SV89 )
= $true )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(568,plain,
! [SV100: $i,SV90: $i,SV99: $i,SV97: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV97 @ SV99 ) @ SV90 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV97 @ SV100 ) @ SV90 ) )
= $true )
| ( ( SV99 = SV100 )
= $true )
| ( ( function @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(569,plain,
! [SV102: $i,SV101: $i,SV91: $i] :
( ( ( ( sK6_B @ SV91 )
= ( ordered_pair @ SV101 @ SV102 ) )
= $false )
| ( ( relation @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(570,plain,
! [SV100: $i,SV90: $i,SV99: $i,SV97: $i] :
( ( ( in @ ( ordered_pair @ SV97 @ SV99 ) @ SV90 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV97 @ SV100 ) @ SV90 ) )
= $true )
| ( ( SV99 = SV100 )
= $true )
| ( ( function @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(571,plain,
! [SV99: $i,SV90: $i,SV100: $i,SV97: $i] :
( ( ( in @ ( ordered_pair @ SV97 @ SV100 ) @ SV90 )
= $false )
| ( ( in @ ( ordered_pair @ SV97 @ SV99 ) @ SV90 )
= $false )
| ( ( SV99 = SV100 )
= $true )
| ( ( function @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(572,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[340,571,569,567,566,561,558,555,550,549,548,541,539,536,535,534,528,522,514,513,509,508,507,504,494,484,482,481,479,475,474,471,470,469,468,467,463,460,456,455,454,431,419,418,416,404,398,385,383,362]) ).
thf(573,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[572,336]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET988+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 15:19:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 32
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 .
% 0.13/0.37 (rf:0,axioms:32,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:34,loop_count:0,foatp_calls:0,translation:fof_full).....................
% 0.43/0.84
% 0.43/0.84 ********************************
% 0.43/0.84 * All subproblems solved! *
% 0.43/0.84 ********************************
% 0.43/0.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:34,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:572,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.76/0.98
% 0.76/0.98 %**** Beginning of derivation protocol ****
% 0.76/0.98 % SZS output start CNFRefutation
% See solution above
% 0.76/0.98
% 0.76/0.98 %**** End of derivation protocol ****
% 0.76/0.98 %**** no. of clauses in derivation: 573 ****
% 0.76/0.98 %**** clause counter: 572 ****
% 0.76/0.98
% 0.76/0.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:34,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:572,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------