TSTP Solution File: SEU151+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU151+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 : n016.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 12:07:12 EDT 2022
% Result : Theorem 225.50s 225.88s
% Output : CNFRefutation 225.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 44
% Syntax : Number of formulae : 474 ( 190 unt; 25 typ; 0 def)
% Number of atoms : 3474 (1408 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 8151 (1583 ~;1357 |; 96 &;5075 @)
% ( 28 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 1481 ( 0 ^1479 !; 2 ?;1481 :)
% 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_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_C,type,
sK12_C: $i > $i > $i ).
thf(tp_sK13_D,type,
sK13_D: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY822,type,
sK2_SY822: $i ).
thf(tp_sK3_SY825,type,
sK3_SY825: $i ).
thf(tp_sK4_SY827,type,
sK4_SY827: $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i > $i ).
thf(tp_sK7_D,type,
sK7_D: $i > $i > $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $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_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(34,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(48,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(73,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(74,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(75,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[74]) ).
thf(76,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $false ),
inference(unfold_def,[status(thm)],[75]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(79,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(80,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(82,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(90,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)],[32]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(92,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(93,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(94,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(95,plain,
( ( ! [SY822: $i,SY823: $i,SY824: $i] :
~ ( ( ( unordered_pair @ sK1_A @ SY822 )
= ( unordered_pair @ SY823 @ SY824 ) )
& ( sK1_A != SY823 )
& ( sK1_A != SY824 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[76]) ).
thf(96,plain,
( ( ! [SY825: $i,SY826: $i] :
~ ( ( ( unordered_pair @ sK1_A @ sK2_SY822 )
= ( unordered_pair @ SY825 @ SY826 ) )
& ( sK1_A != SY825 )
& ( sK1_A != SY826 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(97,plain,
( ( ! [SY827: $i] :
~ ( ( ( unordered_pair @ sK1_A @ sK2_SY822 )
= ( unordered_pair @ sK3_SY825 @ SY827 ) )
& ( sK1_A != sK3_SY825 )
& ( sK1_A != SY827 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[96]) ).
thf(98,plain,
( ( ~ ( ( ( unordered_pair @ sK1_A @ sK2_SY822 )
= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) )
& ( sK1_A != sK3_SY825 )
& ( sK1_A != sK4_SY827 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(99,plain,
( ( ( ( unordered_pair @ sK1_A @ sK2_SY822 )
= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) )
& ( sK1_A != sK3_SY825 )
& ( sK1_A != sK4_SY827 ) )
= $true ),
inference(polarity_switch,[status(thm)],[98]) ).
thf(100,plain,
( ( ( sK1_A != sK4_SY827 )
& ( sK1_A != sK3_SY825 )
& ( ( unordered_pair @ sK1_A @ sK2_SY822 )
= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(103,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(104,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK8_C @ B @ A ) @ A )
& ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(106,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ( in @ ( sK9_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(107,plain,
( ( ! [A: $i] :
( ( in @ ( sK10_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK11_C @ B @ A )
!= A )
| ~ ( in @ ( sK11_C @ B @ A ) @ B ) )
& ( ( ( sK11_C @ B @ A )
= A )
| ( in @ ( sK11_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)],[84]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK12_C @ B @ A ) @ A )
& ( in @ ( sK12_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(113,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(114,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ C )
| ( ( sK13_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ C )
| ( ( sK13_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK13_D @ C @ B @ A ) @ C )
| ( ( sK13_D @ C @ B @ A )
= A )
| ( ( sK13_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)],[90]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(117,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(119,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(121,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ C )
| ( ( sK13_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK13_D @ C @ B @ A ) @ C )
| ( ( sK13_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK13_D @ C @ B @ A ) @ C )
| ( ( sK13_D @ C @ B @ A )
= A )
| ( ( sK13_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)],[114]) ).
thf(122,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK12_C @ B @ A ) @ A )
& ( in @ ( sK12_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(127,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK11_C @ B @ A )
!= A )
| ~ ( in @ ( sK11_C @ B @ A ) @ B ) )
& ( ( ( sK11_C @ B @ A )
= A )
| ( in @ ( sK11_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)],[108]) ).
thf(128,plain,
( ( ! [A: $i] :
( ( in @ ( sK10_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(129,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ( in @ ( sK9_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK8_C @ B @ A ) @ A )
& ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(131,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(132,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(135,plain,
( ( ( sK1_A != sK4_SY827 )
& ( sK1_A != sK3_SY825 )
& ( ( unordered_pair @ sK1_A @ sK2_SY822 )
= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(136,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(137,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK10_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(140,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(141,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(142,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK11_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK11_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK11_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)],[127]) ).
thf(143,plain,
( ( ~ ( ~ ( ( sK1_A != sK4_SY827 ) )
| ~ ~ ( ~ ( ( sK1_A != sK3_SY825 ) )
| ( ( unordered_pair @ sK1_A @ sK2_SY822 )
!= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(144,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(145,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(146,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK13_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK13_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK13_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK13_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)],[121]) ).
thf(147,plain,
! [SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV1 )
= ( singleton @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(148,plain,
! [SV2: $i] :
( ( ! [SY828: $i] :
( ! [SY829: $i] :
( ( singleton @ SV2 )
!= ( unordered_pair @ SY828 @ SY829 ) )
| ( SV2 = SY828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(149,plain,
! [SV3: $i] :
( ( ! [SY830: $i,SY831: $i] :
( ( ( singleton @ SV3 )
!= ( unordered_pair @ SY830 @ SY831 ) )
| ( SY830 = SY831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(150,plain,
! [SV4: $i] :
( ( ! [SY832: $i] :
( ( unordered_pair @ SV4 @ SY832 )
= ( unordered_pair @ SY832 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(151,plain,
! [SV5: $i] :
( ( ( ( singleton @ SV5 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(152,plain,
! [SV6: $i] :
( ( ! [SY833: $i] :
( ~ ( subset @ ( singleton @ SV6 ) @ ( singleton @ SY833 ) )
| ( SV6 = SY833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(153,plain,
! [SV7: $i] :
( ( ! [SY834: $i] :
( ~ ( in @ SV7 @ SY834 )
| ~ ( in @ SY834 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(154,plain,
! [SV8: $i] :
( ( ! [SY835: $i] :
( ~ ( empty @ SY835 )
| ~ ( in @ SV8 @ SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(155,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY836: $i,SY837: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) ) ) )
| ( SY837
= ( set_difference @ SV9 @ SY836 ) ) )
| ~ ! [SY838: $i,SY839: $i] :
( ( SY839
!= ( set_difference @ SV9 @ SY838 ) )
| ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ SV9 )
| ( in @ SY840 @ SY838 )
| ( in @ SY840 @ SY839 ) )
| ~ ~ ( ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SY839 )
| ( in @ SY841 @ SV9 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY839 )
| ~ ( in @ SX3 @ SY838 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(157,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK10_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV10: $i] :
( ( ! [SY843: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SY843 @ SV10 ) @ SV10 )
| ~ ( in @ ( sK5_C @ SY843 @ SV10 ) @ SY843 ) )
| ~ ( ( in @ ( sK5_C @ SY843 @ SV10 ) @ SV10 )
| ( in @ ( sK5_C @ SY843 @ SV10 ) @ SY843 ) ) )
| ( SV10 = SY843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(160,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY844: $i,SY845: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ~ ( ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ( SY845
= ( set_union2 @ SV11 @ SY844 ) ) )
| ~ ! [SY846: $i,SY847: $i] :
( ( SY847
!= ( set_union2 @ SV11 @ SY846 ) )
| ~ ( ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SY847 )
| ( in @ SY848 @ SV11 )
| ( in @ SY848 @ SY846 ) )
| ~ ~ ( ~ ! [SY849: $i] :
( ~ ( in @ SY849 @ SV11 )
| ( in @ SY849 @ SY847 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY846 )
| ( in @ SX3 @ SY847 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(161,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK11_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK11_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK11_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)],[142]) ).
thf(162,plain,
( ( ~ ( ( sK1_A != sK4_SY827 ) )
| ~ ~ ( ~ ( ( sK1_A != sK3_SY825 ) )
| ( ( unordered_pair @ sK1_A @ sK2_SY822 )
!= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY851: $i,SY852: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) ) ) )
| ( SY852
= ( set_intersection2 @ SV12 @ SY851 ) ) )
| ~ ! [SY853: $i,SY854: $i] :
( ( SY854
!= ( set_intersection2 @ SV12 @ SY853 ) )
| ~ ( ~ ! [SY855: $i] :
( ~ ( in @ SY855 @ SV12 )
| ~ ( in @ SY855 @ SY853 )
| ( in @ SY855 @ SY854 ) )
| ~ ~ ( ~ ! [SY856: $i] :
( ~ ( in @ SY856 @ SY854 )
| ( in @ SY856 @ SV12 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY854 )
| ( in @ SX3 @ SY853 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(164,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV13: $i] :
( ( ~ ( ~ ! [SY858: $i,SY859: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SY858 ) ) )
| ~ ( ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SV13 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SY858 ) ) )
| ( SY859
= ( unordered_pair @ SV13 @ SY858 ) ) )
| ~ ! [SY860: $i,SY861: $i] :
( ( SY861
!= ( unordered_pair @ SV13 @ SY860 ) )
| ~ ( ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY861 )
| ( SY862 = SV13 )
| ( SY862 = SY860 ) )
| ~ ~ ( ~ ! [SY863: $i] :
( ( SY863 != SV13 )
| ( in @ SY863 @ SY861 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY860 )
| ( in @ SX3 @ SY861 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV14: $i,SV2: $i] :
( ( ! [SY865: $i] :
( ( singleton @ SV2 )
!= ( unordered_pair @ SV14 @ SY865 ) )
| ( SV2 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(167,plain,
! [SV15: $i,SV3: $i] :
( ( ! [SY866: $i] :
( ( ( singleton @ SV3 )
!= ( unordered_pair @ SV15 @ SY866 ) )
| ( SV15 = SY866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(168,plain,
! [SV16: $i,SV4: $i] :
( ( ( unordered_pair @ SV4 @ SV16 )
= ( unordered_pair @ SV16 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(169,plain,
! [SV5: $i] :
( ( ( singleton @ SV5 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(170,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( subset @ ( singleton @ SV6 ) @ ( singleton @ SV17 ) )
| ( SV6 = SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(171,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV18 )
| ~ ( in @ SV18 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(172,plain,
! [SV8: $i,SV19: $i] :
( ( ~ ( empty @ SV19 )
| ~ ( in @ SV8 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(173,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(174,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(175,plain,
! [SV9: $i] :
( ( ~ ! [SY836: $i,SY837: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) ) ) )
| ( SY837
= ( set_difference @ SV9 @ SY836 ) ) )
| ~ ! [SY838: $i,SY839: $i] :
( ( SY839
!= ( set_difference @ SV9 @ SY838 ) )
| ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ SV9 )
| ( in @ SY840 @ SY838 )
| ( in @ SY840 @ SY839 ) )
| ~ ~ ( ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SY839 )
| ( in @ SY841 @ SV9 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY839 )
| ~ ( in @ SX3 @ SY838 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(176,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK10_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(177,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(178,plain,
! [SV10: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) )
| ~ ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) ) )
| ( SV10 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(179,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(180,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(181,plain,
! [SV11: $i] :
( ( ~ ! [SY844: $i,SY845: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ~ ( ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ( SY845
= ( set_union2 @ SV11 @ SY844 ) ) )
| ~ ! [SY846: $i,SY847: $i] :
( ( SY847
!= ( set_union2 @ SV11 @ SY846 ) )
| ~ ( ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SY847 )
| ( in @ SY848 @ SV11 )
| ( in @ SY848 @ SY846 ) )
| ~ ~ ( ~ ! [SY849: $i] :
( ~ ( in @ SY849 @ SV11 )
| ( in @ SY849 @ SY847 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY846 )
| ( in @ SX3 @ SY847 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(182,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK11_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK11_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(183,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)],[161]) ).
thf(184,plain,
( ( ~ ( ( sK1_A != sK4_SY827 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(185,plain,
( ( ~ ~ ( ~ ( ( sK1_A != sK3_SY825 ) )
| ( ( unordered_pair @ sK1_A @ sK2_SY822 )
!= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(186,plain,
! [SV12: $i] :
( ( ~ ! [SY851: $i,SY852: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) ) ) )
| ( SY852
= ( set_intersection2 @ SV12 @ SY851 ) ) )
| ~ ! [SY853: $i,SY854: $i] :
( ( SY854
!= ( set_intersection2 @ SV12 @ SY853 ) )
| ~ ( ~ ! [SY855: $i] :
( ~ ( in @ SY855 @ SV12 )
| ~ ( in @ SY855 @ SY853 )
| ( in @ SY855 @ SY854 ) )
| ~ ~ ( ~ ! [SY856: $i] :
( ~ ( in @ SY856 @ SY854 )
| ( in @ SY856 @ SV12 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY854 )
| ( in @ SX3 @ SY853 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(187,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(188,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(189,plain,
! [SV13: $i] :
( ( ~ ! [SY858: $i,SY859: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SY858 ) ) )
| ~ ( ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SV13 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SY858 ) ) )
| ( SY859
= ( unordered_pair @ SV13 @ SY858 ) ) )
| ~ ! [SY860: $i,SY861: $i] :
( ( SY861
!= ( unordered_pair @ SV13 @ SY860 ) )
| ~ ( ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY861 )
| ( SY862 = SV13 )
| ( SY862 = SY860 ) )
| ~ ~ ( ~ ! [SY863: $i] :
( ( SY863 != SV13 )
| ( in @ SY863 @ SY861 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY860 )
| ( in @ SX3 @ SY861 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(190,plain,
! [SV14: $i,SV2: $i] :
( ( ( ! [SY865: $i] :
( ( singleton @ SV2 )
!= ( unordered_pair @ SV14 @ SY865 ) ) )
= $true )
| ( ( SV2 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(191,plain,
! [SV21: $i,SV15: $i,SV3: $i] :
( ( ( ( singleton @ SV3 )
!= ( unordered_pair @ SV15 @ SV21 ) )
| ( SV15 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(192,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( subset @ ( singleton @ SV6 ) @ ( singleton @ SV17 ) ) )
= $true )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(193,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(194,plain,
! [SV8: $i,SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(195,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(196,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(197,plain,
! [SV9: $i] :
( ( ~ ! [SY836: $i,SY837: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) ) ) )
| ( SY837
= ( set_difference @ SV9 @ SY836 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(198,plain,
! [SV9: $i] :
( ( ~ ! [SY838: $i,SY839: $i] :
( ( SY839
!= ( set_difference @ SV9 @ SY838 ) )
| ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ SV9 )
| ( in @ SY840 @ SY838 )
| ( in @ SY840 @ SY839 ) )
| ~ ~ ( ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SY839 )
| ( in @ SY841 @ SV9 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY839 )
| ~ ( in @ SX3 @ SY838 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(199,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK10_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(200,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(201,plain,
! [SV10: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) )
| ~ ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) ) ) )
= $true )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(202,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(203,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(204,plain,
! [SV11: $i] :
( ( ~ ! [SY844: $i,SY845: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ~ ( ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ( SY845
= ( set_union2 @ SV11 @ SY844 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(205,plain,
! [SV11: $i] :
( ( ~ ! [SY846: $i,SY847: $i] :
( ( SY847
!= ( set_union2 @ SV11 @ SY846 ) )
| ~ ( ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SY847 )
| ( in @ SY848 @ SV11 )
| ( in @ SY848 @ SY846 ) )
| ~ ~ ( ~ ! [SY849: $i] :
( ~ ( in @ SY849 @ SV11 )
| ( in @ SY849 @ SY847 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY846 )
| ( in @ SX3 @ SY847 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(206,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK11_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK11_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(207,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)],[183]) ).
thf(208,plain,
( ( ( sK1_A != sK4_SY827 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(209,plain,
( ( ~ ( ~ ( ( sK1_A != sK3_SY825 ) )
| ( ( unordered_pair @ sK1_A @ sK2_SY822 )
!= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(210,plain,
! [SV12: $i] :
( ( ~ ! [SY851: $i,SY852: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) ) ) )
| ( SY852
= ( set_intersection2 @ SV12 @ SY851 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(211,plain,
! [SV12: $i] :
( ( ~ ! [SY853: $i,SY854: $i] :
( ( SY854
!= ( set_intersection2 @ SV12 @ SY853 ) )
| ~ ( ~ ! [SY855: $i] :
( ~ ( in @ SY855 @ SV12 )
| ~ ( in @ SY855 @ SY853 )
| ( in @ SY855 @ SY854 ) )
| ~ ~ ( ~ ! [SY856: $i] :
( ~ ( in @ SY856 @ SY854 )
| ( in @ SY856 @ SV12 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY854 )
| ( in @ SX3 @ SY853 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(212,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(213,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(214,plain,
! [SV13: $i] :
( ( ~ ! [SY858: $i,SY859: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SY858 ) ) )
| ~ ( ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SV13 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SY858 ) ) )
| ( SY859
= ( unordered_pair @ SV13 @ SY858 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(215,plain,
! [SV13: $i] :
( ( ~ ! [SY860: $i,SY861: $i] :
( ( SY861
!= ( unordered_pair @ SV13 @ SY860 ) )
| ~ ( ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY861 )
| ( SY862 = SV13 )
| ( SY862 = SY860 ) )
| ~ ~ ( ~ ! [SY863: $i] :
( ( SY863 != SV13 )
| ( in @ SY863 @ SY861 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY860 )
| ( in @ SX3 @ SY861 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(216,plain,
! [SV22: $i,SV14: $i,SV2: $i] :
( ( ( ( ( singleton @ SV2 )
!= ( unordered_pair @ SV14 @ SV22 ) ) )
= $true )
| ( ( SV2 = SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(217,plain,
! [SV21: $i,SV15: $i,SV3: $i] :
( ( ( ( ( singleton @ SV3 )
!= ( unordered_pair @ SV15 @ SV21 ) ) )
= $true )
| ( ( SV15 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(218,plain,
! [SV17: $i,SV6: $i] :
( ( ( subset @ ( singleton @ SV6 ) @ ( singleton @ SV17 ) )
= $false )
| ( ( SV6 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(219,plain,
! [SV18: $i,SV7: $i] :
( ( ( in @ SV7 @ SV18 )
= $false )
| ( ( ~ ( in @ SV18 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(220,plain,
! [SV8: $i,SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( ~ ( in @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(221,plain,
! [SV23: $i] :
( ( ! [SY867: $i] :
( ~ ( in @ SV23 @ SY867 )
| ( subset @ ( singleton @ SV23 ) @ SY867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(222,plain,
! [SV24: $i] :
( ( ! [SY868: $i] :
( ~ ( subset @ ( singleton @ SV24 ) @ SY868 )
| ( in @ SV24 @ SY868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(223,plain,
! [SV9: $i] :
( ( ! [SY836: $i,SY837: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY836 )
| ( in @ ( sK6_D @ SY837 @ SY836 @ SV9 ) @ SY837 ) ) ) )
| ( SY837
= ( set_difference @ SV9 @ SY836 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(224,plain,
! [SV9: $i] :
( ( ! [SY838: $i,SY839: $i] :
( ( SY839
!= ( set_difference @ SV9 @ SY838 ) )
| ~ ( ~ ! [SY840: $i] :
( ~ ( in @ SY840 @ SV9 )
| ( in @ SY840 @ SY838 )
| ( in @ SY840 @ SY839 ) )
| ~ ~ ( ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SY839 )
| ( in @ SY841 @ SV9 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY839 )
| ~ ( in @ SX3 @ SY838 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(225,plain,
! [SV25: $i] :
( ( ( in @ ( sK10_B @ SV25 ) @ SV25 )
| ( SV25 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(226,plain,
! [SV26: $i] :
( ( ( SV26 != empty_set )
| ! [SY869: $i] :
~ ( in @ SY869 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(227,plain,
! [SV10: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) )
| ~ ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) ) )
= $false )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(228,plain,
! [SV27: $i] :
( ( ! [SY870: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SY870 @ SV27 ) @ SV27 )
| ~ ~ ( in @ ( sK8_C @ SY870 @ SV27 ) @ SY870 ) )
| ( subset @ SV27 @ SY870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(229,plain,
! [SV28: $i] :
( ( ! [SY871: $i] :
( ~ ( subset @ SV28 @ SY871 )
| ! [SY872: $i] :
( ~ ( in @ SY872 @ SV28 )
| ( in @ SY872 @ SY871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(230,plain,
! [SV11: $i] :
( ( ! [SY844: $i,SY845: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ~ ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ~ ( ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY845 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SY845 @ SY844 @ SV11 ) @ SY844 ) ) )
| ( SY845
= ( set_union2 @ SV11 @ SY844 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(231,plain,
! [SV11: $i] :
( ( ! [SY846: $i,SY847: $i] :
( ( SY847
!= ( set_union2 @ SV11 @ SY846 ) )
| ~ ( ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SY847 )
| ( in @ SY848 @ SV11 )
| ( in @ SY848 @ SY846 ) )
| ~ ~ ( ~ ! [SY849: $i] :
( ~ ( in @ SY849 @ SV11 )
| ( in @ SY849 @ SY847 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY846 )
| ( in @ SX3 @ SY847 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(232,plain,
! [SV29: $i] :
( ( ! [SY873: $i] :
( ~ ( ~ ( ( ( sK11_C @ SY873 @ SV29 )
!= SV29 )
| ~ ( in @ ( sK11_C @ SY873 @ SV29 ) @ SY873 ) )
| ~ ( ( ( sK11_C @ SY873 @ SV29 )
= SV29 )
| ( in @ ( sK11_C @ SY873 @ SV29 ) @ SY873 ) ) )
| ( SY873
= ( singleton @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(233,plain,
! [SV30: $i] :
( ( ! [SY874: $i] :
( ( SY874
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY875: $i] :
( ( SY875 != SV30 )
| ( in @ SY875 @ SY874 ) )
| ~ ! [SY876: $i] :
( ~ ( in @ SY876 @ SY874 )
| ( SY876 = SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(234,plain,
( ( sK1_A = sK4_SY827 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(235,plain,
( ( ~ ( ( sK1_A != sK3_SY825 ) )
| ( ( unordered_pair @ sK1_A @ sK2_SY822 )
!= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(236,plain,
! [SV12: $i] :
( ( ! [SY851: $i,SY852: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ~ ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) )
| ~ ( ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY851 )
| ( in @ ( sK7_D @ SY852 @ SY851 @ SV12 ) @ SY852 ) ) ) )
| ( SY852
= ( set_intersection2 @ SV12 @ SY851 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(237,plain,
! [SV12: $i] :
( ( ! [SY853: $i,SY854: $i] :
( ( SY854
!= ( set_intersection2 @ SV12 @ SY853 ) )
| ~ ( ~ ! [SY855: $i] :
( ~ ( in @ SY855 @ SV12 )
| ~ ( in @ SY855 @ SY853 )
| ( in @ SY855 @ SY854 ) )
| ~ ~ ( ~ ! [SY856: $i] :
( ~ ( in @ SY856 @ SY854 )
| ( in @ SY856 @ SV12 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY854 )
| ( in @ SX3 @ SY853 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(238,plain,
! [SV31: $i] :
( ( ! [SY877: $i] :
( ( disjoint @ SV31 @ SY877 )
| ~ ( ~ ( in @ ( sK12_C @ SY877 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK12_C @ SY877 @ SV31 ) @ SY877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(239,plain,
! [SV32: $i] :
( ( ! [SY878: $i] :
( ! [SY879: $i] :
( ~ ( in @ SY879 @ SV32 )
| ~ ( in @ SY879 @ SY878 ) )
| ~ ( disjoint @ SV32 @ SY878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(240,plain,
! [SV13: $i] :
( ( ! [SY858: $i,SY859: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
!= SY858 ) ) )
| ~ ( ( in @ ( sK13_D @ SY859 @ SY858 @ SV13 ) @ SY859 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SV13 )
| ( ( sK13_D @ SY859 @ SY858 @ SV13 )
= SY858 ) ) )
| ( SY859
= ( unordered_pair @ SV13 @ SY858 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(241,plain,
! [SV13: $i] :
( ( ! [SY860: $i,SY861: $i] :
( ( SY861
!= ( unordered_pair @ SV13 @ SY860 ) )
| ~ ( ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SY861 )
| ( SY862 = SV13 )
| ( SY862 = SY860 ) )
| ~ ~ ( ~ ! [SY863: $i] :
( ( SY863 != SV13 )
| ( in @ SY863 @ SY861 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY860 )
| ( in @ SX3 @ SY861 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(242,plain,
! [SV22: $i,SV14: $i,SV2: $i] :
( ( ( ( singleton @ SV2 )
= ( unordered_pair @ SV14 @ SV22 ) )
= $false )
| ( ( SV2 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(243,plain,
! [SV21: $i,SV15: $i,SV3: $i] :
( ( ( ( singleton @ SV3 )
= ( unordered_pair @ SV15 @ SV21 ) )
= $false )
| ( ( SV15 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(244,plain,
! [SV7: $i,SV18: $i] :
( ( ( in @ SV18 @ SV7 )
= $false )
| ( ( in @ SV7 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(245,plain,
! [SV19: $i,SV8: $i] :
( ( ( in @ SV8 @ SV19 )
= $false )
| ( ( empty @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(246,plain,
! [SV33: $i,SV23: $i] :
( ( ~ ( in @ SV23 @ SV33 )
| ( subset @ ( singleton @ SV23 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(247,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( subset @ ( singleton @ SV24 ) @ SV34 )
| ( in @ SV24 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(248,plain,
! [SV9: $i,SV35: $i] :
( ( ! [SY880: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY880 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY880 @ SV35 @ SV9 ) @ SV35 )
| ~ ( in @ ( sK6_D @ SY880 @ SV35 @ SV9 ) @ SY880 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY880 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SY880 @ SV35 @ SV9 ) @ SY880 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY880 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SY880 @ SV35 @ SV9 ) @ SY880 ) ) ) )
| ( SY880
= ( set_difference @ SV9 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(249,plain,
! [SV36: $i,SV9: $i] :
( ( ! [SY881: $i] :
( ( SY881
!= ( set_difference @ SV9 @ SV36 ) )
| ~ ( ~ ! [SY882: $i] :
( ~ ( in @ SY882 @ SV9 )
| ( in @ SY882 @ SV36 )
| ( in @ SY882 @ SY881 ) )
| ~ ~ ( ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SY881 )
| ( in @ SY841 @ SV9 ) )
| ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SY881 )
| ~ ( in @ SY884 @ SV36 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(250,plain,
! [SV25: $i] :
( ( ( in @ ( sK10_B @ SV25 ) @ SV25 )
= $true )
| ( ( SV25 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(251,plain,
! [SV26: $i] :
( ( ( ( SV26 != empty_set ) )
= $true )
| ( ( ! [SY869: $i] :
~ ( in @ SY869 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(252,plain,
! [SV10: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) ) )
= $false )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(253,plain,
! [SV10: $i,SV20: $i] :
( ( ( ~ ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) ) )
= $false )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(254,plain,
! [SV27: $i,SV37: $i] :
( ( ~ ( ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV27 )
| ~ ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV37 ) )
| ( subset @ SV27 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(255,plain,
! [SV38: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV38 )
| ! [SY885: $i] :
( ~ ( in @ SY885 @ SV28 )
| ( in @ SY885 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(256,plain,
! [SV11: $i,SV39: $i] :
( ( ! [SY886: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY886 @ SV39 @ SV11 ) @ SY886 )
| ~ ( in @ ( sK9_D @ SY886 @ SV39 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY886 @ SV39 @ SV11 ) @ SY886 )
| ~ ( in @ ( sK9_D @ SY886 @ SV39 @ SV11 ) @ SV39 ) ) )
| ~ ( ( in @ ( sK9_D @ SY886 @ SV39 @ SV11 ) @ SY886 )
| ( in @ ( sK9_D @ SY886 @ SV39 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SY886 @ SV39 @ SV11 ) @ SV39 ) ) )
| ( SY886
= ( set_union2 @ SV11 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(257,plain,
! [SV40: $i,SV11: $i] :
( ( ! [SY887: $i] :
( ( SY887
!= ( set_union2 @ SV11 @ SV40 ) )
| ~ ( ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY887 )
| ( in @ SY888 @ SV11 )
| ( in @ SY888 @ SV40 ) )
| ~ ~ ( ~ ! [SY849: $i] :
( ~ ( in @ SY849 @ SV11 )
| ( in @ SY849 @ SY887 ) )
| ~ ! [SY890: $i] :
( ~ ( in @ SY890 @ SV40 )
| ( in @ SY890 @ SY887 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(258,plain,
! [SV29: $i,SV41: $i] :
( ( ~ ( ~ ( ( ( sK11_C @ SV41 @ SV29 )
!= SV29 )
| ~ ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) )
| ~ ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
| ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) ) )
| ( SV41
= ( singleton @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(259,plain,
! [SV30: $i,SV42: $i] :
( ( ( SV42
!= ( singleton @ SV30 ) )
| ~ ( ~ ! [SY891: $i] :
( ( SY891 != SV30 )
| ( in @ SY891 @ SV42 ) )
| ~ ! [SY892: $i] :
( ~ ( in @ SY892 @ SV42 )
| ( SY892 = SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(260,plain,
( ( ~ ( ( sK1_A != sK3_SY825 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(261,plain,
( ( ( ( unordered_pair @ sK1_A @ sK2_SY822 )
!= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(262,plain,
! [SV12: $i,SV43: $i] :
( ( ! [SY893: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY893 @ SV43 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SY893 @ SV43 @ SV12 ) @ SV43 )
| ~ ( in @ ( sK7_D @ SY893 @ SV43 @ SV12 ) @ SY893 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY893 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SY893 @ SV43 @ SV12 ) @ SY893 ) )
| ~ ( ( in @ ( sK7_D @ SY893 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SY893 @ SV43 @ SV12 ) @ SY893 ) ) ) )
| ( SY893
= ( set_intersection2 @ SV12 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(263,plain,
! [SV44: $i,SV12: $i] :
( ( ! [SY894: $i] :
( ( SY894
!= ( set_intersection2 @ SV12 @ SV44 ) )
| ~ ( ~ ! [SY895: $i] :
( ~ ( in @ SY895 @ SV12 )
| ~ ( in @ SY895 @ SV44 )
| ( in @ SY895 @ SY894 ) )
| ~ ~ ( ~ ! [SY856: $i] :
( ~ ( in @ SY856 @ SY894 )
| ( in @ SY856 @ SV12 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SY894 )
| ( in @ SY897 @ SV44 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(264,plain,
! [SV45: $i,SV31: $i] :
( ( ( disjoint @ SV31 @ SV45 )
| ~ ( ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(265,plain,
! [SV46: $i,SV32: $i] :
( ( ! [SY898: $i] :
( ~ ( in @ SY898 @ SV32 )
| ~ ( in @ SY898 @ SV46 ) )
| ~ ( disjoint @ SV32 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(266,plain,
! [SV13: $i,SV47: $i] :
( ( ! [SY899: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SY899 @ SV47 @ SV13 ) @ SY899 )
| ( ( sK13_D @ SY899 @ SV47 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SY899 @ SV47 @ SV13 ) @ SY899 )
| ( ( sK13_D @ SY899 @ SV47 @ SV13 )
!= SV47 ) ) )
| ~ ( ( in @ ( sK13_D @ SY899 @ SV47 @ SV13 ) @ SY899 )
| ( ( sK13_D @ SY899 @ SV47 @ SV13 )
= SV13 )
| ( ( sK13_D @ SY899 @ SV47 @ SV13 )
= SV47 ) ) )
| ( SY899
= ( unordered_pair @ SV13 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(267,plain,
! [SV48: $i,SV13: $i] :
( ( ! [SY900: $i] :
( ( SY900
!= ( unordered_pair @ SV13 @ SV48 ) )
| ~ ( ~ ! [SY901: $i] :
( ~ ( in @ SY901 @ SY900 )
| ( SY901 = SV13 )
| ( SY901 = SV48 ) )
| ~ ~ ( ~ ! [SY863: $i] :
( ( SY863 != SV13 )
| ( in @ SY863 @ SY900 ) )
| ~ ! [SY903: $i] :
( ( SY903 != SV48 )
| ( in @ SY903 @ SY900 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(268,plain,
! [SV33: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV33 ) )
= $true )
| ( ( subset @ ( singleton @ SV23 ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV34: $i,SV24: $i] :
( ( ( ~ ( subset @ ( singleton @ SV24 ) @ SV34 ) )
= $true )
| ( ( in @ SV24 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(270,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) ) )
| ( SV49
= ( set_difference @ SV9 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(271,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( SV50
!= ( set_difference @ SV9 @ SV36 ) )
| ~ ( ~ ! [SY904: $i] :
( ~ ( in @ SY904 @ SV9 )
| ( in @ SY904 @ SV36 )
| ( in @ SY904 @ SV50 ) )
| ~ ~ ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(272,plain,
! [SV26: $i] :
( ( ( SV26 = empty_set )
= $false )
| ( ( ! [SY869: $i] :
~ ( in @ SY869 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(273,plain,
! [SV10: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) )
= $true )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(274,plain,
! [SV10: $i,SV20: $i] :
( ( ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
| ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) )
= $true )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(275,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV27 )
| ~ ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV37 ) ) )
= $true )
| ( ( subset @ SV27 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(276,plain,
! [SV38: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV38 ) )
= $true )
| ( ( ! [SY885: $i] :
( ~ ( in @ SY885 @ SV28 )
| ( in @ SY885 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(277,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
| ~ ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
| ( SV51
= ( set_union2 @ SV11 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(278,plain,
! [SV40: $i,SV11: $i,SV52: $i] :
( ( ( SV52
!= ( set_union2 @ SV11 @ SV40 ) )
| ~ ( ~ ! [SY907: $i] :
( ~ ( in @ SY907 @ SV52 )
| ( in @ SY907 @ SV11 )
| ( in @ SY907 @ SV40 ) )
| ~ ~ ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) )
| ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(279,plain,
! [SV29: $i,SV41: $i] :
( ( ( ~ ( ~ ( ( ( sK11_C @ SV41 @ SV29 )
!= SV29 )
| ~ ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) )
| ~ ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
| ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) ) ) )
= $true )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(280,plain,
! [SV30: $i,SV42: $i] :
( ( ( ( SV42
!= ( singleton @ SV30 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY891: $i] :
( ( SY891 != SV30 )
| ( in @ SY891 @ SV42 ) )
| ~ ! [SY892: $i] :
( ~ ( in @ SY892 @ SV42 )
| ( SY892 = SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(281,plain,
( ( ( sK1_A != sK3_SY825 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(282,plain,
( ( ( unordered_pair @ sK1_A @ sK2_SY822 )
= ( unordered_pair @ sK3_SY825 @ sK4_SY827 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(283,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) ) )
| ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(284,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( SV54
!= ( set_intersection2 @ SV12 @ SV44 ) )
| ~ ( ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SV12 )
| ~ ( in @ SY910 @ SV44 )
| ( in @ SY910 @ SV54 ) )
| ~ ~ ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(285,plain,
! [SV45: $i,SV31: $i] :
( ( ( disjoint @ SV31 @ SV45 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(286,plain,
! [SV46: $i,SV32: $i] :
( ( ( ! [SY898: $i] :
( ~ ( in @ SY898 @ SV32 )
| ~ ( in @ SY898 @ SV46 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV32 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(287,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) ) )
| ~ ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 ) ) )
| ( SV55
= ( unordered_pair @ SV13 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(288,plain,
! [SV48: $i,SV13: $i,SV56: $i] :
( ( ( SV56
!= ( unordered_pair @ SV13 @ SV48 ) )
| ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SV56 )
| ( SY913 = SV13 )
| ( SY913 = SV48 ) )
| ~ ~ ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) )
| ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(289,plain,
! [SV33: $i,SV23: $i] :
( ( ( in @ SV23 @ SV33 )
= $false )
| ( ( subset @ ( singleton @ SV23 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(290,plain,
! [SV34: $i,SV24: $i] :
( ( ( subset @ ( singleton @ SV24 ) @ SV34 )
= $false )
| ( ( in @ SV24 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(291,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) ) ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(292,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( ( SV50
!= ( set_difference @ SV9 @ SV36 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY904: $i] :
( ~ ( in @ SY904 @ SV9 )
| ( in @ SY904 @ SV36 )
| ( in @ SY904 @ SV50 ) )
| ~ ~ ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(293,plain,
! [SV26: $i,SV57: $i] :
( ( ( ~ ( in @ SV57 @ SV26 ) )
= $true )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(294,plain,
! [SV10: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) )
= $true )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(295,plain,
! [SV10: $i,SV20: $i] :
( ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
= $true )
| ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 )
= $true )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(296,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV27 )
| ~ ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV37 ) )
= $false )
| ( ( subset @ SV27 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(297,plain,
! [SV38: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV38 )
= $false )
| ( ( ! [SY885: $i] :
( ~ ( in @ SY885 @ SV28 )
| ( in @ SY885 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(298,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
| ~ ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(299,plain,
! [SV40: $i,SV11: $i,SV52: $i] :
( ( ( ( SV52
!= ( set_union2 @ SV11 @ SV40 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY907: $i] :
( ~ ( in @ SY907 @ SV52 )
| ( in @ SY907 @ SV11 )
| ( in @ SY907 @ SV40 ) )
| ~ ~ ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) )
| ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(300,plain,
! [SV29: $i,SV41: $i] :
( ( ( ~ ( ( ( sK11_C @ SV41 @ SV29 )
!= SV29 )
| ~ ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) )
| ~ ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
| ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) ) )
= $false )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(301,plain,
! [SV30: $i,SV42: $i] :
( ( ( SV42
= ( singleton @ SV30 ) )
= $false )
| ( ( ~ ( ~ ! [SY891: $i] :
( ( SY891 != SV30 )
| ( in @ SY891 @ SV42 ) )
| ~ ! [SY892: $i] :
( ~ ( in @ SY892 @ SV42 )
| ( SY892 = SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(302,plain,
( ( sK1_A = sK3_SY825 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(303,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) ) ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(304,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( ( SV54
!= ( set_intersection2 @ SV12 @ SV44 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SV12 )
| ~ ( in @ SY910 @ SV44 )
| ( in @ SY910 @ SV54 ) )
| ~ ~ ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(305,plain,
! [SV31: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV45 ) )
= $false )
| ( ( disjoint @ SV31 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(306,plain,
! [SV46: $i,SV32: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV32 )
| ~ ( in @ SV58 @ SV46 ) )
= $true )
| ( ( ~ ( disjoint @ SV32 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(307,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) ) )
| ~ ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 ) ) ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(308,plain,
! [SV48: $i,SV13: $i,SV56: $i] :
( ( ( ( SV56
!= ( unordered_pair @ SV13 @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SV56 )
| ( SY913 = SV13 )
| ( SY913 = SV48 ) )
| ~ ~ ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) )
| ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(309,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) ) )
= $false )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(310,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false )
| ( ( ~ ( ~ ! [SY904: $i] :
( ~ ( in @ SY904 @ SV9 )
| ( in @ SY904 @ SV36 )
| ( in @ SY904 @ SV50 ) )
| ~ ~ ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(311,plain,
! [SV26: $i,SV57: $i] :
( ( ( in @ SV57 @ SV26 )
= $false )
| ( ( SV26 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(312,plain,
! [SV10: $i,SV20: $i] :
( ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 ) )
= $true )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(313,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV27 ) )
= $false )
| ( ( subset @ SV27 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(314,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV37 ) )
= $false )
| ( ( subset @ SV27 @ SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(315,plain,
! [SV38: $i,SV28: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV28 )
| ( in @ SV59 @ SV38 ) )
= $true )
| ( ( subset @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(316,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
| ~ ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(317,plain,
! [SV40: $i,SV11: $i,SV52: $i] :
( ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false )
| ( ( ~ ( ~ ! [SY907: $i] :
( ~ ( in @ SY907 @ SV52 )
| ( in @ SY907 @ SV11 )
| ( in @ SY907 @ SV40 ) )
| ~ ~ ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) )
| ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(318,plain,
! [SV29: $i,SV41: $i] :
( ( ( ~ ( ( ( sK11_C @ SV41 @ SV29 )
!= SV29 )
| ~ ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) ) )
= $false )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(319,plain,
! [SV29: $i,SV41: $i] :
( ( ( ~ ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
| ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) ) )
= $false )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(320,plain,
! [SV42: $i,SV30: $i] :
( ( ( ~ ! [SY891: $i] :
( ( SY891 != SV30 )
| ( in @ SY891 @ SV42 ) )
| ~ ! [SY892: $i] :
( ~ ( in @ SY892 @ SV42 )
| ( SY892 = SV30 ) ) )
= $false )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(321,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) ) )
= $false )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(322,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false )
| ( ( ~ ( ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SV12 )
| ~ ( in @ SY910 @ SV44 )
| ( in @ SY910 @ SV54 ) )
| ~ ~ ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(323,plain,
! [SV31: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV31 ) )
= $false )
| ( ( disjoint @ SV31 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(324,plain,
! [SV31: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV45 ) )
= $false )
| ( ( disjoint @ SV31 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(325,plain,
! [SV46: $i,SV32: $i,SV58: $i] :
( ( ( ~ ( in @ SV58 @ SV32 ) )
= $true )
| ( ( ~ ( in @ SV58 @ SV46 ) )
= $true )
| ( ( ~ ( disjoint @ SV32 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(326,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) ) )
| ~ ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 ) ) )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(327,plain,
! [SV48: $i,SV13: $i,SV56: $i] :
( ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false )
| ( ( ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SV56 )
| ( SY913 = SV13 )
| ( SY913 = SV48 ) )
| ~ ~ ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) )
| ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(328,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(329,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) ) )
= $false )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(330,plain,
! [SV50: $i,SV36: $i,SV9: $i] :
( ( ( ~ ! [SY904: $i] :
( ~ ( in @ SY904 @ SV9 )
| ( in @ SY904 @ SV36 )
| ( in @ SY904 @ SV50 ) )
| ~ ~ ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) ) )
= $false )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(331,plain,
! [SV10: $i,SV20: $i] :
( ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV20 )
= $false )
| ( ( in @ ( sK5_C @ SV20 @ SV10 ) @ SV10 )
= $false )
| ( ( SV10 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(332,plain,
! [SV27: $i,SV37: $i] :
( ( ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV27 )
= $true )
| ( ( subset @ SV27 @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(333,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV37 ) )
= $true )
| ( ( subset @ SV27 @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(334,plain,
! [SV38: $i,SV28: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV28 ) )
= $true )
| ( ( in @ SV59 @ SV38 )
= $true )
| ( ( subset @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(335,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) ) )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(336,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(337,plain,
! [SV40: $i,SV11: $i,SV52: $i] :
( ( ( ~ ! [SY907: $i] :
( ~ ( in @ SY907 @ SV52 )
| ( in @ SY907 @ SV11 )
| ( in @ SY907 @ SV40 ) )
| ~ ~ ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) )
| ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) ) )
= $false )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(338,plain,
! [SV29: $i,SV41: $i] :
( ( ( ( ( sK11_C @ SV41 @ SV29 )
!= SV29 )
| ~ ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) )
= $true )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(339,plain,
! [SV29: $i,SV41: $i] :
( ( ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
| ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) )
= $true )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(340,plain,
! [SV42: $i,SV30: $i] :
( ( ( ~ ! [SY891: $i] :
( ( SY891 != SV30 )
| ( in @ SY891 @ SV42 ) ) )
= $false )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(341,plain,
! [SV30: $i,SV42: $i] :
( ( ( ~ ! [SY892: $i] :
( ~ ( in @ SY892 @ SV42 )
| ( SY892 = SV30 ) ) )
= $false )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(342,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) )
= $false )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(343,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) ) )
= $false )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(344,plain,
! [SV54: $i,SV44: $i,SV12: $i] :
( ( ( ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SV12 )
| ~ ( in @ SY910 @ SV44 )
| ( in @ SY910 @ SV54 ) )
| ~ ~ ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) ) )
= $false )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(345,plain,
! [SV31: $i,SV45: $i] :
( ( ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV31 )
= $true )
| ( ( disjoint @ SV31 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(346,plain,
! [SV31: $i,SV45: $i] :
( ( ( in @ ( sK12_C @ SV45 @ SV31 ) @ SV45 )
= $true )
| ( ( disjoint @ SV31 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(347,plain,
! [SV46: $i,SV32: $i,SV58: $i] :
( ( ( in @ SV58 @ SV32 )
= $false )
| ( ( ~ ( in @ SV58 @ SV46 ) )
= $true )
| ( ( ~ ( disjoint @ SV32 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(348,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) ) ) )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(349,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 ) ) )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(350,plain,
! [SV48: $i,SV13: $i,SV56: $i] :
( ( ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SV56 )
| ( SY913 = SV13 )
| ( SY913 = SV48 ) )
| ~ ~ ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) )
| ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) ) )
= $false )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(351,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(352,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(353,plain,
! [SV50: $i,SV36: $i,SV9: $i] :
( ( ( ~ ! [SY904: $i] :
( ~ ( in @ SY904 @ SV9 )
| ( in @ SY904 @ SV36 )
| ( in @ SY904 @ SV50 ) ) )
= $false )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(354,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) ) )
= $false )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(355,plain,
! [SV27: $i,SV37: $i] :
( ( ( in @ ( sK8_C @ SV37 @ SV27 ) @ SV37 )
= $false )
| ( ( subset @ SV27 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(356,plain,
! [SV38: $i,SV28: $i,SV59: $i] :
( ( ( in @ SV59 @ SV28 )
= $false )
| ( ( in @ SV59 @ SV38 )
= $true )
| ( ( subset @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(357,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(358,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(359,plain,
! [SV40: $i,SV11: $i,SV52: $i] :
( ( ( ~ ! [SY907: $i] :
( ~ ( in @ SY907 @ SV52 )
| ( in @ SY907 @ SV11 )
| ( in @ SY907 @ SV40 ) ) )
= $false )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(360,plain,
! [SV40: $i,SV52: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) )
| ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) ) )
= $false )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(361,plain,
! [SV29: $i,SV41: $i] :
( ( ( ( ( sK11_C @ SV41 @ SV29 )
!= SV29 ) )
= $true )
| ( ( ~ ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) )
= $true )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(362,plain,
! [SV29: $i,SV41: $i] :
( ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
= $true )
| ( ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 )
= $true )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(363,plain,
! [SV42: $i,SV30: $i] :
( ( ( ! [SY891: $i] :
( ( SY891 != SV30 )
| ( in @ SY891 @ SV42 ) ) )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(364,plain,
! [SV30: $i,SV42: $i] :
( ( ( ! [SY892: $i] :
( ~ ( in @ SY892 @ SV42 )
| ( SY892 = SV30 ) ) )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(365,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(366,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(367,plain,
! [SV54: $i,SV44: $i,SV12: $i] :
( ( ( ~ ! [SY910: $i] :
( ~ ( in @ SY910 @ SV12 )
| ~ ( in @ SY910 @ SV44 )
| ( in @ SY910 @ SV54 ) ) )
= $false )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(368,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) ) )
= $false )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(369,plain,
! [SV32: $i,SV46: $i,SV58: $i] :
( ( ( in @ SV58 @ SV46 )
= $false )
| ( ( in @ SV58 @ SV32 )
= $false )
| ( ( ~ ( disjoint @ SV32 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(370,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) ) ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(371,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(372,plain,
! [SV48: $i,SV13: $i,SV56: $i] :
( ( ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ SV56 )
| ( SY913 = SV13 )
| ( SY913 = SV48 ) ) )
= $false )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(373,plain,
! [SV48: $i,SV56: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) )
| ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) ) )
= $false )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(374,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(375,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(376,plain,
! [SV50: $i,SV36: $i,SV9: $i] :
( ( ( ! [SY904: $i] :
( ~ ( in @ SY904 @ SV9 )
| ( in @ SY904 @ SV36 )
| ( in @ SY904 @ SV50 ) ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(377,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( ~ ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(378,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(379,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
= $true )
| ( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
| ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(380,plain,
! [SV40: $i,SV11: $i,SV52: $i] :
( ( ( ! [SY907: $i] :
( ~ ( in @ SY907 @ SV52 )
| ( in @ SY907 @ SV11 )
| ( in @ SY907 @ SV40 ) ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(381,plain,
! [SV40: $i,SV52: $i,SV11: $i] :
( ( ( ~ ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) )
| ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(382,plain,
! [SV29: $i,SV41: $i] :
( ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
= $false )
| ( ( ~ ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 ) )
= $true )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(383,plain,
! [SV42: $i,SV30: $i,SV60: $i] :
( ( ( ( SV60 != SV30 )
| ( in @ SV60 @ SV42 ) )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(384,plain,
! [SV30: $i,SV42: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV42 )
| ( SV61 = SV30 ) )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(385,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(386,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
| ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) )
= $false )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(387,plain,
! [SV54: $i,SV44: $i,SV12: $i] :
( ( ( ! [SY910: $i] :
( ~ ( in @ SY910 @ SV12 )
| ~ ( in @ SY910 @ SV44 )
| ( in @ SY910 @ SV54 ) ) )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(388,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( ~ ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) ) )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(389,plain,
! [SV58: $i,SV46: $i,SV32: $i] :
( ( ( disjoint @ SV32 @ SV46 )
= $false )
| ( ( in @ SV58 @ SV32 )
= $false )
| ( ( in @ SV58 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(390,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
| ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) ) )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(391,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
= $true )
| ( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(392,plain,
! [SV48: $i,SV13: $i,SV56: $i] :
( ( ( ! [SY913: $i] :
( ~ ( in @ SY913 @ SV56 )
| ( SY913 = SV13 )
| ( SY913 = SV48 ) ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(393,plain,
! [SV48: $i,SV56: $i,SV13: $i] :
( ( ( ~ ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) )
| ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(394,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 ) )
= $true )
| ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(395,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(396,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) ) )
= $false )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(397,plain,
! [SV50: $i,SV36: $i,SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ SV9 )
| ( in @ SV62 @ SV36 )
| ( in @ SV62 @ SV50 ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(398,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) )
| ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) )
= $false )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(399,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) ) )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(400,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) ) )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(401,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 )
= $true )
| ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(402,plain,
! [SV40: $i,SV11: $i,SV52: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV52 )
| ( in @ SV63 @ SV11 )
| ( in @ SV63 @ SV40 ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(403,plain,
! [SV40: $i,SV52: $i,SV11: $i] :
( ( ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) )
| ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) )
= $false )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(404,plain,
! [SV29: $i,SV41: $i] :
( ( ( in @ ( sK11_C @ SV41 @ SV29 ) @ SV41 )
= $false )
| ( ( ( sK11_C @ SV41 @ SV29 )
= SV29 )
= $false )
| ( ( SV41
= ( singleton @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(405,plain,
! [SV42: $i,SV30: $i,SV60: $i] :
( ( ( ( SV60 != SV30 ) )
= $true )
| ( ( in @ SV60 @ SV42 )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(406,plain,
! [SV30: $i,SV42: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV42 ) )
= $true )
| ( ( SV61 = SV30 )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(407,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(408,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) )
= $false )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(409,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) ) )
= $false )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(410,plain,
! [SV54: $i,SV44: $i,SV12: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV12 )
| ~ ( in @ SV64 @ SV44 )
| ( in @ SV64 @ SV54 ) )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(411,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) )
= $false )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(412,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) ) )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(413,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) ) )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(414,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
= $true )
| ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 )
= $true )
| ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(415,plain,
! [SV48: $i,SV13: $i,SV56: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV56 )
| ( SV65 = SV13 )
| ( SV65 = SV48 ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(416,plain,
! [SV48: $i,SV56: $i,SV13: $i] :
( ( ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) )
| ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) )
= $false )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(417,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
= $false )
| ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(418,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(419,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
| ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 ) )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(420,plain,
! [SV50: $i,SV36: $i,SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ SV9 )
| ( in @ SV62 @ SV36 ) )
= $true )
| ( ( in @ SV62 @ SV50 )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(421,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) ) )
= $false )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(422,plain,
! [SV9: $i,SV36: $i,SV50: $i] :
( ( ( ~ ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) )
= $false )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(423,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(424,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
| ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(425,plain,
! [SV40: $i,SV11: $i,SV52: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ SV52 ) )
= $true )
| ( ( ( in @ SV63 @ SV11 )
| ( in @ SV63 @ SV40 ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(426,plain,
! [SV40: $i,SV52: $i,SV11: $i] :
( ( ( ~ ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) ) )
= $false )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(427,plain,
! [SV11: $i,SV52: $i,SV40: $i] :
( ( ( ~ ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) )
= $false )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(428,plain,
! [SV42: $i,SV30: $i,SV60: $i] :
( ( ( SV60 = SV30 )
= $false )
| ( ( in @ SV60 @ SV42 )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(429,plain,
! [SV30: $i,SV42: $i,SV61: $i] :
( ( ( in @ SV61 @ SV42 )
= $false )
| ( ( SV61 = SV30 )
= $true )
| ( ( SV42
= ( singleton @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(430,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
= $false )
| ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(431,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(432,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
| ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(433,plain,
! [SV54: $i,SV44: $i,SV12: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV12 )
| ~ ( in @ SV64 @ SV44 ) )
= $true )
| ( ( in @ SV64 @ SV54 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(434,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( ~ ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) ) )
= $false )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(435,plain,
! [SV12: $i,SV44: $i,SV54: $i] :
( ( ( ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) )
= $false )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(436,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(437,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
| ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(438,plain,
! [SV48: $i,SV13: $i,SV56: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV56 ) )
= $true )
| ( ( ( SV65 = SV13 )
| ( SV65 = SV48 ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(439,plain,
! [SV48: $i,SV56: $i,SV13: $i] :
( ( ( ~ ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) ) )
= $false )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(440,plain,
! [SV13: $i,SV56: $i,SV48: $i] :
( ( ( ~ ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) )
= $false )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(441,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 )
= $false )
| ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
= $true )
| ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
= $false )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(442,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV9 )
= $true )
| ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(443,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 ) )
= $true )
| ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(444,plain,
! [SV50: $i,SV36: $i,SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ SV9 ) )
= $true )
| ( ( in @ SV62 @ SV36 )
= $true )
| ( ( in @ SV62 @ SV50 )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(445,plain,
! [SV36: $i,SV9: $i,SV50: $i] :
( ( ( ! [SY905: $i] :
( ~ ( in @ SY905 @ SV50 )
| ( in @ SY905 @ SV9 ) ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(446,plain,
! [SV9: $i,SV36: $i,SV50: $i] :
( ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV50 )
| ~ ( in @ SY906 @ SV36 ) ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(447,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(448,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(449,plain,
! [SV40: $i,SV11: $i,SV52: $i,SV63: $i] :
( ( ( in @ SV63 @ SV52 )
= $false )
| ( ( ( in @ SV63 @ SV11 )
| ( in @ SV63 @ SV40 ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(450,plain,
! [SV40: $i,SV52: $i,SV11: $i] :
( ( ( ! [SY908: $i] :
( ~ ( in @ SY908 @ SV11 )
| ( in @ SY908 @ SV52 ) ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(451,plain,
! [SV11: $i,SV52: $i,SV40: $i] :
( ( ( ! [SY909: $i] :
( ~ ( in @ SY909 @ SV40 )
| ( in @ SY909 @ SV52 ) ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(452,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
= $false )
| ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
= $false )
| ( ( ~ ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 ) )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(453,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
= $true )
| ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(454,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
= $true )
| ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 )
= $true )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(455,plain,
! [SV54: $i,SV44: $i,SV12: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV64 @ SV44 ) )
= $true )
| ( ( in @ SV64 @ SV54 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(456,plain,
! [SV44: $i,SV12: $i,SV54: $i] :
( ( ( ! [SY911: $i] :
( ~ ( in @ SY911 @ SV54 )
| ( in @ SY911 @ SV12 ) ) )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(457,plain,
! [SV12: $i,SV44: $i,SV54: $i] :
( ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ SV54 )
| ( in @ SY912 @ SV44 ) ) )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(458,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 ) )
= $true )
| ( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(459,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 ) )
= $true )
| ( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(460,plain,
! [SV48: $i,SV13: $i,SV56: $i,SV65: $i] :
( ( ( in @ SV65 @ SV56 )
= $false )
| ( ( ( SV65 = SV13 )
| ( SV65 = SV48 ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(461,plain,
! [SV48: $i,SV56: $i,SV13: $i] :
( ( ( ! [SY914: $i] :
( ( SY914 != SV13 )
| ( in @ SY914 @ SV56 ) ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(462,plain,
! [SV13: $i,SV56: $i,SV48: $i] :
( ( ( ! [SY915: $i] :
( ( SY915 != SV48 )
| ( in @ SY915 @ SV56 ) ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(463,plain,
! [SV9: $i,SV35: $i,SV49: $i] :
( ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV35 )
= $false )
| ( ( in @ ( sK6_D @ SV49 @ SV35 @ SV9 ) @ SV49 )
= $true )
| ( ( SV49
= ( set_difference @ SV9 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(464,plain,
! [SV50: $i,SV36: $i,SV9: $i,SV62: $i] :
( ( ( in @ SV62 @ SV9 )
= $false )
| ( ( in @ SV62 @ SV36 )
= $true )
| ( ( in @ SV62 @ SV50 )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(465,plain,
! [SV36: $i,SV9: $i,SV50: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ SV50 )
| ( in @ SV66 @ SV9 ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(466,plain,
! [SV9: $i,SV36: $i,SV50: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV50 )
| ~ ( in @ SV67 @ SV36 ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(467,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(468,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 ) )
= $true )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(469,plain,
! [SV52: $i,SV40: $i,SV11: $i,SV63: $i] :
( ( ( in @ SV63 @ SV11 )
= $true )
| ( ( in @ SV63 @ SV40 )
= $true )
| ( ( in @ SV63 @ SV52 )
= $false )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(470,plain,
! [SV40: $i,SV52: $i,SV11: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV11 )
| ( in @ SV68 @ SV52 ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(471,plain,
! [SV11: $i,SV52: $i,SV40: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ SV40 )
| ( in @ SV69 @ SV52 ) )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(472,plain,
! [SV12: $i,SV43: $i,SV53: $i] :
( ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV53 )
= $false )
| ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV12 )
= $false )
| ( ( in @ ( sK7_D @ SV53 @ SV43 @ SV12 ) @ SV43 )
= $false )
| ( ( SV53
= ( set_intersection2 @ SV12 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(473,plain,
! [SV54: $i,SV44: $i,SV12: $i,SV64: $i] :
( ( ( in @ SV64 @ SV12 )
= $false )
| ( ( ~ ( in @ SV64 @ SV44 ) )
= $true )
| ( ( in @ SV64 @ SV54 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(474,plain,
! [SV44: $i,SV12: $i,SV54: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV54 )
| ( in @ SV70 @ SV12 ) )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(475,plain,
! [SV12: $i,SV44: $i,SV54: $i,SV71: $i] :
( ( ( ~ ( in @ SV71 @ SV54 )
| ( in @ SV71 @ SV44 ) )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(476,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
= $false )
| ( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV13 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(477,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
= $false )
| ( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
!= SV47 ) )
= $true )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(478,plain,
! [SV56: $i,SV48: $i,SV13: $i,SV65: $i] :
( ( ( SV65 = SV13 )
= $true )
| ( ( SV65 = SV48 )
= $true )
| ( ( in @ SV65 @ SV56 )
= $false )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(479,plain,
! [SV48: $i,SV56: $i,SV13: $i,SV72: $i] :
( ( ( ( SV72 != SV13 )
| ( in @ SV72 @ SV56 ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(480,plain,
! [SV13: $i,SV56: $i,SV48: $i,SV73: $i] :
( ( ( ( SV73 != SV48 )
| ( in @ SV73 @ SV56 ) )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(481,plain,
! [SV36: $i,SV9: $i,SV50: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ SV50 ) )
= $true )
| ( ( in @ SV66 @ SV9 )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(482,plain,
! [SV9: $i,SV36: $i,SV50: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV50 ) )
= $true )
| ( ( ~ ( in @ SV67 @ SV36 ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(483,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV11 )
= $false )
| ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(484,plain,
! [SV11: $i,SV39: $i,SV51: $i] :
( ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV39 )
= $false )
| ( ( in @ ( sK9_D @ SV51 @ SV39 @ SV11 ) @ SV51 )
= $false )
| ( ( SV51
= ( set_union2 @ SV11 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(485,plain,
! [SV40: $i,SV52: $i,SV11: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV11 ) )
= $true )
| ( ( in @ SV68 @ SV52 )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(486,plain,
! [SV11: $i,SV52: $i,SV40: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ SV40 ) )
= $true )
| ( ( in @ SV69 @ SV52 )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(487,plain,
! [SV54: $i,SV12: $i,SV44: $i,SV64: $i] :
( ( ( in @ SV64 @ SV44 )
= $false )
| ( ( in @ SV64 @ SV12 )
= $false )
| ( ( in @ SV64 @ SV54 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(488,plain,
! [SV44: $i,SV12: $i,SV54: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV54 ) )
= $true )
| ( ( in @ SV70 @ SV12 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(489,plain,
! [SV12: $i,SV44: $i,SV54: $i,SV71: $i] :
( ( ( ~ ( in @ SV71 @ SV54 ) )
= $true )
| ( ( in @ SV71 @ SV44 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(490,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV13 )
= $false )
| ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(491,plain,
! [SV13: $i,SV47: $i,SV55: $i] :
( ( ( ( sK13_D @ SV55 @ SV47 @ SV13 )
= SV47 )
= $false )
| ( ( in @ ( sK13_D @ SV55 @ SV47 @ SV13 ) @ SV55 )
= $false )
| ( ( SV55
= ( unordered_pair @ SV13 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(492,plain,
! [SV48: $i,SV56: $i,SV13: $i,SV72: $i] :
( ( ( ( SV72 != SV13 ) )
= $true )
| ( ( in @ SV72 @ SV56 )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(493,plain,
! [SV13: $i,SV56: $i,SV48: $i,SV73: $i] :
( ( ( ( SV73 != SV48 ) )
= $true )
| ( ( in @ SV73 @ SV56 )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(494,plain,
! [SV36: $i,SV9: $i,SV50: $i,SV66: $i] :
( ( ( in @ SV66 @ SV50 )
= $false )
| ( ( in @ SV66 @ SV9 )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(495,plain,
! [SV9: $i,SV36: $i,SV50: $i,SV67: $i] :
( ( ( in @ SV67 @ SV50 )
= $false )
| ( ( ~ ( in @ SV67 @ SV36 ) )
= $true )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(496,plain,
! [SV40: $i,SV52: $i,SV11: $i,SV68: $i] :
( ( ( in @ SV68 @ SV11 )
= $false )
| ( ( in @ SV68 @ SV52 )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(497,plain,
! [SV11: $i,SV52: $i,SV40: $i,SV69: $i] :
( ( ( in @ SV69 @ SV40 )
= $false )
| ( ( in @ SV69 @ SV52 )
= $true )
| ( ( SV52
= ( set_union2 @ SV11 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(498,plain,
! [SV44: $i,SV12: $i,SV54: $i,SV70: $i] :
( ( ( in @ SV70 @ SV54 )
= $false )
| ( ( in @ SV70 @ SV12 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(499,plain,
! [SV12: $i,SV44: $i,SV54: $i,SV71: $i] :
( ( ( in @ SV71 @ SV54 )
= $false )
| ( ( in @ SV71 @ SV44 )
= $true )
| ( ( SV54
= ( set_intersection2 @ SV12 @ SV44 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(500,plain,
! [SV48: $i,SV56: $i,SV13: $i,SV72: $i] :
( ( ( SV72 = SV13 )
= $false )
| ( ( in @ SV72 @ SV56 )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(501,plain,
! [SV13: $i,SV56: $i,SV48: $i,SV73: $i] :
( ( ( SV73 = SV48 )
= $false )
| ( ( in @ SV73 @ SV56 )
= $true )
| ( ( SV56
= ( unordered_pair @ SV13 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(502,plain,
! [SV9: $i,SV50: $i,SV36: $i,SV67: $i] :
( ( ( in @ SV67 @ SV36 )
= $false )
| ( ( in @ SV67 @ SV50 )
= $false )
| ( ( SV50
= ( set_difference @ SV9 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(503,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[147,502,501,500,499,498,497,496,494,491,490,487,484,483,478,472,469,464,463,454,453,442,441,429,428,414,404,401,389,362,356,355,346,345,332,331,311,302,295,290,289,282,250,245,244,243,242,234,218,169,168]) ).
thf(504,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[503]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU151+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 15:01:09 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.38 .
% 0.21/0.40
% 0.21/0.40 No.of.Axioms: 73
% 0.21/0.40
% 0.21/0.40 Length.of.Defs: 0
% 0.21/0.40
% 0.21/0.40 Contains.Choice.Funs: false
% 0.21/0.41 ..
% 0.21/0.44 (rf:0,axioms:73,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:75,loop_count:0,foatp_calls:0,translation:fof_full)..............................................................eprover: CPU time limit exceeded, terminating
% 74.60/74.79 .........
% 75.13/75.32 (rf:0,axioms:73,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:75,loop_count:0,foatp_calls:0,translation:fof_full)...........................................................eprover: CPU time limit exceeded, terminating
% 149.36/149.63 .........
% 150.06/150.32 (rf:0,axioms:73,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:75,loop_count:0,foatp_calls:0,translation:fof_full).............................................................eprover: CPU time limit exceeded, terminating
% 224.35/224.71 ...........
% 224.89/225.29 (rf:2,axioms:18,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:75,loop_count:0,foatp_calls:0,translation:fof_full)..................................
% 225.50/225.88
% 225.50/225.88 ********************************
% 225.50/225.88 * All subproblems solved! *
% 225.50/225.88 ********************************
% 225.50/225.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:18,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:503,loop_count:0,foatp_calls:1,translation:fof_full)
% 225.61/225.99
% 225.61/225.99 %**** Beginning of derivation protocol ****
% 225.61/225.99 % SZS output start CNFRefutation
% See solution above
% 225.61/226.00
% 225.61/226.00 %**** End of derivation protocol ****
% 225.61/226.00 %**** no. of clauses in derivation: 449 ****
% 225.61/226.00 %**** clause counter: 503 ****
% 225.61/226.00
% 225.61/226.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:18,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:503,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------