TSTP Solution File: SEU156+2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU156+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:07:16 EDT 2022
% Result : Theorem 226.35s 226.67s
% Output : CNFRefutation 226.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 42
% Syntax : Number of formulae : 412 ( 200 unt; 22 typ; 0 def)
% Number of atoms : 2540 (1428 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 4414 ( 958 ~; 867 |; 42 &;2520 @)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 1088 ( 0 ^1084 !; 4 ?;1088 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY926,type,
sK2_SY926: $i ).
thf(tp_sK3_SY929,type,
sK3_SY929: $i ).
thf(tp_sK4_SY931,type,
sK4_SY931: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_D,type,
sK7_D: $i > $i > $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(19,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(53,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(83,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(84,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(85,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[84]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[85]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(90,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(91,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(94,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(95,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(98,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(101,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(103,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(106,plain,
( ( ! [SY926: $i,SY927: $i,SY928: $i] :
( ( ( ordered_pair @ sK1_A @ SY926 )
= ( ordered_pair @ SY927 @ SY928 ) )
=> ( ( sK1_A = SY927 )
& ( SY926 = SY928 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(107,plain,
( ( ! [SY929: $i,SY930: $i] :
( ( ( ordered_pair @ sK1_A @ sK2_SY926 )
= ( ordered_pair @ SY929 @ SY930 ) )
=> ( ( sK1_A = SY929 )
& ( sK2_SY926 = SY930 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(108,plain,
( ( ! [SY931: $i] :
( ( ( ordered_pair @ sK1_A @ sK2_SY926 )
= ( ordered_pair @ sK3_SY929 @ SY931 ) )
=> ( ( sK1_A = sK3_SY929 )
& ( sK2_SY926 = SY931 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[107]) ).
thf(109,plain,
( ( ( ( ordered_pair @ sK1_A @ sK2_SY926 )
= ( ordered_pair @ sK3_SY929 @ sK4_SY931 ) )
=> ( ( sK1_A = sK3_SY929 )
& ( sK2_SY926 = sK4_SY931 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(110,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY926 )
= ( ordered_pair @ sK3_SY929 @ sK4_SY931 ) )
= $true ),
inference(standard_cnf,[status(thm)],[109]) ).
thf(111,plain,
( ( ( sK1_A = sK3_SY929 )
& ( sK2_SY926 = sK4_SY931 ) )
= $false ),
inference(standard_cnf,[status(thm)],[109]) ).
thf(112,plain,
( ( sK1_A = sK3_SY929 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[111]) ).
thf(113,plain,
( ( sK2_SY926 = sK4_SY931 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[111]) ).
thf(114,plain,
( ( ( sK1_A != sK3_SY929 ) )
= $true ),
inference(polarity_switch,[status(thm)],[112]) ).
thf(115,plain,
( ( ( sK2_SY926 != sK4_SY931 ) )
= $true ),
inference(polarity_switch,[status(thm)],[113]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(118,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(119,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(120,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(122,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(123,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
= A )
| ( ( sK7_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK8_C @ B @ A )
!= A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( sK8_C @ B @ A )
= A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(127,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(129,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(131,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(132,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(134,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(137,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK8_C @ B @ A )
!= A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( sK8_C @ B @ A )
= A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(140,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
= A )
| ( ( sK7_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(141,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(142,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(143,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(144,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(145,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(146,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(148,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(149,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY926 )
= ( ordered_pair @ sK3_SY929 @ sK4_SY931 ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(150,plain,
( ( ( sK1_A != sK3_SY929 ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(151,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(152,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(153,plain,
! [SV1: $i] :
( ( ! [SY932: $i] :
( ( ordered_pair @ SV1 @ SY932 )
= ( unordered_pair @ ( unordered_pair @ SV1 @ SY932 ) @ ( singleton @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(154,plain,
! [SV2: $i] :
( ( ! [SY933: $i] :
~ ( empty @ ( ordered_pair @ SV2 @ SY933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(155,plain,
! [SV3: $i] :
( ( ( ( singleton @ SV3 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(156,plain,
! [SV4: $i] :
( ( ! [SY934: $i,SY935: $i,SY936: $i] :
( ( SV4 = SY936 )
| ( SV4 = SY935 )
| ( ( unordered_pair @ SV4 @ SY934 )
!= ( unordered_pair @ SY935 @ SY936 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(157,plain,
! [SV5: $i] :
( ( ( unordered_pair @ SV5 @ SV5 )
= ( singleton @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(158,plain,
! [SV6: $i] :
( ( ! [SY937: $i] :
( ~ ( subset @ ( singleton @ SV6 ) @ ( singleton @ SY937 ) )
| ( SV6 = SY937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(159,plain,
! [SV7: $i] :
( ( ! [SY938: $i] :
( ! [SY939: $i] :
( ( singleton @ SV7 )
!= ( unordered_pair @ SY938 @ SY939 ) )
| ( SV7 = SY938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(160,plain,
! [SV8: $i] :
( ( ! [SY940: $i,SY941: $i] :
( ( ( singleton @ SV8 )
!= ( unordered_pair @ SY940 @ SY941 ) )
| ( SY940 = SY941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(161,plain,
! [SV9: $i] :
( ( ! [SY942: $i] :
( ( unordered_pair @ SV9 @ SY942 )
= ( unordered_pair @ SY942 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(162,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
| ! [SY943: $i] :
~ ( empty @ ( set_union2 @ SV10 @ SY943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(163,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
| ! [SY944: $i] :
~ ( empty @ ( set_union2 @ SY944 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(164,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV12: $i] :
( ( ~ ( empty @ SV12 )
| ( SV12 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV13: $i] :
( ( ! [SY945: $i] :
( ~ ( empty @ SY945 )
| ~ ( in @ SV13 @ SY945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(167,plain,
! [SV14: $i] :
( ( ! [SY946: $i] :
( ( SV14 = SY946 )
| ~ ( empty @ SV14 )
| ~ ( empty @ SY946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(168,plain,
( ( sK1_A = sK3_SY929 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(169,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(170,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SY947 ) ) )
| ~ ( ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SV15 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SY947 ) ) )
| ( SY948
= ( unordered_pair @ SV15 @ SY947 ) ) )
| ~ ! [SY949: $i,SY950: $i] :
( ( SY950
!= ( unordered_pair @ SV15 @ SY949 ) )
| ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY950 )
| ( SY951 = SV15 )
| ( SY951 = SY949 ) )
| ~ ~ ( ~ ! [SY952: $i] :
( ( SY952 != SV15 )
| ( in @ SY952 @ SY950 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY949 )
| ( in @ SX3 @ SY950 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(171,plain,
! [SV16: $i,SV1: $i] :
( ( ( ordered_pair @ SV1 @ SV16 )
= ( unordered_pair @ ( unordered_pair @ SV1 @ SV16 ) @ ( singleton @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(172,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV2 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(173,plain,
! [SV3: $i] :
( ( ( singleton @ SV3 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(174,plain,
! [SV18: $i,SV4: $i] :
( ( ! [SY954: $i,SY955: $i] :
( ( SV4 = SY955 )
| ( SV4 = SY954 )
| ( ( unordered_pair @ SV4 @ SV18 )
!= ( unordered_pair @ SY954 @ SY955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(175,plain,
! [SV19: $i,SV6: $i] :
( ( ~ ( subset @ ( singleton @ SV6 ) @ ( singleton @ SV19 ) )
| ( SV6 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(176,plain,
! [SV20: $i,SV7: $i] :
( ( ! [SY956: $i] :
( ( singleton @ SV7 )
!= ( unordered_pair @ SV20 @ SY956 ) )
| ( SV7 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(177,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY957: $i] :
( ( ( singleton @ SV8 )
!= ( unordered_pair @ SV21 @ SY957 ) )
| ( SV21 = SY957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(178,plain,
! [SV22: $i,SV9: $i] :
( ( ( unordered_pair @ SV9 @ SV22 )
= ( unordered_pair @ SV22 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ! [SY943: $i] :
~ ( empty @ ( set_union2 @ SV10 @ SY943 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $true )
| ( ( ! [SY944: $i] :
~ ( empty @ ( set_union2 @ SY944 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $true )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV13: $i,SV23: $i] :
( ( ~ ( empty @ SV23 )
| ~ ( in @ SV13 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(183,plain,
! [SV24: $i,SV14: $i] :
( ( ( SV14 = SV24 )
| ~ ( empty @ SV14 )
| ~ ( empty @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(184,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(185,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(186,plain,
! [SV15: $i] :
( ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SY947 ) ) )
| ~ ( ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SV15 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SY947 ) ) )
| ( SY948
= ( unordered_pair @ SV15 @ SY947 ) ) )
| ~ ! [SY949: $i,SY950: $i] :
( ( SY950
!= ( unordered_pair @ SV15 @ SY949 ) )
| ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY950 )
| ( SY951 = SV15 )
| ( SY951 = SY949 ) )
| ~ ~ ( ~ ! [SY952: $i] :
( ( SY952 != SV15 )
| ( in @ SY952 @ SY950 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY949 )
| ( in @ SX3 @ SY950 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(187,plain,
! [SV17: $i,SV2: $i] :
( ( empty @ ( ordered_pair @ SV2 @ SV17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(188,plain,
! [SV18: $i,SV25: $i,SV4: $i] :
( ( ! [SY958: $i] :
( ( SV4 = SY958 )
| ( SV4 = SV25 )
| ( ( unordered_pair @ SV4 @ SV18 )
!= ( unordered_pair @ SV25 @ SY958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(189,plain,
! [SV19: $i,SV6: $i] :
( ( ( ~ ( subset @ ( singleton @ SV6 ) @ ( singleton @ SV19 ) ) )
= $true )
| ( ( SV6 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(190,plain,
! [SV20: $i,SV7: $i] :
( ( ( ! [SY956: $i] :
( ( singleton @ SV7 )
!= ( unordered_pair @ SV20 @ SY956 ) ) )
= $true )
| ( ( SV7 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(191,plain,
! [SV26: $i,SV21: $i,SV8: $i] :
( ( ( ( singleton @ SV8 )
!= ( unordered_pair @ SV21 @ SV26 ) )
| ( SV21 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(192,plain,
! [SV27: $i,SV10: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV10 @ SV27 ) ) )
= $true )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV11: $i,SV28: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV28 @ SV11 ) ) )
= $true )
| ( ( empty @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(194,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(195,plain,
! [SV13: $i,SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(196,plain,
! [SV24: $i,SV14: $i] :
( ( ( ( SV14 = SV24 )
| ~ ( empty @ SV14 ) )
= $true )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(197,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(198,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(199,plain,
! [SV15: $i] :
( ( ~ ! [SY947: $i,SY948: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SY947 ) ) )
| ~ ( ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SV15 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SY947 ) ) )
| ( SY948
= ( unordered_pair @ SV15 @ SY947 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(200,plain,
! [SV15: $i] :
( ( ~ ! [SY949: $i,SY950: $i] :
( ( SY950
!= ( unordered_pair @ SV15 @ SY949 ) )
| ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY950 )
| ( SY951 = SV15 )
| ( SY951 = SY949 ) )
| ~ ~ ( ~ ! [SY952: $i] :
( ( SY952 != SV15 )
| ( in @ SY952 @ SY950 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY949 )
| ( in @ SX3 @ SY950 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(201,plain,
! [SV18: $i,SV25: $i,SV29: $i,SV4: $i] :
( ( ( SV4 = SV29 )
| ( SV4 = SV25 )
| ( ( unordered_pair @ SV4 @ SV18 )
!= ( unordered_pair @ SV25 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(202,plain,
! [SV19: $i,SV6: $i] :
( ( ( subset @ ( singleton @ SV6 ) @ ( singleton @ SV19 ) )
= $false )
| ( ( SV6 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(203,plain,
! [SV30: $i,SV20: $i,SV7: $i] :
( ( ( ( ( singleton @ SV7 )
!= ( unordered_pair @ SV20 @ SV30 ) ) )
= $true )
| ( ( SV7 = SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(204,plain,
! [SV26: $i,SV21: $i,SV8: $i] :
( ( ( ( ( singleton @ SV8 )
!= ( unordered_pair @ SV21 @ SV26 ) ) )
= $true )
| ( ( SV21 = SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV27: $i,SV10: $i] :
( ( ( empty @ ( set_union2 @ SV10 @ SV27 ) )
= $false )
| ( ( empty @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(206,plain,
! [SV11: $i,SV28: $i] :
( ( ( empty @ ( set_union2 @ SV28 @ SV11 ) )
= $false )
| ( ( empty @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV13: $i,SV23: $i] :
( ( ( empty @ SV23 )
= $false )
| ( ( ~ ( in @ SV13 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(208,plain,
! [SV24: $i,SV14: $i] :
( ( ( SV14 = SV24 )
= $true )
| ( ( ~ ( empty @ SV14 ) )
= $true )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV31: $i] :
( ( ! [SY959: $i] :
( ~ ( ~ ( ( ( sK8_C @ SY959 @ SV31 )
!= SV31 )
| ~ ( in @ ( sK8_C @ SY959 @ SV31 ) @ SY959 ) )
| ~ ( ( ( sK8_C @ SY959 @ SV31 )
= SV31 )
| ( in @ ( sK8_C @ SY959 @ SV31 ) @ SY959 ) ) )
| ( SY959
= ( singleton @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV32: $i] :
( ( ! [SY960: $i] :
( ( SY960
!= ( singleton @ SV32 ) )
| ~ ( ~ ! [SY961: $i] :
( ( SY961 != SV32 )
| ( in @ SY961 @ SY960 ) )
| ~ ! [SY962: $i] :
( ~ ( in @ SY962 @ SY960 )
| ( SY962 = SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(211,plain,
! [SV15: $i] :
( ( ! [SY947: $i,SY948: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
!= SY947 ) ) )
| ~ ( ( in @ ( sK7_D @ SY948 @ SY947 @ SV15 ) @ SY948 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SV15 )
| ( ( sK7_D @ SY948 @ SY947 @ SV15 )
= SY947 ) ) )
| ( SY948
= ( unordered_pair @ SV15 @ SY947 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(212,plain,
! [SV15: $i] :
( ( ! [SY949: $i,SY950: $i] :
( ( SY950
!= ( unordered_pair @ SV15 @ SY949 ) )
| ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY950 )
| ( SY951 = SV15 )
| ( SY951 = SY949 ) )
| ~ ~ ( ~ ! [SY952: $i] :
( ( SY952 != SV15 )
| ( in @ SY952 @ SY950 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY949 )
| ( in @ SX3 @ SY950 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(213,plain,
! [SV18: $i,SV25: $i,SV29: $i,SV4: $i] :
( ( ( SV4 = SV29 )
= $true )
| ( ( ( SV4 = SV25 )
| ( ( unordered_pair @ SV4 @ SV18 )
!= ( unordered_pair @ SV25 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(214,plain,
! [SV30: $i,SV20: $i,SV7: $i] :
( ( ( ( singleton @ SV7 )
= ( unordered_pair @ SV20 @ SV30 ) )
= $false )
| ( ( SV7 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(215,plain,
! [SV26: $i,SV21: $i,SV8: $i] :
( ( ( ( singleton @ SV8 )
= ( unordered_pair @ SV21 @ SV26 ) )
= $false )
| ( ( SV21 = SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(216,plain,
! [SV23: $i,SV13: $i] :
( ( ( in @ SV13 @ SV23 )
= $false )
| ( ( empty @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(217,plain,
! [SV24: $i,SV14: $i] :
( ( ( empty @ SV14 )
= $false )
| ( ( SV14 = SV24 )
= $true )
| ( ( ~ ( empty @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV31: $i,SV33: $i] :
( ( ~ ( ~ ( ( ( sK8_C @ SV33 @ SV31 )
!= SV31 )
| ~ ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) )
| ~ ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
| ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) ) )
| ( SV33
= ( singleton @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV32: $i,SV34: $i] :
( ( ( SV34
!= ( singleton @ SV32 ) )
| ~ ( ~ ! [SY963: $i] :
( ( SY963 != SV32 )
| ( in @ SY963 @ SV34 ) )
| ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ SV34 )
| ( SY964 = SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV15: $i,SV35: $i] :
( ( ! [SY965: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY965 @ SV35 @ SV15 ) @ SY965 )
| ( ( sK7_D @ SY965 @ SV35 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY965 @ SV35 @ SV15 ) @ SY965 )
| ( ( sK7_D @ SY965 @ SV35 @ SV15 )
!= SV35 ) ) )
| ~ ( ( in @ ( sK7_D @ SY965 @ SV35 @ SV15 ) @ SY965 )
| ( ( sK7_D @ SY965 @ SV35 @ SV15 )
= SV15 )
| ( ( sK7_D @ SY965 @ SV35 @ SV15 )
= SV35 ) ) )
| ( SY965
= ( unordered_pair @ SV15 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(221,plain,
! [SV36: $i,SV15: $i] :
( ( ! [SY966: $i] :
( ( SY966
!= ( unordered_pair @ SV15 @ SV36 ) )
| ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ SY966 )
| ( SY967 = SV15 )
| ( SY967 = SV36 ) )
| ~ ~ ( ~ ! [SY952: $i] :
( ( SY952 != SV15 )
| ( in @ SY952 @ SY966 ) )
| ~ ! [SY969: $i] :
( ( SY969 != SV36 )
| ( in @ SY969 @ SY966 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(222,plain,
! [SV29: $i,SV18: $i,SV25: $i,SV4: $i] :
( ( ( SV4 = SV25 )
= $true )
| ( ( ( ( unordered_pair @ SV4 @ SV18 )
!= ( unordered_pair @ SV25 @ SV29 ) ) )
= $true )
| ( ( SV4 = SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(223,plain,
! [SV14: $i,SV24: $i] :
( ( ( empty @ SV24 )
= $false )
| ( ( SV14 = SV24 )
= $true )
| ( ( empty @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV31: $i,SV33: $i] :
( ( ( ~ ( ~ ( ( ( sK8_C @ SV33 @ SV31 )
!= SV31 )
| ~ ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) )
| ~ ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
| ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) ) ) )
= $true )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(225,plain,
! [SV32: $i,SV34: $i] :
( ( ( ( SV34
!= ( singleton @ SV32 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY963: $i] :
( ( SY963 != SV32 )
| ( in @ SY963 @ SV34 ) )
| ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ SV34 )
| ( SY964 = SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(226,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) ) )
| ~ ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 ) ) )
| ( SV37
= ( unordered_pair @ SV15 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(227,plain,
! [SV36: $i,SV15: $i,SV38: $i] :
( ( ( SV38
!= ( unordered_pair @ SV15 @ SV36 ) )
| ~ ( ~ ! [SY970: $i] :
( ~ ( in @ SY970 @ SV38 )
| ( SY970 = SV15 )
| ( SY970 = SV36 ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) )
| ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(228,plain,
! [SV29: $i,SV25: $i,SV18: $i,SV4: $i] :
( ( ( ( unordered_pair @ SV4 @ SV18 )
= ( unordered_pair @ SV25 @ SV29 ) )
= $false )
| ( ( SV4 = SV25 )
= $true )
| ( ( SV4 = SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(229,plain,
! [SV31: $i,SV33: $i] :
( ( ( ~ ( ( ( sK8_C @ SV33 @ SV31 )
!= SV31 )
| ~ ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) )
| ~ ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
| ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) ) )
= $false )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(230,plain,
! [SV32: $i,SV34: $i] :
( ( ( SV34
= ( singleton @ SV32 ) )
= $false )
| ( ( ~ ( ~ ! [SY963: $i] :
( ( SY963 != SV32 )
| ( in @ SY963 @ SV34 ) )
| ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ SV34 )
| ( SY964 = SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(231,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) ) )
| ~ ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 ) ) ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(232,plain,
! [SV36: $i,SV15: $i,SV38: $i] :
( ( ( ( SV38
!= ( unordered_pair @ SV15 @ SV36 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY970: $i] :
( ~ ( in @ SY970 @ SV38 )
| ( SY970 = SV15 )
| ( SY970 = SV36 ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) )
| ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(233,plain,
! [SV31: $i,SV33: $i] :
( ( ( ~ ( ( ( sK8_C @ SV33 @ SV31 )
!= SV31 )
| ~ ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) ) )
= $false )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(234,plain,
! [SV31: $i,SV33: $i] :
( ( ( ~ ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
| ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) ) )
= $false )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(235,plain,
! [SV34: $i,SV32: $i] :
( ( ( ~ ! [SY963: $i] :
( ( SY963 != SV32 )
| ( in @ SY963 @ SV34 ) )
| ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ SV34 )
| ( SY964 = SV32 ) ) )
= $false )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(236,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) ) )
| ~ ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 ) ) )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(237,plain,
! [SV36: $i,SV15: $i,SV38: $i] :
( ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false )
| ( ( ~ ( ~ ! [SY970: $i] :
( ~ ( in @ SY970 @ SV38 )
| ( SY970 = SV15 )
| ( SY970 = SV36 ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) )
| ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(238,plain,
! [SV31: $i,SV33: $i] :
( ( ( ( ( sK8_C @ SV33 @ SV31 )
!= SV31 )
| ~ ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) )
= $true )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(239,plain,
! [SV31: $i,SV33: $i] :
( ( ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
| ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) )
= $true )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(240,plain,
! [SV34: $i,SV32: $i] :
( ( ( ~ ! [SY963: $i] :
( ( SY963 != SV32 )
| ( in @ SY963 @ SV34 ) ) )
= $false )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(241,plain,
! [SV32: $i,SV34: $i] :
( ( ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ SV34 )
| ( SY964 = SV32 ) ) )
= $false )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(242,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) ) ) )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(243,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 ) ) )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(244,plain,
! [SV36: $i,SV15: $i,SV38: $i] :
( ( ( ~ ! [SY970: $i] :
( ~ ( in @ SY970 @ SV38 )
| ( SY970 = SV15 )
| ( SY970 = SV36 ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) )
| ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) ) )
= $false )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(245,plain,
! [SV31: $i,SV33: $i] :
( ( ( ( ( sK8_C @ SV33 @ SV31 )
!= SV31 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) )
= $true )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(246,plain,
! [SV31: $i,SV33: $i] :
( ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
= $true )
| ( ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 )
= $true )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(247,plain,
! [SV34: $i,SV32: $i] :
( ( ( ! [SY963: $i] :
( ( SY963 != SV32 )
| ( in @ SY963 @ SV34 ) ) )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(248,plain,
! [SV32: $i,SV34: $i] :
( ( ( ! [SY964: $i] :
( ~ ( in @ SY964 @ SV34 )
| ( SY964 = SV32 ) ) )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(249,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) ) ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(250,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(251,plain,
! [SV36: $i,SV15: $i,SV38: $i] :
( ( ( ~ ! [SY970: $i] :
( ~ ( in @ SY970 @ SV38 )
| ( SY970 = SV15 )
| ( SY970 = SV36 ) ) )
= $false )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(252,plain,
! [SV36: $i,SV38: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) )
| ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) ) )
= $false )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(253,plain,
! [SV31: $i,SV33: $i] :
( ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 ) )
= $true )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV34: $i,SV32: $i,SV39: $i] :
( ( ( ( SV39 != SV32 )
| ( in @ SV39 @ SV34 ) )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(255,plain,
! [SV32: $i,SV34: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV34 )
| ( SV40 = SV32 ) )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(256,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) ) )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(257,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
= $true )
| ( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(258,plain,
! [SV36: $i,SV15: $i,SV38: $i] :
( ( ( ! [SY970: $i] :
( ~ ( in @ SY970 @ SV38 )
| ( SY970 = SV15 )
| ( SY970 = SV36 ) ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(259,plain,
! [SV36: $i,SV38: $i,SV15: $i] :
( ( ( ~ ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) )
| ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(260,plain,
! [SV31: $i,SV33: $i] :
( ( ( in @ ( sK8_C @ SV33 @ SV31 ) @ SV33 )
= $false )
| ( ( ( sK8_C @ SV33 @ SV31 )
= SV31 )
= $false )
| ( ( SV33
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(261,plain,
! [SV34: $i,SV32: $i,SV39: $i] :
( ( ( ( SV39 != SV32 ) )
= $true )
| ( ( in @ SV39 @ SV34 )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(262,plain,
! [SV32: $i,SV34: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV34 ) )
= $true )
| ( ( SV40 = SV32 )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(263,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) ) )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(264,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) ) )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(265,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
= $true )
| ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 )
= $true )
| ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV36: $i,SV15: $i,SV38: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV38 )
| ( SV41 = SV15 )
| ( SV41 = SV36 ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV36: $i,SV38: $i,SV15: $i] :
( ( ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) )
| ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV34: $i,SV32: $i,SV39: $i] :
( ( ( SV39 = SV32 )
= $false )
| ( ( in @ SV39 @ SV34 )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(269,plain,
! [SV32: $i,SV34: $i,SV40: $i] :
( ( ( in @ SV40 @ SV34 )
= $false )
| ( ( SV40 = SV32 )
= $true )
| ( ( SV34
= ( singleton @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(270,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(271,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
| ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(272,plain,
! [SV36: $i,SV15: $i,SV38: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV38 ) )
= $true )
| ( ( ( SV41 = SV15 )
| ( SV41 = SV36 ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(273,plain,
! [SV36: $i,SV38: $i,SV15: $i] :
( ( ( ~ ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(274,plain,
! [SV15: $i,SV38: $i,SV36: $i] :
( ( ( ~ ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(275,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 ) )
= $true )
| ( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(276,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 ) )
= $true )
| ( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(277,plain,
! [SV36: $i,SV15: $i,SV38: $i,SV41: $i] :
( ( ( in @ SV41 @ SV38 )
= $false )
| ( ( ( SV41 = SV15 )
| ( SV41 = SV36 ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(278,plain,
! [SV36: $i,SV38: $i,SV15: $i] :
( ( ( ! [SY971: $i] :
( ( SY971 != SV15 )
| ( in @ SY971 @ SV38 ) ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(279,plain,
! [SV15: $i,SV38: $i,SV36: $i] :
( ( ( ! [SY972: $i] :
( ( SY972 != SV36 )
| ( in @ SY972 @ SV38 ) ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(280,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
= $false )
| ( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV15 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(281,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
= $false )
| ( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
!= SV35 ) )
= $true )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(282,plain,
! [SV38: $i,SV36: $i,SV15: $i,SV41: $i] :
( ( ( SV41 = SV15 )
= $true )
| ( ( SV41 = SV36 )
= $true )
| ( ( in @ SV41 @ SV38 )
= $false )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(283,plain,
! [SV36: $i,SV38: $i,SV15: $i,SV42: $i] :
( ( ( ( SV42 != SV15 )
| ( in @ SV42 @ SV38 ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(284,plain,
! [SV15: $i,SV38: $i,SV36: $i,SV43: $i] :
( ( ( ( SV43 != SV36 )
| ( in @ SV43 @ SV38 ) )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(285,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV15 )
= $false )
| ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(286,plain,
! [SV15: $i,SV35: $i,SV37: $i] :
( ( ( ( sK7_D @ SV37 @ SV35 @ SV15 )
= SV35 )
= $false )
| ( ( in @ ( sK7_D @ SV37 @ SV35 @ SV15 ) @ SV37 )
= $false )
| ( ( SV37
= ( unordered_pair @ SV15 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(287,plain,
! [SV36: $i,SV38: $i,SV15: $i,SV42: $i] :
( ( ( ( SV42 != SV15 ) )
= $true )
| ( ( in @ SV42 @ SV38 )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(288,plain,
! [SV15: $i,SV38: $i,SV36: $i,SV43: $i] :
( ( ( ( SV43 != SV36 ) )
= $true )
| ( ( in @ SV43 @ SV38 )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(289,plain,
! [SV36: $i,SV38: $i,SV15: $i,SV42: $i] :
( ( ( SV42 = SV15 )
= $false )
| ( ( in @ SV42 @ SV38 )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(290,plain,
! [SV15: $i,SV38: $i,SV36: $i,SV43: $i] :
( ( ( SV43 = SV36 )
= $false )
| ( ( in @ SV43 @ SV38 )
= $true )
| ( ( SV38
= ( unordered_pair @ SV15 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(291,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[141,290,289,286,285,282,269,268,265,260,246,228,223,216,215,214,206,205,202,194,187,178,173,171,168,164,157,149,144]) ).
thf(292,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(294,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(295,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(296,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(299,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK8_C @ B @ A )
!= A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( sK8_C @ B @ A )
= A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(302,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ C )
| ( ( sK7_D @ C @ B @ A )
= A )
| ( ( sK7_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(303,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(304,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(305,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(306,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(307,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(308,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(310,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(311,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY926 )
= ( ordered_pair @ sK3_SY929 @ sK4_SY931 ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(312,plain,
( ( ( sK2_SY926 != sK4_SY931 ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(313,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(314,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK7_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(315,plain,
! [SV44: $i] :
( ( ! [SY973: $i] :
( ( ordered_pair @ SV44 @ SY973 )
= ( unordered_pair @ ( unordered_pair @ SV44 @ SY973 ) @ ( singleton @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(316,plain,
! [SV45: $i] :
( ( ! [SY974: $i] :
~ ( empty @ ( ordered_pair @ SV45 @ SY974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(317,plain,
! [SV46: $i] :
( ( ( ( singleton @ SV46 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(318,plain,
! [SV47: $i] :
( ( ! [SY975: $i,SY976: $i,SY977: $i] :
( ( SV47 = SY977 )
| ( SV47 = SY976 )
| ( ( unordered_pair @ SV47 @ SY975 )
!= ( unordered_pair @ SY976 @ SY977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(319,plain,
! [SV48: $i] :
( ( ( unordered_pair @ SV48 @ SV48 )
= ( singleton @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(320,plain,
! [SV49: $i] :
( ( ! [SY978: $i] :
( ~ ( subset @ ( singleton @ SV49 ) @ ( singleton @ SY978 ) )
| ( SV49 = SY978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(321,plain,
! [SV50: $i] :
( ( ! [SY979: $i] :
( ! [SY980: $i] :
( ( singleton @ SV50 )
!= ( unordered_pair @ SY979 @ SY980 ) )
| ( SV50 = SY979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(322,plain,
! [SV51: $i] :
( ( ! [SY981: $i,SY982: $i] :
( ( ( singleton @ SV51 )
!= ( unordered_pair @ SY981 @ SY982 ) )
| ( SY981 = SY982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(323,plain,
! [SV52: $i] :
( ( ! [SY983: $i] :
( ( unordered_pair @ SV52 @ SY983 )
= ( unordered_pair @ SY983 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(324,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
| ! [SY984: $i] :
~ ( empty @ ( set_union2 @ SV53 @ SY984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(325,plain,
! [SV54: $i] :
( ( ( empty @ SV54 )
| ! [SY985: $i] :
~ ( empty @ ( set_union2 @ SY985 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(326,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(327,plain,
! [SV55: $i] :
( ( ~ ( empty @ SV55 )
| ( SV55 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(328,plain,
! [SV56: $i] :
( ( ! [SY986: $i] :
( ~ ( empty @ SY986 )
| ~ ( in @ SV56 @ SY986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(329,plain,
! [SV57: $i] :
( ( ! [SY987: $i] :
( ( SV57 = SY987 )
| ~ ( empty @ SV57 )
| ~ ( empty @ SY987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(330,plain,
( ( sK2_SY926 = sK4_SY931 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(331,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(332,plain,
! [SV58: $i] :
( ( ~ ( ~ ! [SY988: $i,SY989: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SY988 ) ) )
| ~ ( ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SV58 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SY988 ) ) )
| ( SY989
= ( unordered_pair @ SV58 @ SY988 ) ) )
| ~ ! [SY990: $i,SY991: $i] :
( ( SY991
!= ( unordered_pair @ SV58 @ SY990 ) )
| ~ ( ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SY991 )
| ( SY992 = SV58 )
| ( SY992 = SY990 ) )
| ~ ~ ( ~ ! [SY993: $i] :
( ( SY993 != SV58 )
| ( in @ SY993 @ SY991 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY990 )
| ( in @ SX3 @ SY991 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(333,plain,
! [SV59: $i,SV44: $i] :
( ( ( ordered_pair @ SV44 @ SV59 )
= ( unordered_pair @ ( unordered_pair @ SV44 @ SV59 ) @ ( singleton @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(334,plain,
! [SV60: $i,SV45: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV45 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(335,plain,
! [SV46: $i] :
( ( ( singleton @ SV46 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(336,plain,
! [SV61: $i,SV47: $i] :
( ( ! [SY995: $i,SY996: $i] :
( ( SV47 = SY996 )
| ( SV47 = SY995 )
| ( ( unordered_pair @ SV47 @ SV61 )
!= ( unordered_pair @ SY995 @ SY996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(337,plain,
! [SV62: $i,SV49: $i] :
( ( ~ ( subset @ ( singleton @ SV49 ) @ ( singleton @ SV62 ) )
| ( SV49 = SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(338,plain,
! [SV63: $i,SV50: $i] :
( ( ! [SY997: $i] :
( ( singleton @ SV50 )
!= ( unordered_pair @ SV63 @ SY997 ) )
| ( SV50 = SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(339,plain,
! [SV64: $i,SV51: $i] :
( ( ! [SY998: $i] :
( ( ( singleton @ SV51 )
!= ( unordered_pair @ SV64 @ SY998 ) )
| ( SV64 = SY998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(340,plain,
! [SV65: $i,SV52: $i] :
( ( ( unordered_pair @ SV52 @ SV65 )
= ( unordered_pair @ SV65 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(341,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
= $true )
| ( ( ! [SY984: $i] :
~ ( empty @ ( set_union2 @ SV53 @ SY984 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(342,plain,
! [SV54: $i] :
( ( ( empty @ SV54 )
= $true )
| ( ( ! [SY985: $i] :
~ ( empty @ ( set_union2 @ SY985 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(343,plain,
! [SV55: $i] :
( ( ( ~ ( empty @ SV55 ) )
= $true )
| ( ( SV55 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(344,plain,
! [SV56: $i,SV66: $i] :
( ( ~ ( empty @ SV66 )
| ~ ( in @ SV56 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(345,plain,
! [SV67: $i,SV57: $i] :
( ( ( SV57 = SV67 )
| ~ ( empty @ SV57 )
| ~ ( empty @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(346,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(347,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(348,plain,
! [SV58: $i] :
( ( ~ ! [SY988: $i,SY989: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SY988 ) ) )
| ~ ( ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SV58 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SY988 ) ) )
| ( SY989
= ( unordered_pair @ SV58 @ SY988 ) ) )
| ~ ! [SY990: $i,SY991: $i] :
( ( SY991
!= ( unordered_pair @ SV58 @ SY990 ) )
| ~ ( ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SY991 )
| ( SY992 = SV58 )
| ( SY992 = SY990 ) )
| ~ ~ ( ~ ! [SY993: $i] :
( ( SY993 != SV58 )
| ( in @ SY993 @ SY991 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY990 )
| ( in @ SX3 @ SY991 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(349,plain,
! [SV60: $i,SV45: $i] :
( ( empty @ ( ordered_pair @ SV45 @ SV60 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(350,plain,
! [SV61: $i,SV68: $i,SV47: $i] :
( ( ! [SY999: $i] :
( ( SV47 = SY999 )
| ( SV47 = SV68 )
| ( ( unordered_pair @ SV47 @ SV61 )
!= ( unordered_pair @ SV68 @ SY999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(351,plain,
! [SV62: $i,SV49: $i] :
( ( ( ~ ( subset @ ( singleton @ SV49 ) @ ( singleton @ SV62 ) ) )
= $true )
| ( ( SV49 = SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(352,plain,
! [SV63: $i,SV50: $i] :
( ( ( ! [SY997: $i] :
( ( singleton @ SV50 )
!= ( unordered_pair @ SV63 @ SY997 ) ) )
= $true )
| ( ( SV50 = SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(353,plain,
! [SV69: $i,SV64: $i,SV51: $i] :
( ( ( ( singleton @ SV51 )
!= ( unordered_pair @ SV64 @ SV69 ) )
| ( SV64 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(354,plain,
! [SV70: $i,SV53: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV53 @ SV70 ) ) )
= $true )
| ( ( empty @ SV53 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(355,plain,
! [SV54: $i,SV71: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV71 @ SV54 ) ) )
= $true )
| ( ( empty @ SV54 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(356,plain,
! [SV55: $i] :
( ( ( empty @ SV55 )
= $false )
| ( ( SV55 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(357,plain,
! [SV56: $i,SV66: $i] :
( ( ( ~ ( empty @ SV66 ) )
= $true )
| ( ( ~ ( in @ SV56 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(358,plain,
! [SV67: $i,SV57: $i] :
( ( ( ( SV57 = SV67 )
| ~ ( empty @ SV57 ) )
= $true )
| ( ( ~ ( empty @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(359,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK8_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK8_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(360,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(361,plain,
! [SV58: $i] :
( ( ~ ! [SY988: $i,SY989: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SY988 ) ) )
| ~ ( ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SV58 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SY988 ) ) )
| ( SY989
= ( unordered_pair @ SV58 @ SY988 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(362,plain,
! [SV58: $i] :
( ( ~ ! [SY990: $i,SY991: $i] :
( ( SY991
!= ( unordered_pair @ SV58 @ SY990 ) )
| ~ ( ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SY991 )
| ( SY992 = SV58 )
| ( SY992 = SY990 ) )
| ~ ~ ( ~ ! [SY993: $i] :
( ( SY993 != SV58 )
| ( in @ SY993 @ SY991 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY990 )
| ( in @ SX3 @ SY991 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(363,plain,
! [SV61: $i,SV68: $i,SV72: $i,SV47: $i] :
( ( ( SV47 = SV72 )
| ( SV47 = SV68 )
| ( ( unordered_pair @ SV47 @ SV61 )
!= ( unordered_pair @ SV68 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV62: $i,SV49: $i] :
( ( ( subset @ ( singleton @ SV49 ) @ ( singleton @ SV62 ) )
= $false )
| ( ( SV49 = SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(365,plain,
! [SV73: $i,SV63: $i,SV50: $i] :
( ( ( ( ( singleton @ SV50 )
!= ( unordered_pair @ SV63 @ SV73 ) ) )
= $true )
| ( ( SV50 = SV63 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(366,plain,
! [SV69: $i,SV64: $i,SV51: $i] :
( ( ( ( ( singleton @ SV51 )
!= ( unordered_pair @ SV64 @ SV69 ) ) )
= $true )
| ( ( SV64 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(367,plain,
! [SV70: $i,SV53: $i] :
( ( ( empty @ ( set_union2 @ SV53 @ SV70 ) )
= $false )
| ( ( empty @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(368,plain,
! [SV54: $i,SV71: $i] :
( ( ( empty @ ( set_union2 @ SV71 @ SV54 ) )
= $false )
| ( ( empty @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(369,plain,
! [SV56: $i,SV66: $i] :
( ( ( empty @ SV66 )
= $false )
| ( ( ~ ( in @ SV56 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(370,plain,
! [SV67: $i,SV57: $i] :
( ( ( SV57 = SV67 )
= $true )
| ( ( ~ ( empty @ SV57 ) )
= $true )
| ( ( ~ ( empty @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(371,plain,
! [SV74: $i] :
( ( ! [SY1000: $i] :
( ~ ( ~ ( ( ( sK8_C @ SY1000 @ SV74 )
!= SV74 )
| ~ ( in @ ( sK8_C @ SY1000 @ SV74 ) @ SY1000 ) )
| ~ ( ( ( sK8_C @ SY1000 @ SV74 )
= SV74 )
| ( in @ ( sK8_C @ SY1000 @ SV74 ) @ SY1000 ) ) )
| ( SY1000
= ( singleton @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(372,plain,
! [SV75: $i] :
( ( ! [SY1001: $i] :
( ( SY1001
!= ( singleton @ SV75 ) )
| ~ ( ~ ! [SY1002: $i] :
( ( SY1002 != SV75 )
| ( in @ SY1002 @ SY1001 ) )
| ~ ! [SY1003: $i] :
( ~ ( in @ SY1003 @ SY1001 )
| ( SY1003 = SV75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(373,plain,
! [SV58: $i] :
( ( ! [SY988: $i,SY989: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
!= SY988 ) ) )
| ~ ( ( in @ ( sK7_D @ SY989 @ SY988 @ SV58 ) @ SY989 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SV58 )
| ( ( sK7_D @ SY989 @ SY988 @ SV58 )
= SY988 ) ) )
| ( SY989
= ( unordered_pair @ SV58 @ SY988 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(374,plain,
! [SV58: $i] :
( ( ! [SY990: $i,SY991: $i] :
( ( SY991
!= ( unordered_pair @ SV58 @ SY990 ) )
| ~ ( ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SY991 )
| ( SY992 = SV58 )
| ( SY992 = SY990 ) )
| ~ ~ ( ~ ! [SY993: $i] :
( ( SY993 != SV58 )
| ( in @ SY993 @ SY991 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY990 )
| ( in @ SX3 @ SY991 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(375,plain,
! [SV61: $i,SV68: $i,SV72: $i,SV47: $i] :
( ( ( SV47 = SV72 )
= $true )
| ( ( ( SV47 = SV68 )
| ( ( unordered_pair @ SV47 @ SV61 )
!= ( unordered_pair @ SV68 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(376,plain,
! [SV73: $i,SV63: $i,SV50: $i] :
( ( ( ( singleton @ SV50 )
= ( unordered_pair @ SV63 @ SV73 ) )
= $false )
| ( ( SV50 = SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(377,plain,
! [SV69: $i,SV64: $i,SV51: $i] :
( ( ( ( singleton @ SV51 )
= ( unordered_pair @ SV64 @ SV69 ) )
= $false )
| ( ( SV64 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(378,plain,
! [SV66: $i,SV56: $i] :
( ( ( in @ SV56 @ SV66 )
= $false )
| ( ( empty @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(379,plain,
! [SV67: $i,SV57: $i] :
( ( ( empty @ SV57 )
= $false )
| ( ( SV57 = SV67 )
= $true )
| ( ( ~ ( empty @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(380,plain,
! [SV74: $i,SV76: $i] :
( ( ~ ( ~ ( ( ( sK8_C @ SV76 @ SV74 )
!= SV74 )
| ~ ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) )
| ~ ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
| ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) ) )
| ( SV76
= ( singleton @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(381,plain,
! [SV75: $i,SV77: $i] :
( ( ( SV77
!= ( singleton @ SV75 ) )
| ~ ( ~ ! [SY1004: $i] :
( ( SY1004 != SV75 )
| ( in @ SY1004 @ SV77 ) )
| ~ ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV77 )
| ( SY1005 = SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(382,plain,
! [SV58: $i,SV78: $i] :
( ( ! [SY1006: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SY1006 @ SV78 @ SV58 ) @ SY1006 )
| ( ( sK7_D @ SY1006 @ SV78 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SY1006 @ SV78 @ SV58 ) @ SY1006 )
| ( ( sK7_D @ SY1006 @ SV78 @ SV58 )
!= SV78 ) ) )
| ~ ( ( in @ ( sK7_D @ SY1006 @ SV78 @ SV58 ) @ SY1006 )
| ( ( sK7_D @ SY1006 @ SV78 @ SV58 )
= SV58 )
| ( ( sK7_D @ SY1006 @ SV78 @ SV58 )
= SV78 ) ) )
| ( SY1006
= ( unordered_pair @ SV58 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(383,plain,
! [SV79: $i,SV58: $i] :
( ( ! [SY1007: $i] :
( ( SY1007
!= ( unordered_pair @ SV58 @ SV79 ) )
| ~ ( ~ ! [SY1008: $i] :
( ~ ( in @ SY1008 @ SY1007 )
| ( SY1008 = SV58 )
| ( SY1008 = SV79 ) )
| ~ ~ ( ~ ! [SY993: $i] :
( ( SY993 != SV58 )
| ( in @ SY993 @ SY1007 ) )
| ~ ! [SY1010: $i] :
( ( SY1010 != SV79 )
| ( in @ SY1010 @ SY1007 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(384,plain,
! [SV72: $i,SV61: $i,SV68: $i,SV47: $i] :
( ( ( SV47 = SV68 )
= $true )
| ( ( ( ( unordered_pair @ SV47 @ SV61 )
!= ( unordered_pair @ SV68 @ SV72 ) ) )
= $true )
| ( ( SV47 = SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(385,plain,
! [SV57: $i,SV67: $i] :
( ( ( empty @ SV67 )
= $false )
| ( ( SV57 = SV67 )
= $true )
| ( ( empty @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(386,plain,
! [SV74: $i,SV76: $i] :
( ( ( ~ ( ~ ( ( ( sK8_C @ SV76 @ SV74 )
!= SV74 )
| ~ ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) )
| ~ ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
| ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) ) ) )
= $true )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(387,plain,
! [SV75: $i,SV77: $i] :
( ( ( ( SV77
!= ( singleton @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1004: $i] :
( ( SY1004 != SV75 )
| ( in @ SY1004 @ SV77 ) )
| ~ ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV77 )
| ( SY1005 = SV75 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(388,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) ) )
| ~ ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 ) ) )
| ( SV80
= ( unordered_pair @ SV58 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(389,plain,
! [SV79: $i,SV58: $i,SV81: $i] :
( ( ( SV81
!= ( unordered_pair @ SV58 @ SV79 ) )
| ~ ( ~ ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV81 )
| ( SY1011 = SV58 )
| ( SY1011 = SV79 ) )
| ~ ~ ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) )
| ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(390,plain,
! [SV72: $i,SV68: $i,SV61: $i,SV47: $i] :
( ( ( ( unordered_pair @ SV47 @ SV61 )
= ( unordered_pair @ SV68 @ SV72 ) )
= $false )
| ( ( SV47 = SV68 )
= $true )
| ( ( SV47 = SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(391,plain,
! [SV74: $i,SV76: $i] :
( ( ( ~ ( ( ( sK8_C @ SV76 @ SV74 )
!= SV74 )
| ~ ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) )
| ~ ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
| ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) ) )
= $false )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(392,plain,
! [SV75: $i,SV77: $i] :
( ( ( SV77
= ( singleton @ SV75 ) )
= $false )
| ( ( ~ ( ~ ! [SY1004: $i] :
( ( SY1004 != SV75 )
| ( in @ SY1004 @ SV77 ) )
| ~ ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV77 )
| ( SY1005 = SV75 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(393,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) ) )
| ~ ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 ) ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(394,plain,
! [SV79: $i,SV58: $i,SV81: $i] :
( ( ( ( SV81
!= ( unordered_pair @ SV58 @ SV79 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV81 )
| ( SY1011 = SV58 )
| ( SY1011 = SV79 ) )
| ~ ~ ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) )
| ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(395,plain,
! [SV74: $i,SV76: $i] :
( ( ( ~ ( ( ( sK8_C @ SV76 @ SV74 )
!= SV74 )
| ~ ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) ) )
= $false )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(396,plain,
! [SV74: $i,SV76: $i] :
( ( ( ~ ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
| ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) ) )
= $false )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(397,plain,
! [SV77: $i,SV75: $i] :
( ( ( ~ ! [SY1004: $i] :
( ( SY1004 != SV75 )
| ( in @ SY1004 @ SV77 ) )
| ~ ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV77 )
| ( SY1005 = SV75 ) ) )
= $false )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(398,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) ) )
| ~ ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(399,plain,
! [SV79: $i,SV58: $i,SV81: $i] :
( ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false )
| ( ( ~ ( ~ ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV81 )
| ( SY1011 = SV58 )
| ( SY1011 = SV79 ) )
| ~ ~ ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) )
| ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(400,plain,
! [SV74: $i,SV76: $i] :
( ( ( ( ( sK8_C @ SV76 @ SV74 )
!= SV74 )
| ~ ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) )
= $true )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(401,plain,
! [SV74: $i,SV76: $i] :
( ( ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
| ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) )
= $true )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(402,plain,
! [SV77: $i,SV75: $i] :
( ( ( ~ ! [SY1004: $i] :
( ( SY1004 != SV75 )
| ( in @ SY1004 @ SV77 ) ) )
= $false )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(403,plain,
! [SV75: $i,SV77: $i] :
( ( ( ~ ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV77 )
| ( SY1005 = SV75 ) ) )
= $false )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(404,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(405,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(406,plain,
! [SV79: $i,SV58: $i,SV81: $i] :
( ( ( ~ ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV81 )
| ( SY1011 = SV58 )
| ( SY1011 = SV79 ) )
| ~ ~ ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) )
| ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) ) )
= $false )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(407,plain,
! [SV74: $i,SV76: $i] :
( ( ( ( ( sK8_C @ SV76 @ SV74 )
!= SV74 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) )
= $true )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(408,plain,
! [SV74: $i,SV76: $i] :
( ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
= $true )
| ( ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 )
= $true )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(409,plain,
! [SV77: $i,SV75: $i] :
( ( ( ! [SY1004: $i] :
( ( SY1004 != SV75 )
| ( in @ SY1004 @ SV77 ) ) )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(410,plain,
! [SV75: $i,SV77: $i] :
( ( ( ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV77 )
| ( SY1005 = SV75 ) ) )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(411,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) ) ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(412,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(413,plain,
! [SV79: $i,SV58: $i,SV81: $i] :
( ( ( ~ ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV81 )
| ( SY1011 = SV58 )
| ( SY1011 = SV79 ) ) )
= $false )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(414,plain,
! [SV79: $i,SV81: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) )
| ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) ) )
= $false )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(415,plain,
! [SV74: $i,SV76: $i] :
( ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 ) )
= $true )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(416,plain,
! [SV77: $i,SV75: $i,SV82: $i] :
( ( ( ( SV82 != SV75 )
| ( in @ SV82 @ SV77 ) )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(417,plain,
! [SV75: $i,SV77: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV77 )
| ( SV83 = SV75 ) )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(418,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
| ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(419,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
= $true )
| ( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(420,plain,
! [SV79: $i,SV58: $i,SV81: $i] :
( ( ( ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV81 )
| ( SY1011 = SV58 )
| ( SY1011 = SV79 ) ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(421,plain,
! [SV79: $i,SV81: $i,SV58: $i] :
( ( ( ~ ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) )
| ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(422,plain,
! [SV74: $i,SV76: $i] :
( ( ( in @ ( sK8_C @ SV76 @ SV74 ) @ SV76 )
= $false )
| ( ( ( sK8_C @ SV76 @ SV74 )
= SV74 )
= $false )
| ( ( SV76
= ( singleton @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(423,plain,
! [SV77: $i,SV75: $i,SV82: $i] :
( ( ( ( SV82 != SV75 ) )
= $true )
| ( ( in @ SV82 @ SV77 )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(424,plain,
! [SV75: $i,SV77: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV77 ) )
= $true )
| ( ( SV83 = SV75 )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(425,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(426,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) ) )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(427,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
= $true )
| ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 )
= $true )
| ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(428,plain,
! [SV79: $i,SV58: $i,SV81: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ SV81 )
| ( SV84 = SV58 )
| ( SV84 = SV79 ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(429,plain,
! [SV79: $i,SV81: $i,SV58: $i] :
( ( ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) )
| ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) )
= $false )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(430,plain,
! [SV77: $i,SV75: $i,SV82: $i] :
( ( ( SV82 = SV75 )
= $false )
| ( ( in @ SV82 @ SV77 )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(431,plain,
! [SV75: $i,SV77: $i,SV83: $i] :
( ( ( in @ SV83 @ SV77 )
= $false )
| ( ( SV83 = SV75 )
= $true )
| ( ( SV77
= ( singleton @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(432,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(433,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
| ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(434,plain,
! [SV79: $i,SV58: $i,SV81: $i,SV84: $i] :
( ( ( ~ ( in @ SV84 @ SV81 ) )
= $true )
| ( ( ( SV84 = SV58 )
| ( SV84 = SV79 ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(435,plain,
! [SV79: $i,SV81: $i,SV58: $i] :
( ( ( ~ ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) ) )
= $false )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(436,plain,
! [SV58: $i,SV81: $i,SV79: $i] :
( ( ( ~ ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) )
= $false )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(437,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 ) )
= $true )
| ( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(438,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 ) )
= $true )
| ( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(439,plain,
! [SV79: $i,SV58: $i,SV81: $i,SV84: $i] :
( ( ( in @ SV84 @ SV81 )
= $false )
| ( ( ( SV84 = SV58 )
| ( SV84 = SV79 ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(440,plain,
! [SV79: $i,SV81: $i,SV58: $i] :
( ( ( ! [SY1012: $i] :
( ( SY1012 != SV58 )
| ( in @ SY1012 @ SV81 ) ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(441,plain,
! [SV58: $i,SV81: $i,SV79: $i] :
( ( ( ! [SY1013: $i] :
( ( SY1013 != SV79 )
| ( in @ SY1013 @ SV81 ) ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(442,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
= $false )
| ( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV58 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(443,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
= $false )
| ( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
!= SV78 ) )
= $true )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(444,plain,
! [SV81: $i,SV79: $i,SV58: $i,SV84: $i] :
( ( ( SV84 = SV58 )
= $true )
| ( ( SV84 = SV79 )
= $true )
| ( ( in @ SV84 @ SV81 )
= $false )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(445,plain,
! [SV79: $i,SV81: $i,SV58: $i,SV85: $i] :
( ( ( ( SV85 != SV58 )
| ( in @ SV85 @ SV81 ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(446,plain,
! [SV58: $i,SV81: $i,SV79: $i,SV86: $i] :
( ( ( ( SV86 != SV79 )
| ( in @ SV86 @ SV81 ) )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(447,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV58 )
= $false )
| ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(448,plain,
! [SV58: $i,SV78: $i,SV80: $i] :
( ( ( ( sK7_D @ SV80 @ SV78 @ SV58 )
= SV78 )
= $false )
| ( ( in @ ( sK7_D @ SV80 @ SV78 @ SV58 ) @ SV80 )
= $false )
| ( ( SV80
= ( unordered_pair @ SV58 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(449,plain,
! [SV79: $i,SV81: $i,SV58: $i,SV85: $i] :
( ( ( ( SV85 != SV58 ) )
= $true )
| ( ( in @ SV85 @ SV81 )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(450,plain,
! [SV58: $i,SV81: $i,SV79: $i,SV86: $i] :
( ( ( ( SV86 != SV79 ) )
= $true )
| ( ( in @ SV86 @ SV81 )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(451,plain,
! [SV79: $i,SV81: $i,SV58: $i,SV85: $i] :
( ( ( SV85 = SV58 )
= $false )
| ( ( in @ SV85 @ SV81 )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(452,plain,
! [SV58: $i,SV81: $i,SV79: $i,SV86: $i] :
( ( ( SV86 = SV79 )
= $false )
| ( ( in @ SV86 @ SV81 )
= $true )
| ( ( SV81
= ( unordered_pair @ SV58 @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(453,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[303,452,451,448,447,444,431,430,427,422,408,390,385,378,377,376,368,367,364,356,349,340,335,333,330,326,319,311,306]) ).
thf(454,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[453,291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU156+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n008.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 Jun 19 10:34:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 ..
% 0.13/0.38
% 0.13/0.38 No.of.Axioms: 83
% 0.13/0.38
% 0.13/0.38 Length.of.Defs: 0
% 0.13/0.38
% 0.13/0.38 Contains.Choice.Funs: false
% 0.19/0.41 ..
% 0.19/0.42 (rf:0,axioms:83,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:85,loop_count:0,foatp_calls:0,translation:fof_full).....................................................................eprover: CPU time limit exceeded, terminating
% 74.60/74.81 .........
% 75.15/75.35 (rf:0,axioms:83,ps:2,u:1,ude:false,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:85,loop_count:0,foatp_calls:0,translation:fof_full)..................................................................eprover: CPU time limit exceeded, terminating
% 149.48/149.74 ..........
% 150.30/150.53 (rf:0,axioms:83,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:85,loop_count:0,foatp_calls:0,translation:fof_full).....................................................................eprover: CPU time limit exceeded, terminating
% 224.65/224.95 ...........
% 225.06/225.37 (rf:2,axioms:19,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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:85,loop_count:0,foatp_calls:0,translation:fof_full)......................
% 226.35/226.67
% 226.35/226.67 ********************************
% 226.35/226.67 * All subproblems solved! *
% 226.35/226.67 ********************************
% 226.35/226.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:20,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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:453,loop_count:0,foatp_calls:1,translation:fof_full)
% 226.43/226.74
% 226.43/226.74 %**** Beginning of derivation protocol ****
% 226.43/226.74 % SZS output start CNFRefutation
% See solution above
% 226.43/226.74
% 226.43/226.74 %**** End of derivation protocol ****
% 226.43/226.74 %**** no. of clauses in derivation: 390 ****
% 226.43/226.74 %**** clause counter: 453 ****
% 226.43/226.74
% 226.43/226.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:20,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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:453,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------