%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:05 AM UTC 2026
% Result : Theorem 0.39s 0.32s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 302 ( 204 unt; 0 typ; 0 def)
% Number of atoms : 1445 ( 473 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 2349 ( 563 ~; 290 |; 16 &;1427 @)
% ( 14 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 5 con; 0-2 aty)
% Number of variables : 467 ( 0 ^; 451 !; 16 ?; 467 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_k1_pcomps_1,type,
k1_pcomps_1: $i > $i ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_element,type,
proper_element: $i > $i > $o ).
thf(tp_sK10_SY42,type,
sK10_SY42: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY27,type,
sK2_SY27: $i ).
thf(tp_sK3_SY31,type,
sK3_SY31: $i > $i ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i > $i ).
thf(tp_sK5_SY38,type,
sK5_SY38: $i > $i ).
thf(tp_sK6_SY37,type,
sK6_SY37: $i > $i ).
thf(tp_sK7_SY40,type,
sK7_SY40: $i > $i ).
thf(tp_sK8_SY44,type,
sK8_SY44: $i > $i ).
thf(tp_sK9_SY48,type,
sK9_SY48: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $i > $o ).
thf(tp_v2_membered,type,
v2_membered: $i > $o ).
thf(tp_v3_membered,type,
v3_membered: $i > $o ).
thf(tp_v4_membered,type,
v4_membered: $i > $o ).
thf(tp_v5_membered,type,
v5_membered: $i > $o ).
thf(1,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(12,axiom,
! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
thf(14,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(15,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(18,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(19,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(25,axiom,
! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pcomps_1) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
thf(35,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(43,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
thf(44,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[43]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(47,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(51,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(52,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(53,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(54,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(56,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(61,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(64,plain,
( ( ! [SY27: $i] :
( ( element @ SY27 @ ( powerset @ sK1_A ) )
=> ( ( proper_element @ SY27 @ ( powerset @ sK1_A ) )
<=> ( SY27 != sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(65,plain,
( ( ( element @ sK2_SY27 @ ( powerset @ sK1_A ) )
=> ( ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
<=> ( sK2_SY27 != sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(66,plain,
( ( element @ sK2_SY27 @ ( powerset @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[65]) ).
thf(67,plain,
( ( ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
<=> ( sK2_SY27 != sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[65]) ).
thf(68,plain,
( ( ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
=> ( sK2_SY27 != sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[67]) ).
thf(69,plain,
( ( ( sK2_SY27 != sK1_A )
=> ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[67]) ).
thf(70,plain,
( ( ~ ( ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
=> ( sK2_SY27 != sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[68]) ).
thf(71,plain,
( ( ~ ( ( sK2_SY27 != sK1_A )
=> ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[69]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(74,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(75,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(76,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(77,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(79,plain,
$true = $true,
inference(copy,[status(thm)],[56]) ).
thf(80,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(81,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(82,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(83,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(84,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(85,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(90,plain,
( ( element @ sK2_SY27 @ ( powerset @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(91,plain,
( ( ~ ( ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
=> ( sK2_SY27 != sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(94,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(95,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(96,plain,
( ( ~ ( ~ ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
| ( sK2_SY27 != sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ~ ( ~ ( ~ ( proper_element @ SX1 @ SX0 )
| ( SX1
!= ( union @ SX0 ) ) )
| ~ ( ~ ( ( SX1
!= ( union @ SX0 ) ) )
| ( proper_element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(98,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(101,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(102,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(103,plain,
! [SV1: $i] :
( ( element @ ( k1_pcomps_1 @ SV1 ) @ ( powerset @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(104,plain,
! [SV2: $i] :
( ( ~ ( empty @ ( powerset @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(105,plain,
! [SV3: $i] :
( ( ( k1_pcomps_1 @ SV3 )
= ( powerset @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(106,plain,
! [SV4: $i] :
( ( ( union @ ( powerset @ SV4 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(107,plain,
! [SV5: $i] :
( ( ! [SY28: $i] :
( ~ ( in @ SV5 @ SY28 )
| ( element @ SV5 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV6: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SY29 )
| ~ ( element @ SY29 @ ( powerset @ SY30 ) ) )
| ( element @ SV6 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV7: $i] :
( ( ~ ! [SY31: $i] :
~ ~ ( ~ ( element @ SY31 @ ( powerset @ SV7 ) )
| ~ ( empty @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV8: $i] :
( ( ~ ( v1_membered @ SV8 )
| ! [SY32: $i] :
( ~ ( element @ SY32 @ ( powerset @ SV8 ) )
| ( v1_membered @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
( ( ~ ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
| ( sK2_SY27 != sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV9: $i] :
( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ SV9 )
| ~ ( ~ ( ~ ( proper_element @ SY33 @ SV9 )
| ( SY33
!= ( union @ SV9 ) ) )
| ~ ( ~ ( ( SY33
!= ( union @ SV9 ) ) )
| ( proper_element @ SY33 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV10: $i] :
( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ SV10 ) )
| ~ ~ ( proper_element @ SY34 @ ( powerset @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV11: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ~ ( element @ SV11 @ ( powerset @ SY35 ) )
| ( subset @ SV11 @ SY35 ) )
| ~ ( ~ ( subset @ SV11 @ SY35 )
| ( element @ SV11 @ ( powerset @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV12: $i] :
( ( ! [SY36: $i] :
( ~ ( element @ SY36 @ ( powerset @ ( powerset @ SV12 ) ) )
| ( element @ ( union_of_subsets @ SV12 @ SY36 ) @ ( powerset @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV13: $i] :
( ( ~ ~ ( empty @ SV13 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( element @ SY37 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV14: $i] :
( ( ~ ! [SY38: $i] :
~ ( element @ SY38 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV2: $i] :
( ( empty @ ( powerset @ SV2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(119,plain,
! [SV15: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV15 )
| ( element @ SV5 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV16: $i,SV6: $i] :
( ( ! [SY39: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SV16 )
| ~ ( element @ SV16 @ ( powerset @ SY39 ) ) )
| ( element @ SV6 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV7: $i] :
( ( ! [SY31: $i] :
~ ~ ( ~ ( element @ SY31 @ ( powerset @ SV7 ) )
| ~ ( empty @ SY31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV8: $i] :
( ( ( ~ ( v1_membered @ SV8 ) )
= $true )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( powerset @ SV8 ) )
| ( v1_membered @ SY32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(123,plain,
( ( ~ ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(124,plain,
( ( sK2_SY27 != sK1_A )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(125,plain,
! [SV9: $i,SV17: $i] :
( ( ~ ( element @ SV17 @ SV9 )
| ~ ( ~ ( ~ ( proper_element @ SV17 @ SV9 )
| ( SV17
!= ( union @ SV9 ) ) )
| ~ ( ~ ( ( SV17
!= ( union @ SV9 ) ) )
| ( proper_element @ SV17 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV10: $i] :
( ( ! [SY34: $i] :
~ ~ ( ~ ( element @ SY34 @ ( powerset @ SV10 ) )
| ~ ~ ( proper_element @ SY34 @ ( powerset @ SV10 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( element @ SV11 @ ( powerset @ SV18 ) )
| ( subset @ SV11 @ SV18 ) )
| ~ ( ~ ( subset @ SV11 @ SV18 )
| ( element @ SV11 @ ( powerset @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV12: $i,SV19: $i] :
( ( ~ ( element @ SV19 @ ( powerset @ ( powerset @ SV12 ) ) )
| ( element @ ( union_of_subsets @ SV12 @ SV19 ) @ ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( element @ SY37 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(130,plain,
! [SV14: $i] :
( ( ! [SY38: $i] :
~ ( element @ SY38 @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV15 ) )
= $true )
| ( ( element @ SV5 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV20: $i,SV16: $i,SV6: $i] :
( ( ~ ~ ( ~ ( in @ SV6 @ SV16 )
| ~ ( element @ SV16 @ ( powerset @ SV20 ) ) )
| ( element @ SV6 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ( element @ ( sK3_SY31 @ SV7 ) @ ( powerset @ SV7 ) )
| ~ ( empty @ ( sK3_SY31 @ SV7 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(134,plain,
! [SV8: $i] :
( ( ( v1_membered @ SV8 )
= $false )
| ( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( powerset @ SV8 ) )
| ( v1_membered @ SY32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(135,plain,
( ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(136,plain,
( ( sK2_SY27 = sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(137,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV17 @ SV9 )
| ( SV17
!= ( union @ SV9 ) ) )
| ~ ( ~ ( ( SV17
!= ( union @ SV9 ) ) )
| ( proper_element @ SV17 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ( element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ~ ( proper_element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(139,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( ~ ( element @ SV11 @ ( powerset @ SV18 ) )
| ( subset @ SV11 @ SV18 ) )
| ~ ( ~ ( subset @ SV11 @ SV18 )
| ( element @ SV11 @ ( powerset @ SV18 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV12: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ ( powerset @ ( powerset @ SV12 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV12 @ SV19 ) @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $false )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( element @ SY37 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV14: $i] :
( ( ~ ( element @ ( sK5_SY38 @ SV14 ) @ SV14 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(143,plain,
! [SV15: $i,SV5: $i] :
( ( ( in @ SV5 @ SV15 )
= $false )
| ( ( element @ SV5 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV20: $i,SV16: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ SV6 @ SV16 )
| ~ ( element @ SV16 @ ( powerset @ SV20 ) ) ) )
= $true )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV7: $i] :
( ( ~ ( ~ ( element @ ( sK3_SY31 @ SV7 ) @ ( powerset @ SV7 ) )
| ~ ( empty @ ( sK3_SY31 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(146,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( powerset @ SV8 ) )
| ( v1_membered @ SV21 ) )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV9: $i,SV17: $i] :
( ( ( element @ SV17 @ SV9 )
= $false )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV17 @ SV9 )
| ( SV17
!= ( union @ SV9 ) ) )
| ~ ( ~ ( ( SV17
!= ( union @ SV9 ) ) )
| ( proper_element @ SV17 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV10: $i] :
( ( ~ ( ~ ( element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ~ ( proper_element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(149,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( ~ ( element @ SV11 @ ( powerset @ SV18 ) )
| ( subset @ SV11 @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(150,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ SV18 )
| ( element @ SV11 @ ( powerset @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(151,plain,
! [SV12: $i,SV19: $i] :
( ( ( element @ SV19 @ ( powerset @ ( powerset @ SV12 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV12 @ SV19 ) @ ( powerset @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( element @ SY37 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(153,plain,
! [SV14: $i] :
( ( element @ ( sK5_SY38 @ SV14 ) @ SV14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(154,plain,
! [SV20: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ SV6 @ SV16 )
| ~ ( element @ SV16 @ ( powerset @ SV20 ) ) ) )
= $false )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV7: $i] :
( ( ~ ( element @ ( sK3_SY31 @ SV7 ) @ ( powerset @ SV7 ) )
| ~ ( empty @ ( sK3_SY31 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( v1_membered @ SV21 )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ~ ( proper_element @ SV17 @ SV9 )
| ( SV17
!= ( union @ SV9 ) ) )
| ~ ( ~ ( ( SV17
!= ( union @ SV9 ) ) )
| ( proper_element @ SV17 @ SV9 ) ) )
= $false )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV10: $i] :
( ( ~ ( element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ~ ( proper_element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( element @ SV11 @ ( powerset @ SV18 ) )
| ( subset @ SV11 @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(160,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV18 )
| ( element @ SV11 @ ( powerset @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(161,plain,
! [SV13: $i] :
( ( ( ! [SY37: $i] :
~ ~ ( ~ ( element @ SY37 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY37 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV20: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV16 )
| ~ ( element @ SV16 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV7: $i] :
( ( ~ ( element @ ( sK3_SY31 @ SV7 ) @ ( powerset @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(164,plain,
! [SV7: $i] :
( ( ~ ( empty @ ( sK3_SY31 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(165,plain,
! [SV8: $i,SV21: $i] :
( ( ( element @ SV21 @ ( powerset @ SV8 ) )
= $false )
| ( ( v1_membered @ SV21 )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ~ ( proper_element @ SV17 @ SV9 )
| ( SV17
!= ( union @ SV9 ) ) ) )
= $false )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(167,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ~ ( ( SV17
!= ( union @ SV9 ) ) )
| ( proper_element @ SV17 @ SV9 ) ) )
= $false )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(168,plain,
! [SV10: $i] :
( ( ~ ( element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(169,plain,
! [SV10: $i] :
( ( ~ ~ ( proper_element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(170,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( element @ SV11 @ ( powerset @ SV18 ) ) )
= $true )
| ( ( subset @ SV11 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(171,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV18 ) )
= $true )
| ( ( element @ SV11 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(172,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK6_SY37 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK6_SY37 @ SV13 ) ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[161]) ).
thf(173,plain,
! [SV20: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV16 ) )
= $true )
| ( ( ~ ( element @ SV16 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(174,plain,
! [SV7: $i] :
( ( element @ ( sK3_SY31 @ SV7 ) @ ( powerset @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(175,plain,
! [SV7: $i] :
( ( empty @ ( sK3_SY31 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(176,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( proper_element @ SV17 @ SV9 )
| ( SV17
!= ( union @ SV9 ) ) )
= $true )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(177,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( union @ SV9 ) ) )
| ( proper_element @ SV17 @ SV9 ) )
= $true )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV10: $i] :
( ( element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(179,plain,
! [SV10: $i] :
( ( ~ ( proper_element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(180,plain,
! [SV18: $i,SV11: $i] :
( ( ( element @ SV11 @ ( powerset @ SV18 ) )
= $false )
| ( ( subset @ SV11 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV18: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV18 )
= $false )
| ( ( element @ SV11 @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( element @ ( sK6_SY37 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK6_SY37 @ SV13 ) ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(183,plain,
! [SV20: $i,SV16: $i,SV6: $i] :
( ( ( in @ SV6 @ SV16 )
= $false )
| ( ( ~ ( element @ SV16 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( proper_element @ SV17 @ SV9 ) )
= $true )
| ( ( SV17
!= ( union @ SV9 ) )
= $true )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( union @ SV9 ) ) ) )
= $true )
| ( ( proper_element @ SV17 @ SV9 )
= $true )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV10: $i] :
( ( proper_element @ ( sK4_SY34 @ SV10 ) @ ( powerset @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(187,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK6_SY37 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK6_SY37 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(188,plain,
! [SV6: $i,SV20: $i,SV16: $i] :
( ( ( element @ SV16 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV6 @ SV16 )
= $false )
| ( ( element @ SV6 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(189,plain,
! [SV9: $i,SV17: $i] :
( ( ( proper_element @ SV17 @ SV9 )
= $false )
| ( ( SV17
!= ( union @ SV9 ) )
= $true )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(190,plain,
! [SV9: $i,SV17: $i] :
( ( ( SV17
!= ( union @ SV9 ) )
= $false )
| ( ( proper_element @ SV17 @ SV9 )
= $true )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(191,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK6_SY37 @ SV13 ) @ ( powerset @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(192,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ ( sK6_SY37 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(193,plain,
! [SV9: $i,SV17: $i] :
( ( ( SV17
= ( union @ SV9 ) )
= $false )
| ( ( proper_element @ SV17 @ SV9 )
= $false )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(194,plain,
! [SV9: $i,SV17: $i] :
( ( ( SV17
= ( union @ SV9 ) )
= $true )
| ( ( proper_element @ SV17 @ SV9 )
= $true )
| ( ( element @ SV17 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(195,plain,
! [SV13: $i] :
( ( ( element @ ( sK6_SY37 @ SV13 ) @ ( powerset @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(196,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ ( sK6_SY37 @ SV13 ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(197,plain,
! [SV13: $i] :
( ( ( empty @ ( sK6_SY37 @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(198,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,197,195,194,193,188,186,181,180,178,175,174,165,153,151,143,136,135,118,106,105,103,90,79,77,76]) ).
thf(199,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ A )
=> ( ( proper_element @ B @ A )
<=> ( B
!= ( union @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(201,plain,
( ( ! [A: $i] : ( element @ ( k1_pcomps_1 @ A ) @ ( powerset @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(202,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(203,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(204,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(205,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(206,plain,
$true = $true,
inference(copy,[status(thm)],[56]) ).
thf(207,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(208,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(209,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(210,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(211,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( proper_element @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(212,plain,
( ( ! [A: $i] :
( ( k1_pcomps_1 @ A )
= ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(214,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(215,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(216,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(217,plain,
( ( element @ sK2_SY27 @ ( powerset @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(218,plain,
( ( ~ ( ( sK2_SY27 != sK1_A )
=> ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(219,plain,
( ( ~ ( ~ ( ( sK2_SY27 != sK1_A ) )
| ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(220,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(221,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(222,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(223,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ~ ( ~ ( ~ ( proper_element @ SX1 @ SX0 )
| ( SX1
!= ( union @ SX0 ) ) )
| ~ ( ~ ( ( SX1
!= ( union @ SX0 ) ) )
| ( proper_element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(224,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(225,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(226,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(227,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(228,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(229,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( union_of_subsets @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(230,plain,
! [SV22: $i] :
( ( element @ ( k1_pcomps_1 @ SV22 ) @ ( powerset @ ( powerset @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(231,plain,
! [SV23: $i] :
( ( ~ ( empty @ ( powerset @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(232,plain,
! [SV24: $i] :
( ( ( k1_pcomps_1 @ SV24 )
= ( powerset @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(233,plain,
! [SV25: $i] :
( ( ( union @ ( powerset @ SV25 ) )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(234,plain,
( ( ~ ( ( sK2_SY27 != sK1_A ) )
| ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(235,plain,
! [SV26: $i] :
( ( ~ ! [SY40: $i] :
~ ~ ( ~ ( element @ SY40 @ ( powerset @ SV26 ) )
| ~ ( empty @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(236,plain,
! [SV27: $i] :
( ( ! [SY41: $i] :
~ ( ~ ( ~ ( element @ SV27 @ ( powerset @ SY41 ) )
| ( subset @ SV27 @ SY41 ) )
| ~ ( ~ ( subset @ SV27 @ SY41 )
| ( element @ SV27 @ ( powerset @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(237,plain,
! [SV28: $i] :
( ( ~ ~ ( empty @ SV28 )
| ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(238,plain,
! [SV29: $i] :
( ( ! [SY43: $i] :
( ~ ( element @ SY43 @ SV29 )
| ~ ( ~ ( ~ ( proper_element @ SY43 @ SV29 )
| ( SY43
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SY43
!= ( union @ SV29 ) ) )
| ( proper_element @ SY43 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV30: $i] :
( ( ~ ! [SY44: $i] :
~ ( element @ SY44 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(240,plain,
! [SV31: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ~ ( ~ ( in @ SV31 @ SY45 )
| ~ ( element @ SY45 @ ( powerset @ SY46 ) ) )
| ( element @ SV31 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(241,plain,
! [SV32: $i] :
( ( ~ ( v1_membered @ SV32 )
| ! [SY47: $i] :
( ~ ( element @ SY47 @ ( powerset @ SV32 ) )
| ( v1_membered @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(242,plain,
! [SV33: $i] :
( ( ~ ! [SY48: $i] :
~ ~ ( ~ ( element @ SY48 @ ( powerset @ SV33 ) )
| ~ ~ ( proper_element @ SY48 @ ( powerset @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(243,plain,
! [SV34: $i] :
( ( ! [SY49: $i] :
( ~ ( in @ SV34 @ SY49 )
| ( element @ SV34 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(244,plain,
! [SV35: $i] :
( ( ! [SY50: $i] :
( ~ ( element @ SY50 @ ( powerset @ ( powerset @ SV35 ) ) )
| ( element @ ( union_of_subsets @ SV35 @ SY50 ) @ ( powerset @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV23: $i] :
( ( empty @ ( powerset @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(246,plain,
( ( ~ ( ( sK2_SY27 != sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(247,plain,
( ( proper_element @ sK2_SY27 @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(248,plain,
! [SV26: $i] :
( ( ! [SY40: $i] :
~ ~ ( ~ ( element @ SY40 @ ( powerset @ SV26 ) )
| ~ ( empty @ SY40 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(249,plain,
! [SV36: $i,SV27: $i] :
( ( ~ ( ~ ( ~ ( element @ SV27 @ ( powerset @ SV36 ) )
| ( subset @ SV27 @ SV36 ) )
| ~ ( ~ ( subset @ SV27 @ SV36 )
| ( element @ SV27 @ ( powerset @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(250,plain,
! [SV28: $i] :
( ( ( ~ ~ ( empty @ SV28 ) )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(251,plain,
! [SV29: $i,SV37: $i] :
( ( ~ ( element @ SV37 @ SV29 )
| ~ ( ~ ( ~ ( proper_element @ SV37 @ SV29 )
| ( SV37
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV37
!= ( union @ SV29 ) ) )
| ( proper_element @ SV37 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(252,plain,
! [SV30: $i] :
( ( ! [SY44: $i] :
~ ( element @ SY44 @ SV30 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(253,plain,
! [SV38: $i,SV31: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ( in @ SV31 @ SV38 )
| ~ ( element @ SV38 @ ( powerset @ SY51 ) ) )
| ( element @ SV31 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(254,plain,
! [SV32: $i] :
( ( ( ~ ( v1_membered @ SV32 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( element @ SY47 @ ( powerset @ SV32 ) )
| ( v1_membered @ SY47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(255,plain,
! [SV33: $i] :
( ( ! [SY48: $i] :
~ ~ ( ~ ( element @ SY48 @ ( powerset @ SV33 ) )
| ~ ~ ( proper_element @ SY48 @ ( powerset @ SV33 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(256,plain,
! [SV39: $i,SV34: $i] :
( ( ~ ( in @ SV34 @ SV39 )
| ( element @ SV34 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(257,plain,
! [SV35: $i,SV40: $i] :
( ( ~ ( element @ SV40 @ ( powerset @ ( powerset @ SV35 ) ) )
| ( element @ ( union_of_subsets @ SV35 @ SV40 ) @ ( powerset @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(258,plain,
( ( sK2_SY27 != sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(259,plain,
! [SV26: $i] :
( ( ~ ~ ( ~ ( element @ ( sK7_SY40 @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ( empty @ ( sK7_SY40 @ SV26 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[248]) ).
thf(260,plain,
! [SV36: $i,SV27: $i] :
( ( ~ ( ~ ( element @ SV27 @ ( powerset @ SV36 ) )
| ( subset @ SV27 @ SV36 ) )
| ~ ( ~ ( subset @ SV27 @ SV36 )
| ( element @ SV27 @ ( powerset @ SV36 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(261,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ SV28 ) )
= $false )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(262,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV37 @ SV29 )
| ( SV37
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV37
!= ( union @ SV29 ) ) )
| ( proper_element @ SV37 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(263,plain,
! [SV30: $i] :
( ( ~ ( element @ ( sK8_SY44 @ SV30 ) @ SV30 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[252]) ).
thf(264,plain,
! [SV41: $i,SV38: $i,SV31: $i] :
( ( ~ ~ ( ~ ( in @ SV31 @ SV38 )
| ~ ( element @ SV38 @ ( powerset @ SV41 ) ) )
| ( element @ SV31 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV32: $i] :
( ( ( v1_membered @ SV32 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( element @ SY47 @ ( powerset @ SV32 ) )
| ( v1_membered @ SY47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV33: $i] :
( ( ~ ~ ( ~ ( element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) )
| ~ ~ ( proper_element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[255]) ).
thf(267,plain,
! [SV39: $i,SV34: $i] :
( ( ( ~ ( in @ SV34 @ SV39 ) )
= $true )
| ( ( element @ SV34 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(268,plain,
! [SV35: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ ( powerset @ SV35 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV35 @ SV40 ) @ ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(269,plain,
( ( sK2_SY27 = sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV26: $i] :
( ( ~ ( ~ ( element @ ( sK7_SY40 @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ( empty @ ( sK7_SY40 @ SV26 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(271,plain,
! [SV36: $i,SV27: $i] :
( ( ~ ( ~ ( element @ SV27 @ ( powerset @ SV36 ) )
| ( subset @ SV27 @ SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(272,plain,
! [SV36: $i,SV27: $i] :
( ( ~ ( ~ ( subset @ SV27 @ SV36 )
| ( element @ SV27 @ ( powerset @ SV36 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(273,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(274,plain,
! [SV29: $i,SV37: $i] :
( ( ( element @ SV37 @ SV29 )
= $false )
| ( ( ~ ( ~ ( ~ ( proper_element @ SV37 @ SV29 )
| ( SV37
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV37
!= ( union @ SV29 ) ) )
| ( proper_element @ SV37 @ SV29 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(275,plain,
! [SV30: $i] :
( ( element @ ( sK8_SY44 @ SV30 ) @ SV30 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(276,plain,
! [SV41: $i,SV38: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( in @ SV31 @ SV38 )
| ~ ( element @ SV38 @ ( powerset @ SV41 ) ) ) )
= $true )
| ( ( element @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(277,plain,
! [SV32: $i,SV42: $i] :
( ( ( ~ ( element @ SV42 @ ( powerset @ SV32 ) )
| ( v1_membered @ SV42 ) )
= $true )
| ( ( v1_membered @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(278,plain,
! [SV33: $i] :
( ( ~ ( ~ ( element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) )
| ~ ~ ( proper_element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(279,plain,
! [SV39: $i,SV34: $i] :
( ( ( in @ SV34 @ SV39 )
= $false )
| ( ( element @ SV34 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(280,plain,
! [SV35: $i,SV40: $i] :
( ( ( element @ SV40 @ ( powerset @ ( powerset @ SV35 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV35 @ SV40 ) @ ( powerset @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(281,plain,
! [SV26: $i] :
( ( ~ ( element @ ( sK7_SY40 @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ( empty @ ( sK7_SY40 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(282,plain,
! [SV36: $i,SV27: $i] :
( ( ~ ( element @ SV27 @ ( powerset @ SV36 ) )
| ( subset @ SV27 @ SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(283,plain,
! [SV36: $i,SV27: $i] :
( ( ~ ( subset @ SV27 @ SV36 )
| ( element @ SV27 @ ( powerset @ SV36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(284,plain,
! [SV28: $i] :
( ( ( ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(285,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( ~ ( proper_element @ SV37 @ SV29 )
| ( SV37
!= ( union @ SV29 ) ) )
| ~ ( ~ ( ( SV37
!= ( union @ SV29 ) ) )
| ( proper_element @ SV37 @ SV29 ) ) )
= $false )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(286,plain,
! [SV41: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ SV31 @ SV38 )
| ~ ( element @ SV38 @ ( powerset @ SV41 ) ) ) )
= $false )
| ( ( element @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV32: $i,SV42: $i] :
( ( ( ~ ( element @ SV42 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( v1_membered @ SV42 )
= $true )
| ( ( v1_membered @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(288,plain,
! [SV33: $i] :
( ( ~ ( element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) )
| ~ ~ ( proper_element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(289,plain,
! [SV26: $i] :
( ( ~ ( element @ ( sK7_SY40 @ SV26 ) @ ( powerset @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(290,plain,
! [SV26: $i] :
( ( ~ ( empty @ ( sK7_SY40 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(291,plain,
! [SV36: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( powerset @ SV36 ) ) )
= $true )
| ( ( subset @ SV27 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(292,plain,
! [SV36: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV36 ) )
= $true )
| ( ( element @ SV27 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(293,plain,
! [SV28: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_SY42 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK10_SY42 @ SV28 ) ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[284]) ).
thf(294,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( ~ ( proper_element @ SV37 @ SV29 )
| ( SV37
!= ( union @ SV29 ) ) ) )
= $false )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(295,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( ~ ( ( SV37
!= ( union @ SV29 ) ) )
| ( proper_element @ SV37 @ SV29 ) ) )
= $false )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(296,plain,
! [SV41: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV38 )
| ~ ( element @ SV38 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( element @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(297,plain,
! [SV32: $i,SV42: $i] :
( ( ( element @ SV42 @ ( powerset @ SV32 ) )
= $false )
| ( ( v1_membered @ SV42 )
= $true )
| ( ( v1_membered @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(298,plain,
! [SV33: $i] :
( ( ~ ( element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(299,plain,
! [SV33: $i] :
( ( ~ ~ ( proper_element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(300,plain,
! [SV26: $i] :
( ( element @ ( sK7_SY40 @ SV26 ) @ ( powerset @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(301,plain,
! [SV26: $i] :
( ( empty @ ( sK7_SY40 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(302,plain,
! [SV36: $i,SV27: $i] :
( ( ( element @ SV27 @ ( powerset @ SV36 ) )
= $false )
| ( ( subset @ SV27 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(303,plain,
! [SV36: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV36 )
= $false )
| ( ( element @ SV27 @ ( powerset @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(304,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_SY42 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK10_SY42 @ SV28 ) ) ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(305,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( proper_element @ SV37 @ SV29 )
| ( SV37
!= ( union @ SV29 ) ) )
= $true )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(306,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( ( SV37
!= ( union @ SV29 ) ) )
| ( proper_element @ SV37 @ SV29 ) )
= $true )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(307,plain,
! [SV41: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV38 ) )
= $true )
| ( ( ~ ( element @ SV38 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( element @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(308,plain,
! [SV33: $i] :
( ( element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(309,plain,
! [SV33: $i] :
( ( ~ ( proper_element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(310,plain,
! [SV28: $i] :
( ( ( ~ ( element @ ( sK10_SY42 @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK10_SY42 @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(311,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( proper_element @ SV37 @ SV29 ) )
= $true )
| ( ( SV37
!= ( union @ SV29 ) )
= $true )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(312,plain,
! [SV29: $i,SV37: $i] :
( ( ( ~ ( ( SV37
!= ( union @ SV29 ) ) ) )
= $true )
| ( ( proper_element @ SV37 @ SV29 )
= $true )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(313,plain,
! [SV41: $i,SV38: $i,SV31: $i] :
( ( ( in @ SV31 @ SV38 )
= $false )
| ( ( ~ ( element @ SV38 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( element @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(314,plain,
! [SV33: $i] :
( ( proper_element @ ( sK9_SY48 @ SV33 ) @ ( powerset @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(315,plain,
! [SV28: $i] :
( ( ( ~ ( element @ ( sK10_SY42 @ SV28 ) @ ( powerset @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(316,plain,
! [SV28: $i] :
( ( ( ~ ~ ( empty @ ( sK10_SY42 @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(317,plain,
! [SV29: $i,SV37: $i] :
( ( ( proper_element @ SV37 @ SV29 )
= $false )
| ( ( SV37
!= ( union @ SV29 ) )
= $true )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(318,plain,
! [SV29: $i,SV37: $i] :
( ( ( SV37
!= ( union @ SV29 ) )
= $false )
| ( ( proper_element @ SV37 @ SV29 )
= $true )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(319,plain,
! [SV31: $i,SV41: $i,SV38: $i] :
( ( ( element @ SV38 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV31 @ SV38 )
= $false )
| ( ( element @ SV31 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(320,plain,
! [SV28: $i] :
( ( ( element @ ( sK10_SY42 @ SV28 ) @ ( powerset @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(321,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ ( sK10_SY42 @ SV28 ) ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(322,plain,
! [SV29: $i,SV37: $i] :
( ( ( SV37
= ( union @ SV29 ) )
= $false )
| ( ( proper_element @ SV37 @ SV29 )
= $false )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(323,plain,
! [SV29: $i,SV37: $i] :
( ( ( SV37
= ( union @ SV29 ) )
= $true )
| ( ( proper_element @ SV37 @ SV29 )
= $true )
| ( ( element @ SV37 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(324,plain,
! [SV28: $i] :
( ( ( empty @ ( sK10_SY42 @ SV28 ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(325,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[202,324,323,322,320,319,314,308,303,302,301,300,297,280,279,275,269,247,245,233,232,230,217,206,204,203]) ).
thf(326,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[325,198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 15:14:59 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.32
% 0.39/0.32 No.of.Axioms: 18
% 0.39/0.32
% 0.39/0.32 Length.of.Defs: 0
% 0.39/0.32
% 0.39/0.32 Contains.Choice.Funs: false
% 0.39/0.32 .......
% 0.39/0.32
% 0.39/0.32 ********************************
% 0.39/0.32 * All subproblems solved! *
% 0.39/0.32 ********************************
% 0.39/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:325,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.39/0.32
% 0.39/0.32 %**** Beginning of derivation protocol ****
% 0.39/0.32 % SZS output start CNFRefutation
% See solution above
% 0.39/0.33
% 0.39/0.33 %**** End of derivation protocol ****
% 0.39/0.33 %**** no. of clauses in derivation: 302 ****
% 0.39/0.33 %**** clause counter: 325 ****
% 0.39/0.33
% 0.39/0.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:325,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------