%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU326+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:43:59 AM UTC 2026
% Result : Theorem 0.57s 0.28s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 272 ( 175 unt; 0 typ; 0 def)
% Number of atoms : 1327 ( 491 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 2141 ( 496 ~; 252 |; 40 &;1308 @)
% ( 4 <=>; 41 =>; 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 : 28 ( 25 usr; 5 con; 0-2 aty)
% Number of variables : 433 ( 0 ^; 421 !; 12 ?; 433 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
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_natural,type,
natural: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_SY28,type,
sK3_SY28: $i > $i ).
thf(tp_sK4_SY36,type,
sK4_SY36: $i > $i ).
thf(tp_sK5_SY27,type,
sK5_SY27: $i > $i ).
thf(tp_sK6_SY41,type,
sK6_SY41: $i > $i ).
thf(tp_sK7_SY47,type,
sK7_SY47: $i > $i ).
thf(tp_sK8_SY42,type,
sK8_SY42: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
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(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(12,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(16,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(18,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(30,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(38,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
thf(39,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[38]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ A @ B )
!= empty_set )
& ( B = empty_set ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(46,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(47,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(49,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(50,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[18]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(53,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(54,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(56,plain,
( ( ! [SY25: $i] :
( ( element @ SY25 @ ( powerset @ ( powerset @ sK1_A ) ) )
=> ( ~ ( ( SY25 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ SY25 )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ sK1_A @ SY25 )
!= empty_set )
& ( SY25 = empty_set ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(57,plain,
( ( ( element @ sK2_SY25 @ ( powerset @ ( powerset @ sK1_A ) ) )
=> ( ~ ( ( sK2_SY25 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set )
& ( sK2_SY25 = empty_set ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(58,plain,
( ( element @ sK2_SY25 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[57]) ).
thf(59,plain,
( ( ~ ( ( sK2_SY25 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
= empty_set ) )
& ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set )
& ( sK2_SY25 = empty_set ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ( ( sK2_SY25 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
= empty_set ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[59]) ).
thf(61,plain,
( ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set )
& ( sK2_SY25 = empty_set ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[59]) ).
thf(62,plain,
( ( ( sK2_SY25 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
= empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[60]) ).
thf(63,plain,
( ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set )
& ( sK2_SY25 = empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[61]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(65,plain,
$true = $true,
inference(copy,[status(thm)],[54]) ).
thf(66,plain,
$true = $true,
inference(copy,[status(thm)],[53]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(68,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(69,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(70,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(72,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(73,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(77,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(79,plain,
( ( element @ sK2_SY25 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(80,plain,
( ( ( sK2_SY25 != empty_set )
& ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(81,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(83,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( complements_of_subsets @ SX0 @ ( complements_of_subsets @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(85,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)],[75]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( complements_of_subsets @ SX0 @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(90,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(91,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(92,plain,
( ( ~ ( ~ ( ( sK2_SY25 != empty_set ) )
| ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(93,plain,
! [SV1: $i] :
( ( ~ ( empty @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(94,plain,
! [SV2: $i] :
( ( ~ ( v1_membered @ SV2 )
| ! [SY26: $i] :
( ~ ( element @ SY26 @ ( powerset @ SV2 ) )
| ( v1_membered @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV3: $i] :
( ( ~ ~ ( empty @ SV3 )
| ~ ! [SY27: $i] :
~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV4: $i] :
( ( ~ ! [SY28: $i] :
~ ~ ( ~ ( element @ SY28 @ ( powerset @ SV4 ) )
| ~ ( empty @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV5: $i] :
( ( ! [SY29: $i] :
( ~ ( element @ SY29 @ ( powerset @ ( powerset @ SV5 ) ) )
| ( ( complements_of_subsets @ SV5 @ ( complements_of_subsets @ SV5 @ SY29 ) )
= SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV6: $i] :
( ( ! [SY30: $i] :
~ ( ~ ( ~ ( element @ SV6 @ ( powerset @ SY30 ) )
| ( subset @ SV6 @ SY30 ) )
| ~ ( ~ ( subset @ SV6 @ SY30 )
| ( element @ SV6 @ ( powerset @ SY30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV7: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SV7 @ SY31 )
| ( element @ SV7 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV8: $i] :
( ( ! [SY32: $i] :
( ~ ( element @ SY32 @ ( powerset @ ( powerset @ SV8 ) ) )
| ( element @ ( complements_of_subsets @ SV8 @ SY32 ) @ ( powerset @ ( powerset @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV9: $i] :
( ( ! [SY33: $i] :
( ~ ( element @ SY33 @ ( powerset @ ( powerset @ SV9 ) ) )
| ~ ~ ( ~ ( ( SY33 != empty_set ) )
| ( ( complements_of_subsets @ SV9 @ SY33 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV10: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ~ ( ~ ( in @ SV10 @ SY34 )
| ~ ( element @ SY34 @ ( powerset @ SY35 ) ) )
| ( element @ SV10 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV11: $i] :
( ( ~ ( empty @ SV11 )
| ( SV11 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV12: $i] :
( ( ~ ! [SY36: $i] :
~ ( element @ SY36 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
( ( ~ ( ( sK2_SY25 != empty_set ) )
| ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV1: $i] :
( ( empty @ ( powerset @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV2: $i] :
( ( ( ~ ( v1_membered @ SV2 ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( powerset @ SV2 ) )
| ( v1_membered @ SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(108,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty @ SV3 ) )
= $true )
| ( ( ~ ! [SY27: $i] :
~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
~ ~ ( ~ ( element @ SY28 @ ( powerset @ SV4 ) )
| ~ ( empty @ SY28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV5: $i,SV13: $i] :
( ( ~ ( element @ SV13 @ ( powerset @ ( powerset @ SV5 ) ) )
| ( ( complements_of_subsets @ SV5 @ ( complements_of_subsets @ SV5 @ SV13 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( element @ SV6 @ ( powerset @ SV14 ) )
| ( subset @ SV6 @ SV14 ) )
| ~ ( ~ ( subset @ SV6 @ SV14 )
| ( element @ SV6 @ ( powerset @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV15 )
| ( element @ SV7 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV8: $i,SV16: $i] :
( ( ~ ( element @ SV16 @ ( powerset @ ( powerset @ SV8 ) ) )
| ( element @ ( complements_of_subsets @ SV8 @ SV16 ) @ ( powerset @ ( powerset @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV9: $i,SV17: $i] :
( ( ~ ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
| ~ ~ ( ~ ( ( SV17 != empty_set ) )
| ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV18: $i,SV10: $i] :
( ( ! [SY37: $i] :
( ~ ~ ( ~ ( in @ SV10 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SY37 ) ) )
| ( element @ SV10 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV11: $i] :
( ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( SV11 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV12: $i] :
( ( ! [SY36: $i] :
~ ( element @ SY36 @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(118,plain,
( ( ~ ( ( sK2_SY25 != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(119,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(120,plain,
! [SV2: $i] :
( ( ( v1_membered @ SV2 )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( powerset @ SV2 ) )
| ( v1_membered @ SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $false )
| ( ( ~ ! [SY27: $i] :
~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(122,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( element @ ( sK3_SY28 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ( empty @ ( sK3_SY28 @ SV4 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(123,plain,
! [SV5: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( powerset @ ( powerset @ SV5 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV5 @ ( complements_of_subsets @ SV5 @ SV13 ) )
= SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( ~ ( element @ SV6 @ ( powerset @ SV14 ) )
| ( subset @ SV6 @ SV14 ) )
| ~ ( ~ ( subset @ SV6 @ SV14 )
| ( element @ SV6 @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV15 ) )
= $true )
| ( ( element @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV8: $i,SV16: $i] :
( ( ( ~ ( element @ SV16 @ ( powerset @ ( powerset @ SV8 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV8 @ SV16 ) @ ( powerset @ ( powerset @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV17 != empty_set ) )
| ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV19: $i,SV18: $i,SV10: $i] :
( ( ~ ~ ( ~ ( in @ SV10 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV19 ) ) )
| ( element @ SV10 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $false )
| ( ( SV11 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(130,plain,
! [SV12: $i] :
( ( ~ ( element @ ( sK4_SY36 @ SV12 ) @ SV12 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[117]) ).
thf(131,plain,
( ( sK2_SY25 != empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(132,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(133,plain,
! [SV2: $i,SV20: $i] :
( ( ( ~ ( element @ SV20 @ ( powerset @ SV2 ) )
| ( v1_membered @ SV20 ) )
= $true )
| ( ( v1_membered @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $true )
| ( ( ~ ! [SY27: $i] :
~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(135,plain,
! [SV4: $i] :
( ( ~ ( ~ ( element @ ( sK3_SY28 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ( empty @ ( sK3_SY28 @ SV4 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(136,plain,
! [SV5: $i,SV13: $i] :
( ( ( element @ SV13 @ ( powerset @ ( powerset @ SV5 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV5 @ ( complements_of_subsets @ SV5 @ SV13 ) )
= SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(137,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( ~ ( element @ SV6 @ ( powerset @ SV14 ) )
| ( subset @ SV6 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(138,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( ~ ( subset @ SV6 @ SV14 )
| ( element @ SV6 @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(139,plain,
! [SV15: $i,SV7: $i] :
( ( ( in @ SV7 @ SV15 )
= $false )
| ( ( element @ SV7 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV8: $i,SV16: $i] :
( ( ( element @ SV16 @ ( powerset @ ( powerset @ SV8 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV8 @ SV16 ) @ ( powerset @ ( powerset @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV9: $i,SV17: $i] :
( ( ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV17 != empty_set ) )
| ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV19: $i,SV18: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( in @ SV10 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV19 ) ) ) )
= $true )
| ( ( element @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV12: $i] :
( ( element @ ( sK4_SY36 @ SV12 ) @ SV12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(144,plain,
( ( sK2_SY25 = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(145,plain,
! [SV2: $i,SV20: $i] :
( ( ( ~ ( element @ SV20 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( v1_membered @ SV20 )
= $true )
| ( ( v1_membered @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV3: $i] :
( ( ( ! [SY27: $i] :
~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ SY27 ) ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV4: $i] :
( ( ~ ( element @ ( sK3_SY28 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ( empty @ ( sK3_SY28 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( element @ SV6 @ ( powerset @ SV14 ) )
| ( subset @ SV6 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV14 )
| ( element @ SV6 @ ( powerset @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(150,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ~ ( ( SV17 != empty_set ) )
| ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV19: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV19 ) ) ) )
= $false )
| ( ( element @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(152,plain,
! [SV2: $i,SV20: $i] :
( ( ( element @ SV20 @ ( powerset @ SV2 ) )
= $false )
| ( ( v1_membered @ SV20 )
= $true )
| ( ( v1_membered @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_SY27 @ SV3 ) @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ ( sK5_SY27 @ SV3 ) ) ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[146]) ).
thf(154,plain,
! [SV4: $i] :
( ( ~ ( element @ ( sK3_SY28 @ SV4 ) @ ( powerset @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(155,plain,
! [SV4: $i] :
( ( ~ ( empty @ ( sK3_SY28 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV14: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( subset @ SV6 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(157,plain,
! [SV14: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV14 ) )
= $true )
| ( ( element @ SV6 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(158,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ( SV17 != empty_set ) )
| ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set ) )
= $true )
| ( ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(159,plain,
! [SV19: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( element @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(160,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_SY27 @ SV3 ) @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ ( sK5_SY27 @ SV3 ) ) ) )
= $true )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(161,plain,
! [SV4: $i] :
( ( element @ ( sK3_SY28 @ SV4 ) @ ( powerset @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(162,plain,
! [SV4: $i] :
( ( empty @ ( sK3_SY28 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(163,plain,
! [SV14: $i,SV6: $i] :
( ( ( element @ SV6 @ ( powerset @ SV14 ) )
= $false )
| ( ( subset @ SV6 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(164,plain,
! [SV14: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV14 )
= $false )
| ( ( element @ SV6 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(165,plain,
! [SV9: $i,SV17: $i] :
( ( ( ~ ( ( SV17 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set )
= $true )
| ( ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(166,plain,
! [SV19: $i,SV18: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV18 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( element @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(167,plain,
! [SV3: $i] :
( ( ( ~ ( element @ ( sK5_SY27 @ SV3 ) @ ( powerset @ SV3 ) )
| ~ ~ ( empty @ ( sK5_SY27 @ SV3 ) ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(168,plain,
! [SV9: $i,SV17: $i] :
( ( ( SV17 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set )
= $true )
| ( ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(169,plain,
! [SV19: $i,SV18: $i,SV10: $i] :
( ( ( in @ SV10 @ SV18 )
= $false )
| ( ( ~ ( element @ SV18 @ ( powerset @ SV19 ) ) )
= $true )
| ( ( element @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(170,plain,
! [SV3: $i] :
( ( ( ~ ( element @ ( sK5_SY27 @ SV3 ) @ ( powerset @ SV3 ) ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(171,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty @ ( sK5_SY27 @ SV3 ) ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(172,plain,
! [SV9: $i,SV17: $i] :
( ( ( SV17 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV9 @ SV17 )
!= empty_set )
= $true )
| ( ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(173,plain,
! [SV10: $i,SV19: $i,SV18: $i] :
( ( ( element @ SV18 @ ( powerset @ SV19 ) )
= $false )
| ( ( in @ SV10 @ SV18 )
= $false )
| ( ( element @ SV10 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(174,plain,
! [SV3: $i] :
( ( ( element @ ( sK5_SY27 @ SV3 ) @ ( powerset @ SV3 ) )
= $true )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(175,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ ( sK5_SY27 @ SV3 ) ) )
= $true )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(176,plain,
! [SV17: $i,SV9: $i] :
( ( ( ( complements_of_subsets @ SV9 @ SV17 )
= empty_set )
= $false )
| ( ( SV17 = empty_set )
= $true )
| ( ( element @ SV17 @ ( powerset @ ( powerset @ SV9 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV3: $i] :
( ( ( empty @ ( sK5_SY27 @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(178,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,177,176,174,173,164,163,162,161,152,144,143,140,139,136,132,129,106,79,68,66]) ).
thf(179,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(180,plain,
$true = $true,
inference(copy,[status(thm)],[54]) ).
thf(181,plain,
$true = $true,
inference(copy,[status(thm)],[53]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(183,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(184,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(185,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(187,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(188,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(191,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(192,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(193,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(194,plain,
( ( element @ sK2_SY25 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(195,plain,
( ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set )
& ( sK2_SY25 = empty_set ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(196,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ~ ( ~ ( ( SX1 != empty_set ) )
| ( ( complements_of_subsets @ SX0 @ SX1 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(197,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(198,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)],[190]) ).
thf(199,plain,
( ( ! [SX0: $i] :
( ~ ( v1_membered @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(200,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(201,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(202,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(203,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( ( complements_of_subsets @ SX0 @ ( complements_of_subsets @ SX0 @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(204,plain,
( ( ~ ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set ) )
| ( sK2_SY25 != empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(205,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(206,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(207,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( element @ ( complements_of_subsets @ SX0 @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(208,plain,
! [SV21: $i] :
( ( ~ ( empty @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(209,plain,
! [SV22: $i] :
( ( ! [SY38: $i] :
( ~ ( element @ SY38 @ ( powerset @ ( powerset @ SV22 ) ) )
| ~ ~ ( ~ ( ( SY38 != empty_set ) )
| ( ( complements_of_subsets @ SV22 @ SY38 )
!= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(210,plain,
! [SV23: $i] :
( ( ~ ( empty @ SV23 )
| ( SV23 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(211,plain,
! [SV24: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ~ ( element @ SV24 @ ( powerset @ SY39 ) )
| ( subset @ SV24 @ SY39 ) )
| ~ ( ~ ( subset @ SV24 @ SY39 )
| ( element @ SV24 @ ( powerset @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(212,plain,
! [SV25: $i] :
( ( ~ ( v1_membered @ SV25 )
| ! [SY40: $i] :
( ~ ( element @ SY40 @ ( powerset @ SV25 ) )
| ( v1_membered @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(213,plain,
! [SV26: $i] :
( ( ~ ! [SY41: $i] :
~ ( element @ SY41 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(214,plain,
! [SV27: $i] :
( ( ~ ~ ( empty @ SV27 )
| ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(215,plain,
! [SV28: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ~ ( ~ ( in @ SV28 @ SY43 )
| ~ ( element @ SY43 @ ( powerset @ SY44 ) ) )
| ( element @ SV28 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(216,plain,
! [SV29: $i] :
( ( ! [SY45: $i] :
( ~ ( element @ SY45 @ ( powerset @ ( powerset @ SV29 ) ) )
| ( ( complements_of_subsets @ SV29 @ ( complements_of_subsets @ SV29 @ SY45 ) )
= SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(217,plain,
( ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set ) )
| ( sK2_SY25 != empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(218,plain,
! [SV30: $i] :
( ( ! [SY46: $i] :
( ~ ( in @ SV30 @ SY46 )
| ( element @ SV30 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(219,plain,
! [SV31: $i] :
( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ SV31 ) )
| ~ ( empty @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(220,plain,
! [SV32: $i] :
( ( ! [SY48: $i] :
( ~ ( element @ SY48 @ ( powerset @ ( powerset @ SV32 ) ) )
| ( element @ ( complements_of_subsets @ SV32 @ SY48 ) @ ( powerset @ ( powerset @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(221,plain,
! [SV21: $i] :
( ( empty @ ( powerset @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(222,plain,
! [SV22: $i,SV33: $i] :
( ( ~ ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
| ~ ~ ( ~ ( ( SV33 != empty_set ) )
| ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(223,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $true )
| ( ( SV23 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(224,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( element @ SV24 @ ( powerset @ SV34 ) )
| ( subset @ SV24 @ SV34 ) )
| ~ ( ~ ( subset @ SV24 @ SV34 )
| ( element @ SV24 @ ( powerset @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(225,plain,
! [SV25: $i] :
( ( ( ~ ( v1_membered @ SV25 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ( element @ SY40 @ ( powerset @ SV25 ) )
| ( v1_membered @ SY40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(226,plain,
! [SV26: $i] :
( ( ! [SY41: $i] :
~ ( element @ SY41 @ SV26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(227,plain,
! [SV27: $i] :
( ( ( ~ ~ ( empty @ SV27 ) )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(228,plain,
! [SV35: $i,SV28: $i] :
( ( ! [SY49: $i] :
( ~ ~ ( ~ ( in @ SV28 @ SV35 )
| ~ ( element @ SV35 @ ( powerset @ SY49 ) ) )
| ( element @ SV28 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(229,plain,
! [SV29: $i,SV36: $i] :
( ( ~ ( element @ SV36 @ ( powerset @ ( powerset @ SV29 ) ) )
| ( ( complements_of_subsets @ SV29 @ ( complements_of_subsets @ SV29 @ SV36 ) )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(230,plain,
( ( ~ ( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(231,plain,
( ( sK2_SY25 != empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(232,plain,
! [SV37: $i,SV30: $i] :
( ( ~ ( in @ SV30 @ SV37 )
| ( element @ SV30 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(233,plain,
! [SV31: $i] :
( ( ! [SY47: $i] :
~ ~ ( ~ ( element @ SY47 @ ( powerset @ SV31 ) )
| ~ ( empty @ SY47 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(234,plain,
! [SV32: $i,SV38: $i] :
( ( ~ ( element @ SV38 @ ( powerset @ ( powerset @ SV32 ) ) )
| ( element @ ( complements_of_subsets @ SV32 @ SV38 ) @ ( powerset @ ( powerset @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(235,plain,
! [SV22: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( SV33 != empty_set ) )
| ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(236,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $false )
| ( ( SV23 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(237,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( ~ ( element @ SV24 @ ( powerset @ SV34 ) )
| ( subset @ SV24 @ SV34 ) )
| ~ ( ~ ( subset @ SV24 @ SV34 )
| ( element @ SV24 @ ( powerset @ SV34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(238,plain,
! [SV25: $i] :
( ( ( v1_membered @ SV25 )
= $false )
| ( ( ! [SY40: $i] :
( ~ ( element @ SY40 @ ( powerset @ SV25 ) )
| ( v1_membered @ SY40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(239,plain,
! [SV26: $i] :
( ( ~ ( element @ ( sK6_SY41 @ SV26 ) @ SV26 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[226]) ).
thf(240,plain,
! [SV27: $i] :
( ( ( ~ ( empty @ SV27 ) )
= $false )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(241,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ~ ~ ( ~ ( in @ SV28 @ SV35 )
| ~ ( element @ SV35 @ ( powerset @ SV39 ) ) )
| ( element @ SV28 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(242,plain,
! [SV29: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( powerset @ ( powerset @ SV29 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV29 @ ( complements_of_subsets @ SV29 @ SV36 ) )
= SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(243,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
!= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(244,plain,
( ( sK2_SY25 = empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(245,plain,
! [SV37: $i,SV30: $i] :
( ( ( ~ ( in @ SV30 @ SV37 ) )
= $true )
| ( ( element @ SV30 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(246,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ( element @ ( sK7_SY47 @ SV31 ) @ ( powerset @ SV31 ) )
| ~ ( empty @ ( sK7_SY47 @ SV31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[233]) ).
thf(247,plain,
! [SV32: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( powerset @ ( powerset @ SV32 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV32 @ SV38 ) @ ( powerset @ ( powerset @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(248,plain,
! [SV22: $i,SV33: $i] :
( ( ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( SV33 != empty_set ) )
| ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(249,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( ~ ( element @ SV24 @ ( powerset @ SV34 ) )
| ( subset @ SV24 @ SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(250,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( ~ ( subset @ SV24 @ SV34 )
| ( element @ SV24 @ ( powerset @ SV34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(251,plain,
! [SV25: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ SV25 ) )
| ( v1_membered @ SV40 ) )
= $true )
| ( ( v1_membered @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(252,plain,
! [SV26: $i] :
( ( element @ ( sK6_SY41 @ SV26 ) @ SV26 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(253,plain,
! [SV27: $i] :
( ( ( empty @ SV27 )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(254,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( in @ SV28 @ SV35 )
| ~ ( element @ SV35 @ ( powerset @ SV39 ) ) ) )
= $true )
| ( ( element @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(255,plain,
! [SV29: $i,SV36: $i] :
( ( ( element @ SV36 @ ( powerset @ ( powerset @ SV29 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV29 @ ( complements_of_subsets @ SV29 @ SV36 ) )
= SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(256,plain,
( ( ( complements_of_subsets @ sK1_A @ sK2_SY25 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(257,plain,
! [SV37: $i,SV30: $i] :
( ( ( in @ SV30 @ SV37 )
= $false )
| ( ( element @ SV30 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(258,plain,
! [SV31: $i] :
( ( ~ ( ~ ( element @ ( sK7_SY47 @ SV31 ) @ ( powerset @ SV31 ) )
| ~ ( empty @ ( sK7_SY47 @ SV31 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(259,plain,
! [SV32: $i,SV38: $i] :
( ( ( element @ SV38 @ ( powerset @ ( powerset @ SV32 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV32 @ SV38 ) @ ( powerset @ ( powerset @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(260,plain,
! [SV22: $i,SV33: $i] :
( ( ( ~ ( ~ ( ( SV33 != empty_set ) )
| ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set ) ) )
= $false )
| ( ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( element @ SV24 @ ( powerset @ SV34 ) )
| ( subset @ SV24 @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(262,plain,
! [SV34: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV34 )
| ( element @ SV24 @ ( powerset @ SV34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(263,plain,
! [SV25: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( v1_membered @ SV40 )
= $true )
| ( ( v1_membered @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(264,plain,
! [SV27: $i] :
( ( ( ! [SY42: $i] :
~ ~ ( ~ ( element @ SY42 @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ SY42 ) ) )
= $false )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ( ~ ( in @ SV28 @ SV35 )
| ~ ( element @ SV35 @ ( powerset @ SV39 ) ) ) )
= $false )
| ( ( element @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV31: $i] :
( ( ~ ( element @ ( sK7_SY47 @ SV31 ) @ ( powerset @ SV31 ) )
| ~ ( empty @ ( sK7_SY47 @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV22: $i,SV33: $i] :
( ( ( ~ ( ( SV33 != empty_set ) )
| ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set ) )
= $true )
| ( ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(268,plain,
! [SV34: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( powerset @ SV34 ) ) )
= $true )
| ( ( subset @ SV24 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(269,plain,
! [SV34: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV34 ) )
= $true )
| ( ( element @ SV24 @ ( powerset @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(270,plain,
! [SV25: $i,SV40: $i] :
( ( ( element @ SV40 @ ( powerset @ SV25 ) )
= $false )
| ( ( v1_membered @ SV40 )
= $true )
| ( ( v1_membered @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(271,plain,
! [SV27: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_SY42 @ SV27 ) @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ ( sK8_SY42 @ SV27 ) ) ) )
= $false )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[264]) ).
thf(272,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV35 )
| ~ ( element @ SV35 @ ( powerset @ SV39 ) ) )
= $true )
| ( ( element @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(273,plain,
! [SV31: $i] :
( ( ~ ( element @ ( sK7_SY47 @ SV31 ) @ ( powerset @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(274,plain,
! [SV31: $i] :
( ( ~ ( empty @ ( sK7_SY47 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(275,plain,
! [SV22: $i,SV33: $i] :
( ( ( ~ ( ( SV33 != empty_set ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set )
= $true )
| ( ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(276,plain,
! [SV34: $i,SV24: $i] :
( ( ( element @ SV24 @ ( powerset @ SV34 ) )
= $false )
| ( ( subset @ SV24 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV34: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV34 )
= $false )
| ( ( element @ SV24 @ ( powerset @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(278,plain,
! [SV27: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_SY42 @ SV27 ) @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ ( sK8_SY42 @ SV27 ) ) ) )
= $true )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(279,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV35 ) )
= $true )
| ( ( ~ ( element @ SV35 @ ( powerset @ SV39 ) ) )
= $true )
| ( ( element @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(280,plain,
! [SV31: $i] :
( ( element @ ( sK7_SY47 @ SV31 ) @ ( powerset @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(281,plain,
! [SV31: $i] :
( ( empty @ ( sK7_SY47 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(282,plain,
! [SV22: $i,SV33: $i] :
( ( ( SV33 != empty_set )
= $false )
| ( ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set )
= $true )
| ( ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(283,plain,
! [SV27: $i] :
( ( ( ~ ( element @ ( sK8_SY42 @ SV27 ) @ ( powerset @ SV27 ) )
| ~ ~ ( empty @ ( sK8_SY42 @ SV27 ) ) )
= $false )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(284,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( in @ SV28 @ SV35 )
= $false )
| ( ( ~ ( element @ SV35 @ ( powerset @ SV39 ) ) )
= $true )
| ( ( element @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(285,plain,
! [SV22: $i,SV33: $i] :
( ( ( SV33 = empty_set )
= $true )
| ( ( ( complements_of_subsets @ SV22 @ SV33 )
!= empty_set )
= $true )
| ( ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(286,plain,
! [SV27: $i] :
( ( ( ~ ( element @ ( sK8_SY42 @ SV27 ) @ ( powerset @ SV27 ) ) )
= $false )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(287,plain,
! [SV27: $i] :
( ( ( ~ ~ ( empty @ ( sK8_SY42 @ SV27 ) ) )
= $false )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(288,plain,
! [SV28: $i,SV39: $i,SV35: $i] :
( ( ( element @ SV35 @ ( powerset @ SV39 ) )
= $false )
| ( ( in @ SV28 @ SV35 )
= $false )
| ( ( element @ SV28 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(289,plain,
! [SV33: $i,SV22: $i] :
( ( ( ( complements_of_subsets @ SV22 @ SV33 )
= empty_set )
= $false )
| ( ( SV33 = empty_set )
= $true )
| ( ( element @ SV33 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(290,plain,
! [SV27: $i] :
( ( ( element @ ( sK8_SY42 @ SV27 ) @ ( powerset @ SV27 ) )
= $true )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(291,plain,
! [SV27: $i] :
( ( ( ~ ( empty @ ( sK8_SY42 @ SV27 ) ) )
= $true )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(292,plain,
! [SV27: $i] :
( ( ( empty @ ( sK8_SY42 @ SV27 ) )
= $false )
| ( ( empty @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(293,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[180,292,290,289,288,281,280,277,276,270,259,257,256,255,252,244,236,221,194,183,181]) ).
thf(294,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[293,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n020.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 15:14:51 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.28
% 0.57/0.28 No.of.Axioms: 15
% 0.57/0.28
% 0.57/0.28 Length.of.Defs: 0
% 0.57/0.28
% 0.57/0.28 Contains.Choice.Funs: false
% 0.57/0.28 ......
% 0.57/0.28
% 0.57/0.28 ********************************
% 0.57/0.28 * All subproblems solved! *
% 0.57/0.28 ********************************
% 0.57/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,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:293,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.28
% 0.57/0.28 %**** Beginning of derivation protocol ****
% 0.57/0.28 % SZS output start CNFRefutation
% See solution above
% 0.57/0.28
% 0.57/0.28 %**** End of derivation protocol ****
% 0.57/0.28 %**** no. of clauses in derivation: 272 ****
% 0.57/0.28 %**** clause counter: 293 ****
% 0.57/0.28
% 0.57/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,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:293,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------