TSTP Solution File: SET611+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:03:27 EDT 2022
% Result : Theorem 31.99s 32.36s
% Output : CNFRefutation 32.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 415 ( 247 unt; 12 typ; 0 def)
% Number of atoms : 2453 ( 819 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 4853 ( 972 ~; 806 |; 49 &;2997 @)
% ( 21 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 1109 ( 0 ^1109 !; 0 ?;1109 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i ).
thf(tp_sK4_D,type,
sK4_D: $i > $i > $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
thf(2,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(6,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(7,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(8,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(9,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
thf(10,axiom,
! [B: $i,C: $i] :
( ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_equal) ).
thf(11,conjecture,
! [B: $i,C: $i] :
( ( ( intersection @ B @ C )
= empty_set )
<=> ( ( difference @ B @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th84) ).
thf(12,negated_conjecture,
( ( ! [B: $i,C: $i] :
( ( ( intersection @ B @ C )
= empty_set )
<=> ( ( difference @ B @ C )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
( ( ! [B: $i,C: $i] :
( ( ( intersection @ B @ C )
= empty_set )
<=> ( ( difference @ B @ C )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ! [B: $i,C: $i] :
( ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [SY25: $i] :
( ( ( intersection @ sK1_B @ SY25 )
= empty_set )
<=> ( ( difference @ sK1_B @ SY25 )
= sK1_B ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(25,plain,
( ( ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set )
<=> ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(26,plain,
( ( ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set )
=> ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(27,plain,
( ( ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B )
=> ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(28,plain,
( ( ~ ( ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set )
=> ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B )
=> ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(30,plain,
( ( ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set )
& ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(31,plain,
( ( ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B )
& ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(32,plain,
( ( ! [B: $i] :
( ( member @ ( sK3_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(33,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK4_D @ C @ B ) @ B )
& ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(34,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK5_D @ C @ B ) @ B )
| ~ ( member @ ( sK5_D @ C @ B ) @ C ) )
& ( ( member @ ( sK5_D @ C @ B ) @ B )
| ( member @ ( sK5_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(35,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ C @ B )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(36,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C )
| ( member @ D @ ( difference @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ~ ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(37,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C )
| ( member @ D @ ( intersection @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(38,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK6_D @ C @ B ) @ B )
| ~ ( member @ ( sK6_D @ C @ B ) @ C ) )
& ( ( member @ ( sK6_D @ C @ B ) @ B )
| ( member @ ( sK6_D @ C @ B ) @ C ) ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(39,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK6_D @ C @ B ) @ B )
| ~ ( member @ ( sK6_D @ C @ B ) @ C ) )
& ( ( member @ ( sK6_D @ C @ B ) @ B )
| ( member @ ( sK6_D @ C @ B ) @ C ) ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C )
| ( member @ D @ ( intersection @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(41,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C )
| ( member @ D @ ( difference @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ~ ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(42,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(43,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ C @ B )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(44,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK5_D @ C @ B ) @ B )
| ~ ( member @ ( sK5_D @ C @ B ) @ C ) )
& ( ( member @ ( sK5_D @ C @ B ) @ B )
| ( member @ ( sK5_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(46,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK4_D @ C @ B ) @ B )
& ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(47,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(48,plain,
( ( ! [B: $i] :
( ( member @ ( sK3_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set )
& ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(52,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(53,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( difference @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ~ ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(54,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(55,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(56,plain,
( ( ~ ( ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set )
| ~ ( ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(57,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(58,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(59,plain,
! [SV2: $i] :
( ( ! [SY26: $i] :
( ( intersection @ SV2 @ SY26 )
= ( intersection @ SY26 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV3: $i] :
( ( subset @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV4: $i] :
( ( ! [SY27: $i] :
( ~ ( ~ ( ~ ( member @ ( sK6_D @ SY27 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK6_D @ SY27 @ SV4 ) @ SY27 ) )
| ~ ( ( member @ ( sK6_D @ SY27 @ SV4 ) @ SV4 )
| ( member @ ( sK6_D @ SY27 @ SV4 ) @ SY27 ) ) )
| ( SV4 = SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(63,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ SV5 )
| ( member @ SY29 @ SY28 )
| ( member @ SY29 @ ( difference @ SV5 @ SY28 ) ) )
| ~ ~ ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ ( difference @ SV5 @ SY30 ) )
| ( member @ SY31 @ SV5 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV5 @ SY32 ) )
| ~ ( member @ SY33 @ SY32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(65,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(66,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(67,plain,
( ( ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set )
| ~ ( ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ SV6 )
| ~ ( member @ SY35 @ SY34 )
| ( member @ SY35 @ ( intersection @ SV6 @ SY34 ) ) )
| ~ ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( member @ SY37 @ ( intersection @ SV6 @ SY36 ) )
| ( member @ SY37 @ SV6 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SY39 @ ( intersection @ SV6 @ SY38 ) )
| ( member @ SY39 @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV7: $i,SV2: $i] :
( ( ( intersection @ SV2 @ SV7 )
= ( intersection @ SV7 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(71,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(72,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(73,plain,
! [SV4: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) )
| ~ ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) ) )
| ( SV4 = SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(74,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(75,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(76,plain,
! [SV5: $i] :
( ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ SV5 )
| ( member @ SY29 @ SY28 )
| ( member @ SY29 @ ( difference @ SV5 @ SY28 ) ) )
| ~ ~ ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ ( difference @ SV5 @ SY30 ) )
| ( member @ SY31 @ SV5 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV5 @ SY32 ) )
| ~ ( member @ SY33 @ SY32 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(77,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(78,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(79,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(80,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(81,plain,
( ( ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(82,plain,
( ( ~ ( ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(83,plain,
! [SV6: $i] :
( ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ SV6 )
| ~ ( member @ SY35 @ SY34 )
| ( member @ SY35 @ ( intersection @ SV6 @ SY34 ) ) )
| ~ ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( member @ SY37 @ ( intersection @ SV6 @ SY36 ) )
| ( member @ SY37 @ SV6 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SY39 @ ( intersection @ SV6 @ SY38 ) )
| ( member @ SY39 @ SY38 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(85,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(86,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) )
| ~ ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) ) ) )
= $true )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(89,plain,
! [SV5: $i] :
( ( ~ ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ SV5 )
| ( member @ SY29 @ SY28 )
| ( member @ SY29 @ ( difference @ SV5 @ SY28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(90,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ ( difference @ SV5 @ SY30 ) )
| ( member @ SY31 @ SV5 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV5 @ SY32 ) )
| ~ ( member @ SY33 @ SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(93,plain,
( ( ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(95,plain,
( ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(96,plain,
( ( ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(97,plain,
! [SV6: $i] :
( ( ~ ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ SV6 )
| ~ ( member @ SY35 @ SY34 )
| ( member @ SY35 @ ( intersection @ SV6 @ SY34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(98,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( member @ SY37 @ ( intersection @ SV6 @ SY36 ) )
| ( member @ SY37 @ SV6 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SY39 @ ( intersection @ SV6 @ SY38 ) )
| ( member @ SY39 @ SY38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(99,plain,
! [SV9: $i] :
( ( ! [SY40: $i] :
( ~ ( subset @ SV9 @ SY40 )
| ~ ( subset @ SY40 @ SV9 )
| ( SV9 = SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) )
| ~ ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) ) )
= $false )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV10: $i] :
( ( ! [SY41: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SY41 @ SV10 ) @ SV10 )
| ~ ~ ( member @ ( sK4_D @ SY41 @ SV10 ) @ SY41 ) )
| ( subset @ SV10 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV11: $i] :
( ( ! [SY42: $i] :
( ~ ( subset @ SV11 @ SY42 )
| ! [SY43: $i] :
( ~ ( member @ SY43 @ SV11 )
| ( member @ SY43 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV5: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ( member @ SY29 @ SV5 )
| ( member @ SY29 @ SY28 )
| ( member @ SY29 @ ( difference @ SV5 @ SY28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(105,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ ( difference @ SV5 @ SY30 ) )
| ( member @ SY31 @ SV5 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV5 @ SY32 ) )
| ~ ( member @ SY33 @ SY32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(106,plain,
! [SV12: $i] :
( ( ! [SY44: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SY44 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK5_D @ SY44 @ SV12 ) @ SY44 ) )
| ~ ( ( member @ ( sK5_D @ SY44 @ SV12 ) @ SV12 )
| ( member @ ( sK5_D @ SY44 @ SV12 ) @ SY44 ) ) )
| ( SV12 = SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV13: $i] :
( ( ! [SY45: $i] :
( ( SV13 != SY45 )
| ~ ( ~ ! [SY46: $i] :
( ~ ( member @ SY46 @ SV13 )
| ( member @ SY46 @ SY45 ) )
| ~ ! [SY47: $i] :
( ~ ( member @ SY47 @ SY45 )
| ( member @ SY47 @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV14: $i] :
( ( ( member @ ( sK3_C @ SV14 ) @ SV14 )
| ( empty @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV15: $i] :
( ( ~ ( empty @ SV15 )
| ! [SY48: $i] :
~ ( member @ SY48 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
( ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(111,plain,
! [SV6: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( member @ SY35 @ SV6 )
| ~ ( member @ SY35 @ SY34 )
| ( member @ SY35 @ ( intersection @ SV6 @ SY34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(112,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( member @ SY37 @ ( intersection @ SV6 @ SY36 ) )
| ( member @ SY37 @ SV6 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SY39 @ ( intersection @ SV6 @ SY38 ) )
| ( member @ SY39 @ SY38 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(113,plain,
! [SV16: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV16 )
| ~ ( subset @ SV16 @ SV9 )
| ( SV9 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(114,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(115,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(116,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) ) )
= $false )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(117,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) ) )
= $false )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(118,plain,
! [SV10: $i,SV17: $i] :
( ( ~ ( ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV10 )
| ~ ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV17 ) )
| ( subset @ SV10 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV18 )
| ! [SY49: $i] :
( ~ ( member @ SY49 @ SV11 )
| ( member @ SY49 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV19: $i,SV5: $i] :
( ( ! [SY50: $i] :
( ~ ( member @ SY50 @ SV5 )
| ( member @ SY50 @ SV19 )
| ( member @ SY50 @ ( difference @ SV5 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV5: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ ( difference @ SV5 @ SY30 ) )
| ( member @ SY31 @ SV5 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV5 @ SY32 ) )
| ~ ( member @ SY33 @ SY32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV12: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) )
| ~ ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) ) )
| ( SV12 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV21: $i,SV13: $i] :
( ( ( SV13 != SV21 )
| ~ ( ~ ! [SY51: $i] :
( ~ ( member @ SY51 @ SV13 )
| ( member @ SY51 @ SV21 ) )
| ~ ! [SY52: $i] :
( ~ ( member @ SY52 @ SV21 )
| ( member @ SY52 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(124,plain,
! [SV14: $i] :
( ( ( member @ ( sK3_C @ SV14 ) @ SV14 )
= $true )
| ( ( empty @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( ! [SY48: $i] :
~ ( member @ SY48 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY53: $i] :
( ~ ( member @ SY53 @ SV6 )
| ~ ( member @ SY53 @ SV22 )
| ( member @ SY53 @ ( intersection @ SV6 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV6: $i] :
( ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( member @ SY37 @ ( intersection @ SV6 @ SY36 ) )
| ( member @ SY37 @ SV6 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SY39 @ ( intersection @ SV6 @ SY38 ) )
| ( member @ SY39 @ SY38 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV16 )
| ~ ( subset @ SV16 @ SV9 ) )
= $true )
| ( ( SV9 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(131,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(132,plain,
! [SV4: $i,SV8: $i] :
( ( ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
| ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(133,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV10 )
| ~ ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV17 ) ) )
= $true )
| ( ( subset @ SV10 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(134,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV18 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( member @ SY49 @ SV11 )
| ( member @ SY49 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(135,plain,
! [SV19: $i,SV5: $i,SV23: $i] :
( ( ~ ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV19 )
| ( member @ SV23 @ ( difference @ SV5 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(136,plain,
! [SV5: $i] :
( ( ~ ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ ( difference @ SV5 @ SY30 ) )
| ( member @ SY31 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(137,plain,
! [SV5: $i] :
( ( ~ ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV5 @ SY32 ) )
| ~ ( member @ SY33 @ SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(138,plain,
! [SV12: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) )
| ~ ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) ) ) )
= $true )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV21: $i,SV13: $i] :
( ( ( ( SV13 != SV21 ) )
= $true )
| ( ( ~ ( ~ ! [SY51: $i] :
( ~ ( member @ SY51 @ SV13 )
| ( member @ SY51 @ SV21 ) )
| ~ ! [SY52: $i] :
( ~ ( member @ SY52 @ SV21 )
| ( member @ SY52 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( ! [SY48: $i] :
~ ( member @ SY48 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(141,plain,
! [SV22: $i,SV6: $i,SV24: $i] :
( ( ~ ( member @ SV24 @ SV6 )
| ~ ( member @ SV24 @ SV22 )
| ( member @ SV24 @ ( intersection @ SV6 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(142,plain,
! [SV6: $i] :
( ( ~ ! [SY36: $i,SY37: $i] :
( ~ ( member @ SY37 @ ( intersection @ SV6 @ SY36 ) )
| ( member @ SY37 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(143,plain,
! [SV6: $i] :
( ( ~ ! [SY38: $i,SY39: $i] :
( ~ ( member @ SY39 @ ( intersection @ SV6 @ SY38 ) )
| ( member @ SY39 @ SY38 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(144,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV16 ) )
= $true )
| ( ( ~ ( subset @ SV16 @ SV9 ) )
= $true )
| ( ( SV9 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV25: $i] :
( ( ! [SY54: $i] :
( ( SV25 != SY54 )
| ( subset @ SV25 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(146,plain,
! [SV26: $i] :
( ( ! [SY55: $i] :
( ( SV26 != SY55 )
| ( subset @ SY55 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(147,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 ) )
= $true )
| ( ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(148,plain,
! [SV4: $i,SV8: $i] :
( ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
= $true )
| ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 )
= $true )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(149,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV10 )
| ~ ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV17 ) )
= $false )
| ( ( subset @ SV10 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(150,plain,
! [SV18: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV18 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( member @ SY49 @ SV11 )
| ( member @ SY49 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV19: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV5 )
| ( member @ SV23 @ SV19 ) )
= $true )
| ( ( member @ SV23 @ ( difference @ SV5 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV5: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( member @ SY31 @ ( difference @ SV5 @ SY30 ) )
| ( member @ SY31 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(153,plain,
! [SV5: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ( member @ SY33 @ ( difference @ SV5 @ SY32 ) )
| ~ ( member @ SY33 @ SY32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(154,plain,
! [SV12: $i,SV20: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) )
| ~ ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) ) )
= $false )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV21: $i,SV13: $i] :
( ( ( SV13 = SV21 )
= $false )
| ( ( ~ ( ~ ! [SY51: $i] :
( ~ ( member @ SY51 @ SV13 )
| ( member @ SY51 @ SV21 ) )
| ~ ! [SY52: $i] :
( ~ ( member @ SY52 @ SV21 )
| ( member @ SY52 @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV15: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV22: $i,SV6: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV6 )
| ~ ( member @ SV24 @ SV22 ) )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV6: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( member @ SY37 @ ( intersection @ SV6 @ SY36 ) )
| ( member @ SY37 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(159,plain,
! [SV6: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ( member @ SY39 @ ( intersection @ SV6 @ SY38 ) )
| ( member @ SY39 @ SY38 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(160,plain,
! [SV16: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV16 )
= $false )
| ( ( ~ ( subset @ SV16 @ SV9 ) )
= $true )
| ( ( SV9 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(161,plain,
! [SV28: $i,SV25: $i] :
( ( ( SV25 != SV28 )
| ( subset @ SV25 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(162,plain,
! [SV29: $i,SV26: $i] :
( ( ( SV26 != SV29 )
| ( subset @ SV29 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(163,plain,
! [SV4: $i,SV8: $i] :
( ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
= $false )
| ( ( ~ ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 ) )
= $true )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV10 ) )
= $false )
| ( ( subset @ SV10 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(165,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV17 ) )
= $false )
| ( ( subset @ SV10 @ SV17 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(166,plain,
! [SV18: $i,SV11: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ SV11 )
| ( member @ SV30 @ SV18 ) )
= $true )
| ( ( subset @ SV11 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(167,plain,
! [SV19: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( member @ SV23 @ SV5 ) )
= $true )
| ( ( member @ SV23 @ SV19 )
= $true )
| ( ( member @ SV23 @ ( difference @ SV5 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(168,plain,
! [SV31: $i,SV5: $i] :
( ( ! [SY56: $i] :
( ~ ( member @ SY56 @ ( difference @ SV5 @ SV31 ) )
| ( member @ SY56 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV32: $i,SV5: $i] :
( ( ! [SY57: $i] :
( ~ ( member @ SY57 @ ( difference @ SV5 @ SV32 ) )
| ~ ( member @ SY57 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV12: $i,SV20: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) ) )
= $false )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(171,plain,
! [SV12: $i,SV20: $i] :
( ( ( ~ ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) ) )
= $false )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(172,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ! [SY51: $i] :
( ~ ( member @ SY51 @ SV13 )
| ( member @ SY51 @ SV21 ) )
| ~ ! [SY52: $i] :
( ~ ( member @ SY52 @ SV21 )
| ( member @ SY52 @ SV13 ) ) )
= $false )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(173,plain,
! [SV15: $i,SV27: $i] :
( ( ( member @ SV27 @ SV15 )
= $false )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(174,plain,
! [SV22: $i,SV6: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV6 ) )
= $true )
| ( ( ~ ( member @ SV24 @ SV22 ) )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(175,plain,
! [SV33: $i,SV6: $i] :
( ( ! [SY58: $i] :
( ~ ( member @ SY58 @ ( intersection @ SV6 @ SV33 ) )
| ( member @ SY58 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(176,plain,
! [SV34: $i,SV6: $i] :
( ( ! [SY59: $i] :
( ~ ( member @ SY59 @ ( intersection @ SV6 @ SV34 ) )
| ( member @ SY59 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(177,plain,
! [SV9: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV9 )
= $false )
| ( ( subset @ SV9 @ SV16 )
= $false )
| ( ( SV9 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(178,plain,
! [SV28: $i,SV25: $i] :
( ( ( ( SV25 != SV28 ) )
= $true )
| ( ( subset @ SV25 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV29: $i,SV26: $i] :
( ( ( ( SV26 != SV29 ) )
= $true )
| ( ( subset @ SV29 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV4: $i,SV8: $i] :
( ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV8 )
= $false )
| ( ( member @ ( sK6_D @ SV8 @ SV4 ) @ SV4 )
= $false )
| ( ( SV4 = SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV10: $i,SV17: $i] :
( ( ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV10 )
= $true )
| ( ( subset @ SV10 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(182,plain,
! [SV10: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV17 ) )
= $true )
| ( ( subset @ SV10 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(183,plain,
! [SV18: $i,SV11: $i,SV30: $i] :
( ( ( ~ ( member @ SV30 @ SV11 ) )
= $true )
| ( ( member @ SV30 @ SV18 )
= $true )
| ( ( subset @ SV11 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(184,plain,
! [SV19: $i,SV5: $i,SV23: $i] :
( ( ( member @ SV23 @ SV5 )
= $false )
| ( ( member @ SV23 @ SV19 )
= $true )
| ( ( member @ SV23 @ ( difference @ SV5 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV31: $i,SV5: $i,SV35: $i] :
( ( ~ ( member @ SV35 @ ( difference @ SV5 @ SV31 ) )
| ( member @ SV35 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV32: $i,SV5: $i,SV36: $i] :
( ( ~ ( member @ SV36 @ ( difference @ SV5 @ SV32 ) )
| ~ ( member @ SV36 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(187,plain,
! [SV12: $i,SV20: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) )
= $true )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(188,plain,
! [SV12: $i,SV20: $i] :
( ( ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
| ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) )
= $true )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(189,plain,
! [SV21: $i,SV13: $i] :
( ( ( ~ ! [SY51: $i] :
( ~ ( member @ SY51 @ SV13 )
| ( member @ SY51 @ SV21 ) ) )
= $false )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(190,plain,
! [SV13: $i,SV21: $i] :
( ( ( ~ ! [SY52: $i] :
( ~ ( member @ SY52 @ SV21 )
| ( member @ SY52 @ SV13 ) ) )
= $false )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(191,plain,
! [SV22: $i,SV6: $i,SV24: $i] :
( ( ( member @ SV24 @ SV6 )
= $false )
| ( ( ~ ( member @ SV24 @ SV22 ) )
= $true )
| ( ( member @ SV24 @ ( intersection @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(192,plain,
! [SV33: $i,SV6: $i,SV37: $i] :
( ( ~ ( member @ SV37 @ ( intersection @ SV6 @ SV33 ) )
| ( member @ SV37 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV34: $i,SV6: $i,SV38: $i] :
( ( ~ ( member @ SV38 @ ( intersection @ SV6 @ SV34 ) )
| ( member @ SV38 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV28: $i,SV25: $i] :
( ( ( SV25 = SV28 )
= $false )
| ( ( subset @ SV25 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV29: $i,SV26: $i] :
( ( ( SV26 = SV29 )
= $false )
| ( ( subset @ SV29 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV10: $i,SV17: $i] :
( ( ( member @ ( sK4_D @ SV17 @ SV10 ) @ SV17 )
= $false )
| ( ( subset @ SV10 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(197,plain,
! [SV18: $i,SV11: $i,SV30: $i] :
( ( ( member @ SV30 @ SV11 )
= $false )
| ( ( member @ SV30 @ SV18 )
= $true )
| ( ( subset @ SV11 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(198,plain,
! [SV31: $i,SV5: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ ( difference @ SV5 @ SV31 ) ) )
= $true )
| ( ( member @ SV35 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(199,plain,
! [SV32: $i,SV5: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ ( difference @ SV5 @ SV32 ) ) )
= $true )
| ( ( ~ ( member @ SV36 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(200,plain,
! [SV12: $i,SV20: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 ) )
= $true )
| ( ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) )
= $true )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(201,plain,
! [SV12: $i,SV20: $i] :
( ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
= $true )
| ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 )
= $true )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(202,plain,
! [SV21: $i,SV13: $i] :
( ( ( ! [SY51: $i] :
( ~ ( member @ SY51 @ SV13 )
| ( member @ SY51 @ SV21 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(203,plain,
! [SV13: $i,SV21: $i] :
( ( ( ! [SY52: $i] :
( ~ ( member @ SY52 @ SV21 )
| ( member @ SY52 @ SV13 ) ) )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(204,plain,
! [SV6: $i,SV22: $i,SV24: $i] :
( ( ( member @ SV24 @ SV22 )
= $false )
| ( ( member @ SV24 @ SV6 )
= $false )
| ( ( member @ SV24 @ ( intersection @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV33: $i,SV6: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ ( intersection @ SV6 @ SV33 ) ) )
= $true )
| ( ( member @ SV37 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(206,plain,
! [SV34: $i,SV6: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ ( intersection @ SV6 @ SV34 ) ) )
= $true )
| ( ( member @ SV38 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV31: $i,SV5: $i,SV35: $i] :
( ( ( member @ SV35 @ ( difference @ SV5 @ SV31 ) )
= $false )
| ( ( member @ SV35 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV32: $i,SV5: $i,SV36: $i] :
( ( ( member @ SV36 @ ( difference @ SV5 @ SV32 ) )
= $false )
| ( ( ~ ( member @ SV36 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(209,plain,
! [SV12: $i,SV20: $i] :
( ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
= $false )
| ( ( ~ ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 ) )
= $true )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(210,plain,
! [SV21: $i,SV13: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV13 )
| ( member @ SV39 @ SV21 ) )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV13: $i,SV21: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV21 )
| ( member @ SV40 @ SV13 ) )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV33: $i,SV6: $i,SV37: $i] :
( ( ( member @ SV37 @ ( intersection @ SV6 @ SV33 ) )
= $false )
| ( ( member @ SV37 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(213,plain,
! [SV34: $i,SV6: $i,SV38: $i] :
( ( ( member @ SV38 @ ( intersection @ SV6 @ SV34 ) )
= $false )
| ( ( member @ SV38 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(214,plain,
! [SV5: $i,SV32: $i,SV36: $i] :
( ( ( member @ SV36 @ SV32 )
= $false )
| ( ( member @ SV36 @ ( difference @ SV5 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(215,plain,
! [SV12: $i,SV20: $i] :
( ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV20 )
= $false )
| ( ( member @ ( sK5_D @ SV20 @ SV12 ) @ SV12 )
= $false )
| ( ( SV12 = SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV21: $i,SV13: $i,SV39: $i] :
( ( ( ~ ( member @ SV39 @ SV13 ) )
= $true )
| ( ( member @ SV39 @ SV21 )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(217,plain,
! [SV13: $i,SV21: $i,SV40: $i] :
( ( ( ~ ( member @ SV40 @ SV21 ) )
= $true )
| ( ( member @ SV40 @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(218,plain,
! [SV21: $i,SV13: $i,SV39: $i] :
( ( ( member @ SV39 @ SV13 )
= $false )
| ( ( member @ SV39 @ SV21 )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(219,plain,
! [SV13: $i,SV21: $i,SV40: $i] :
( ( ( member @ SV40 @ SV21 )
= $false )
| ( ( member @ SV40 @ SV13 )
= $true )
| ( ( SV13 = SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(220,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,219,218,215,214,213,212,207,204,201,197,196,195,194,184,181,180,177,173,148,124,110,95,70,69]) ).
thf(221,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK6_D @ C @ B ) @ B )
| ~ ( member @ ( sK6_D @ C @ B ) @ C ) )
& ( ( member @ ( sK6_D @ C @ B ) @ B )
| ( member @ ( sK6_D @ C @ B ) @ C ) ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(222,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C )
| ( member @ D @ ( intersection @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(223,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C )
| ( member @ D @ ( difference @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ~ ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(224,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(225,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ C @ B )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(226,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(227,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK5_D @ C @ B ) @ B )
| ~ ( member @ ( sK5_D @ C @ B ) @ C ) )
& ( ( member @ ( sK5_D @ C @ B ) @ B )
| ( member @ ( sK5_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(228,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK4_D @ C @ B ) @ B )
& ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(229,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(230,plain,
( ( ! [B: $i] :
( ( member @ ( sK3_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(231,plain,
( ( ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B )
& ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(232,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(233,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( difference @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ~ ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(234,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(235,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(236,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(237,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(238,plain,
( ( ~ ( ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B )
| ~ ( ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(239,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(240,plain,
! [SV41: $i] :
( ( ~ ( member @ SV41 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(241,plain,
! [SV42: $i] :
( ( ! [SY60: $i] :
( ( intersection @ SV42 @ SY60 )
= ( intersection @ SY60 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(242,plain,
! [SV43: $i] :
( ( subset @ SV43 @ SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(243,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV44: $i] :
( ( ~ ( ~ ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ SV44 )
| ( member @ SY62 @ SY61 )
| ( member @ SY62 @ ( difference @ SV44 @ SY61 ) ) )
| ~ ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ ( difference @ SV44 @ SY63 ) )
| ( member @ SY64 @ SV44 ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ ( difference @ SV44 @ SY65 ) )
| ~ ( member @ SY66 @ SY65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(245,plain,
! [SV45: $i] :
( ( ~ ( ~ ! [SY67: $i,SY68: $i] :
( ~ ( member @ SY68 @ SV45 )
| ~ ( member @ SY68 @ SY67 )
| ( member @ SY68 @ ( intersection @ SV45 @ SY67 ) ) )
| ~ ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( member @ SY70 @ ( intersection @ SV45 @ SY69 ) )
| ( member @ SY70 @ SV45 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( member @ SY72 @ ( intersection @ SV45 @ SY71 ) )
| ( member @ SY72 @ SY71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(246,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(247,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(248,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(249,plain,
( ( ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B )
| ~ ( ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(250,plain,
! [SV46: $i] :
( ( ! [SY73: $i] :
( ~ ( ~ ( ~ ( member @ ( sK6_D @ SY73 @ SV46 ) @ SV46 )
| ~ ( member @ ( sK6_D @ SY73 @ SV46 ) @ SY73 ) )
| ~ ( ( member @ ( sK6_D @ SY73 @ SV46 ) @ SV46 )
| ( member @ ( sK6_D @ SY73 @ SV46 ) @ SY73 ) ) )
| ( SV46 = SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(251,plain,
! [SV41: $i] :
( ( member @ SV41 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(252,plain,
! [SV47: $i,SV42: $i] :
( ( ( intersection @ SV42 @ SV47 )
= ( intersection @ SV47 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(253,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(254,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(255,plain,
! [SV44: $i] :
( ( ~ ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ SV44 )
| ( member @ SY62 @ SY61 )
| ( member @ SY62 @ ( difference @ SV44 @ SY61 ) ) )
| ~ ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ ( difference @ SV44 @ SY63 ) )
| ( member @ SY64 @ SV44 ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ ( difference @ SV44 @ SY65 ) )
| ~ ( member @ SY66 @ SY65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(256,plain,
! [SV45: $i] :
( ( ~ ! [SY67: $i,SY68: $i] :
( ~ ( member @ SY68 @ SV45 )
| ~ ( member @ SY68 @ SY67 )
| ( member @ SY68 @ ( intersection @ SV45 @ SY67 ) ) )
| ~ ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( member @ SY70 @ ( intersection @ SV45 @ SY69 ) )
| ( member @ SY70 @ SV45 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( member @ SY72 @ ( intersection @ SV45 @ SY71 ) )
| ( member @ SY72 @ SY71 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(257,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(258,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(259,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(260,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(261,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(262,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(263,plain,
( ( ( ( difference @ sK1_B @ sK2_SY25 )
!= sK1_B ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(264,plain,
( ( ~ ( ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(265,plain,
! [SV46: $i,SV48: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) )
| ~ ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) ) )
| ( SV46 = SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(266,plain,
( ( ! [SX0: $i] :
( ( member @ ( sK3_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(267,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(268,plain,
! [SV44: $i] :
( ( ~ ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ SV44 )
| ( member @ SY62 @ SY61 )
| ( member @ SY62 @ ( difference @ SV44 @ SY61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(269,plain,
! [SV44: $i] :
( ( ~ ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ ( difference @ SV44 @ SY63 ) )
| ( member @ SY64 @ SV44 ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ ( difference @ SV44 @ SY65 ) )
| ~ ( member @ SY66 @ SY65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(270,plain,
! [SV45: $i] :
( ( ~ ! [SY67: $i,SY68: $i] :
( ~ ( member @ SY68 @ SV45 )
| ~ ( member @ SY68 @ SY67 )
| ( member @ SY68 @ ( intersection @ SV45 @ SY67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(271,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( member @ SY70 @ ( intersection @ SV45 @ SY69 ) )
| ( member @ SY70 @ SV45 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( member @ SY72 @ ( intersection @ SV45 @ SY71 ) )
| ( member @ SY72 @ SY71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(272,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(274,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(276,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(277,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(278,plain,
( ( ( difference @ sK1_B @ sK2_SY25 )
= sK1_B )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(279,plain,
( ( ( ( intersection @ sK1_B @ sK2_SY25 )
!= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(280,plain,
! [SV46: $i,SV48: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) )
| ~ ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) ) ) )
= $true )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(281,plain,
! [SV49: $i] :
( ( ( member @ ( sK3_C @ SV49 ) @ SV49 )
| ( empty @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(282,plain,
! [SV50: $i] :
( ( ~ ( empty @ SV50 )
| ! [SY74: $i] :
~ ( member @ SY74 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(283,plain,
! [SV44: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ SV44 )
| ( member @ SY62 @ SY61 )
| ( member @ SY62 @ ( difference @ SV44 @ SY61 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(284,plain,
! [SV44: $i] :
( ( ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ ( difference @ SV44 @ SY63 ) )
| ( member @ SY64 @ SV44 ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ ( difference @ SV44 @ SY65 ) )
| ~ ( member @ SY66 @ SY65 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(285,plain,
! [SV45: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( member @ SY68 @ SV45 )
| ~ ( member @ SY68 @ SY67 )
| ( member @ SY68 @ ( intersection @ SV45 @ SY67 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(286,plain,
! [SV45: $i] :
( ( ~ ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( member @ SY70 @ ( intersection @ SV45 @ SY69 ) )
| ( member @ SY70 @ SV45 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( member @ SY72 @ ( intersection @ SV45 @ SY71 ) )
| ( member @ SY72 @ SY71 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(287,plain,
! [SV51: $i] :
( ( ! [SY75: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SY75 @ SV51 ) @ SV51 )
| ~ ~ ( member @ ( sK4_D @ SY75 @ SV51 ) @ SY75 ) )
| ( subset @ SV51 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(288,plain,
! [SV52: $i] :
( ( ! [SY76: $i] :
( ~ ( subset @ SV52 @ SY76 )
| ! [SY77: $i] :
( ~ ( member @ SY77 @ SV52 )
| ( member @ SY77 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(289,plain,
! [SV53: $i] :
( ( ! [SY78: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SY78 @ SV53 ) @ SV53 )
| ~ ( member @ ( sK5_D @ SY78 @ SV53 ) @ SY78 ) )
| ~ ( ( member @ ( sK5_D @ SY78 @ SV53 ) @ SV53 )
| ( member @ ( sK5_D @ SY78 @ SV53 ) @ SY78 ) ) )
| ( SV53 = SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(290,plain,
! [SV54: $i] :
( ( ! [SY79: $i] :
( ( SV54 != SY79 )
| ~ ( ~ ! [SY80: $i] :
( ~ ( member @ SY80 @ SV54 )
| ( member @ SY80 @ SY79 ) )
| ~ ! [SY81: $i] :
( ~ ( member @ SY81 @ SY79 )
| ( member @ SY81 @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(291,plain,
! [SV55: $i] :
( ( ! [SY82: $i] :
( ~ ( subset @ SV55 @ SY82 )
| ~ ( subset @ SY82 @ SV55 )
| ( SV55 = SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(292,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(293,plain,
( ( ( intersection @ sK1_B @ sK2_SY25 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(294,plain,
! [SV46: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) )
| ~ ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) ) )
= $false )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(295,plain,
! [SV49: $i] :
( ( ( member @ ( sK3_C @ SV49 ) @ SV49 )
= $true )
| ( ( empty @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(296,plain,
! [SV50: $i] :
( ( ( ~ ( empty @ SV50 ) )
= $true )
| ( ( ! [SY74: $i] :
~ ( member @ SY74 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(297,plain,
! [SV56: $i,SV44: $i] :
( ( ! [SY83: $i] :
( ~ ( member @ SY83 @ SV44 )
| ( member @ SY83 @ SV56 )
| ( member @ SY83 @ ( difference @ SV44 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(298,plain,
! [SV44: $i] :
( ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ ( difference @ SV44 @ SY63 ) )
| ( member @ SY64 @ SV44 ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ ( difference @ SV44 @ SY65 ) )
| ~ ( member @ SY66 @ SY65 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(299,plain,
! [SV57: $i,SV45: $i] :
( ( ! [SY84: $i] :
( ~ ( member @ SY84 @ SV45 )
| ~ ( member @ SY84 @ SV57 )
| ( member @ SY84 @ ( intersection @ SV45 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(300,plain,
! [SV45: $i] :
( ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( member @ SY70 @ ( intersection @ SV45 @ SY69 ) )
| ( member @ SY70 @ SV45 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( member @ SY72 @ ( intersection @ SV45 @ SY71 ) )
| ( member @ SY72 @ SY71 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(301,plain,
! [SV51: $i,SV58: $i] :
( ( ~ ( ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV51 )
| ~ ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV58 ) )
| ( subset @ SV51 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(302,plain,
! [SV59: $i,SV52: $i] :
( ( ~ ( subset @ SV52 @ SV59 )
| ! [SY85: $i] :
( ~ ( member @ SY85 @ SV52 )
| ( member @ SY85 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(303,plain,
! [SV53: $i,SV60: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) )
| ~ ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) ) )
| ( SV53 = SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(304,plain,
! [SV61: $i,SV54: $i] :
( ( ( SV54 != SV61 )
| ~ ( ~ ! [SY86: $i] :
( ~ ( member @ SY86 @ SV54 )
| ( member @ SY86 @ SV61 ) )
| ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV61 )
| ( member @ SY87 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(305,plain,
! [SV62: $i,SV55: $i] :
( ( ~ ( subset @ SV55 @ SV62 )
| ~ ( subset @ SV62 @ SV55 )
| ( SV55 = SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(306,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(307,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(308,plain,
! [SV46: $i,SV48: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) ) )
= $false )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(309,plain,
! [SV46: $i,SV48: $i] :
( ( ( ~ ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) ) )
= $false )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(310,plain,
! [SV50: $i] :
( ( ( empty @ SV50 )
= $false )
| ( ( ! [SY74: $i] :
~ ( member @ SY74 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(311,plain,
! [SV56: $i,SV44: $i,SV63: $i] :
( ( ~ ( member @ SV63 @ SV44 )
| ( member @ SV63 @ SV56 )
| ( member @ SV63 @ ( difference @ SV44 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(312,plain,
! [SV44: $i] :
( ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ ( difference @ SV44 @ SY63 ) )
| ( member @ SY64 @ SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(313,plain,
! [SV44: $i] :
( ( ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ ( difference @ SV44 @ SY65 ) )
| ~ ( member @ SY66 @ SY65 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(314,plain,
! [SV57: $i,SV45: $i,SV64: $i] :
( ( ~ ( member @ SV64 @ SV45 )
| ~ ( member @ SV64 @ SV57 )
| ( member @ SV64 @ ( intersection @ SV45 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(315,plain,
! [SV45: $i] :
( ( ~ ! [SY69: $i,SY70: $i] :
( ~ ( member @ SY70 @ ( intersection @ SV45 @ SY69 ) )
| ( member @ SY70 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(316,plain,
! [SV45: $i] :
( ( ~ ! [SY71: $i,SY72: $i] :
( ~ ( member @ SY72 @ ( intersection @ SV45 @ SY71 ) )
| ( member @ SY72 @ SY71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(317,plain,
! [SV51: $i,SV58: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV51 )
| ~ ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV58 ) ) )
= $true )
| ( ( subset @ SV51 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(318,plain,
! [SV59: $i,SV52: $i] :
( ( ( ~ ( subset @ SV52 @ SV59 ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( member @ SY85 @ SV52 )
| ( member @ SY85 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(319,plain,
! [SV53: $i,SV60: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) )
| ~ ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) ) ) )
= $true )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(320,plain,
! [SV61: $i,SV54: $i] :
( ( ( ( SV54 != SV61 ) )
= $true )
| ( ( ~ ( ~ ! [SY86: $i] :
( ~ ( member @ SY86 @ SV54 )
| ( member @ SY86 @ SV61 ) )
| ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV61 )
| ( member @ SY87 @ SV54 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(321,plain,
! [SV62: $i,SV55: $i] :
( ( ( ~ ( subset @ SV55 @ SV62 )
| ~ ( subset @ SV62 @ SV55 ) )
= $true )
| ( ( SV55 = SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(322,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(323,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(324,plain,
! [SV46: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) )
= $true )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(325,plain,
! [SV46: $i,SV48: $i] :
( ( ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
| ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) )
= $true )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(326,plain,
! [SV50: $i,SV65: $i] :
( ( ( ~ ( member @ SV65 @ SV50 ) )
= $true )
| ( ( empty @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(327,plain,
! [SV56: $i,SV44: $i,SV63: $i] :
( ( ( ~ ( member @ SV63 @ SV44 )
| ( member @ SV63 @ SV56 ) )
= $true )
| ( ( member @ SV63 @ ( difference @ SV44 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(328,plain,
! [SV44: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ ( difference @ SV44 @ SY63 ) )
| ( member @ SY64 @ SV44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(329,plain,
! [SV44: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ ( difference @ SV44 @ SY65 ) )
| ~ ( member @ SY66 @ SY65 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(330,plain,
! [SV57: $i,SV45: $i,SV64: $i] :
( ( ( ~ ( member @ SV64 @ SV45 )
| ~ ( member @ SV64 @ SV57 ) )
= $true )
| ( ( member @ SV64 @ ( intersection @ SV45 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(331,plain,
! [SV45: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( member @ SY70 @ ( intersection @ SV45 @ SY69 ) )
| ( member @ SY70 @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(332,plain,
! [SV45: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( member @ SY72 @ ( intersection @ SV45 @ SY71 ) )
| ( member @ SY72 @ SY71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(333,plain,
! [SV51: $i,SV58: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV51 )
| ~ ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV58 ) )
= $false )
| ( ( subset @ SV51 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(334,plain,
! [SV59: $i,SV52: $i] :
( ( ( subset @ SV52 @ SV59 )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( member @ SY85 @ SV52 )
| ( member @ SY85 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(335,plain,
! [SV53: $i,SV60: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) )
| ~ ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) ) )
= $false )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(336,plain,
! [SV61: $i,SV54: $i] :
( ( ( SV54 = SV61 )
= $false )
| ( ( ~ ( ~ ! [SY86: $i] :
( ~ ( member @ SY86 @ SV54 )
| ( member @ SY86 @ SV61 ) )
| ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV61 )
| ( member @ SY87 @ SV54 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(337,plain,
! [SV62: $i,SV55: $i] :
( ( ( ~ ( subset @ SV55 @ SV62 ) )
= $true )
| ( ( ~ ( subset @ SV62 @ SV55 ) )
= $true )
| ( ( SV55 = SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(338,plain,
! [SV66: $i] :
( ( ! [SY88: $i] :
( ( SV66 != SY88 )
| ( subset @ SV66 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(339,plain,
! [SV67: $i] :
( ( ! [SY89: $i] :
( ( SV67 != SY89 )
| ( subset @ SY89 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(340,plain,
! [SV46: $i,SV48: $i] :
( ( ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 ) )
= $true )
| ( ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) )
= $true )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(341,plain,
! [SV46: $i,SV48: $i] :
( ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
= $true )
| ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 )
= $true )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(342,plain,
! [SV50: $i,SV65: $i] :
( ( ( member @ SV65 @ SV50 )
= $false )
| ( ( empty @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(343,plain,
! [SV56: $i,SV44: $i,SV63: $i] :
( ( ( ~ ( member @ SV63 @ SV44 ) )
= $true )
| ( ( member @ SV63 @ SV56 )
= $true )
| ( ( member @ SV63 @ ( difference @ SV44 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(344,plain,
! [SV68: $i,SV44: $i] :
( ( ! [SY90: $i] :
( ~ ( member @ SY90 @ ( difference @ SV44 @ SV68 ) )
| ( member @ SY90 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(345,plain,
! [SV69: $i,SV44: $i] :
( ( ! [SY91: $i] :
( ~ ( member @ SY91 @ ( difference @ SV44 @ SV69 ) )
| ~ ( member @ SY91 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(346,plain,
! [SV57: $i,SV45: $i,SV64: $i] :
( ( ( ~ ( member @ SV64 @ SV45 ) )
= $true )
| ( ( ~ ( member @ SV64 @ SV57 ) )
= $true )
| ( ( member @ SV64 @ ( intersection @ SV45 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(347,plain,
! [SV70: $i,SV45: $i] :
( ( ! [SY92: $i] :
( ~ ( member @ SY92 @ ( intersection @ SV45 @ SV70 ) )
| ( member @ SY92 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(348,plain,
! [SV71: $i,SV45: $i] :
( ( ! [SY93: $i] :
( ~ ( member @ SY93 @ ( intersection @ SV45 @ SV71 ) )
| ( member @ SY93 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(349,plain,
! [SV51: $i,SV58: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV51 ) )
= $false )
| ( ( subset @ SV51 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(350,plain,
! [SV51: $i,SV58: $i] :
( ( ( ~ ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV58 ) )
= $false )
| ( ( subset @ SV51 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(351,plain,
! [SV59: $i,SV52: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV52 )
| ( member @ SV72 @ SV59 ) )
= $true )
| ( ( subset @ SV52 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(352,plain,
! [SV53: $i,SV60: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) ) )
= $false )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(353,plain,
! [SV53: $i,SV60: $i] :
( ( ( ~ ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) ) )
= $false )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(354,plain,
! [SV61: $i,SV54: $i] :
( ( ( ~ ! [SY86: $i] :
( ~ ( member @ SY86 @ SV54 )
| ( member @ SY86 @ SV61 ) )
| ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV61 )
| ( member @ SY87 @ SV54 ) ) )
= $false )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(355,plain,
! [SV62: $i,SV55: $i] :
( ( ( subset @ SV55 @ SV62 )
= $false )
| ( ( ~ ( subset @ SV62 @ SV55 ) )
= $true )
| ( ( SV55 = SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(356,plain,
! [SV73: $i,SV66: $i] :
( ( ( SV66 != SV73 )
| ( subset @ SV66 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(357,plain,
! [SV74: $i,SV67: $i] :
( ( ( SV67 != SV74 )
| ( subset @ SV74 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(358,plain,
! [SV46: $i,SV48: $i] :
( ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
= $false )
| ( ( ~ ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 ) )
= $true )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(359,plain,
! [SV56: $i,SV44: $i,SV63: $i] :
( ( ( member @ SV63 @ SV44 )
= $false )
| ( ( member @ SV63 @ SV56 )
= $true )
| ( ( member @ SV63 @ ( difference @ SV44 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(360,plain,
! [SV68: $i,SV44: $i,SV75: $i] :
( ( ~ ( member @ SV75 @ ( difference @ SV44 @ SV68 ) )
| ( member @ SV75 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(361,plain,
! [SV69: $i,SV44: $i,SV76: $i] :
( ( ~ ( member @ SV76 @ ( difference @ SV44 @ SV69 ) )
| ~ ( member @ SV76 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(362,plain,
! [SV57: $i,SV45: $i,SV64: $i] :
( ( ( member @ SV64 @ SV45 )
= $false )
| ( ( ~ ( member @ SV64 @ SV57 ) )
= $true )
| ( ( member @ SV64 @ ( intersection @ SV45 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(363,plain,
! [SV70: $i,SV45: $i,SV77: $i] :
( ( ~ ( member @ SV77 @ ( intersection @ SV45 @ SV70 ) )
| ( member @ SV77 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(364,plain,
! [SV71: $i,SV45: $i,SV78: $i] :
( ( ~ ( member @ SV78 @ ( intersection @ SV45 @ SV71 ) )
| ( member @ SV78 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(365,plain,
! [SV51: $i,SV58: $i] :
( ( ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV51 )
= $true )
| ( ( subset @ SV51 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(366,plain,
! [SV51: $i,SV58: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV58 ) )
= $true )
| ( ( subset @ SV51 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(367,plain,
! [SV59: $i,SV52: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV52 ) )
= $true )
| ( ( member @ SV72 @ SV59 )
= $true )
| ( ( subset @ SV52 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(368,plain,
! [SV53: $i,SV60: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) )
= $true )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(369,plain,
! [SV53: $i,SV60: $i] :
( ( ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
| ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) )
= $true )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(370,plain,
! [SV61: $i,SV54: $i] :
( ( ( ~ ! [SY86: $i] :
( ~ ( member @ SY86 @ SV54 )
| ( member @ SY86 @ SV61 ) ) )
= $false )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(371,plain,
! [SV54: $i,SV61: $i] :
( ( ( ~ ! [SY87: $i] :
( ~ ( member @ SY87 @ SV61 )
| ( member @ SY87 @ SV54 ) ) )
= $false )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(372,plain,
! [SV55: $i,SV62: $i] :
( ( ( subset @ SV62 @ SV55 )
= $false )
| ( ( subset @ SV55 @ SV62 )
= $false )
| ( ( SV55 = SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(373,plain,
! [SV73: $i,SV66: $i] :
( ( ( ( SV66 != SV73 ) )
= $true )
| ( ( subset @ SV66 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(374,plain,
! [SV74: $i,SV67: $i] :
( ( ( ( SV67 != SV74 ) )
= $true )
| ( ( subset @ SV74 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(375,plain,
! [SV46: $i,SV48: $i] :
( ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV48 )
= $false )
| ( ( member @ ( sK6_D @ SV48 @ SV46 ) @ SV46 )
= $false )
| ( ( SV46 = SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(376,plain,
! [SV68: $i,SV44: $i,SV75: $i] :
( ( ( ~ ( member @ SV75 @ ( difference @ SV44 @ SV68 ) ) )
= $true )
| ( ( member @ SV75 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(377,plain,
! [SV69: $i,SV44: $i,SV76: $i] :
( ( ( ~ ( member @ SV76 @ ( difference @ SV44 @ SV69 ) ) )
= $true )
| ( ( ~ ( member @ SV76 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(378,plain,
! [SV45: $i,SV57: $i,SV64: $i] :
( ( ( member @ SV64 @ SV57 )
= $false )
| ( ( member @ SV64 @ SV45 )
= $false )
| ( ( member @ SV64 @ ( intersection @ SV45 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(379,plain,
! [SV70: $i,SV45: $i,SV77: $i] :
( ( ( ~ ( member @ SV77 @ ( intersection @ SV45 @ SV70 ) ) )
= $true )
| ( ( member @ SV77 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(380,plain,
! [SV71: $i,SV45: $i,SV78: $i] :
( ( ( ~ ( member @ SV78 @ ( intersection @ SV45 @ SV71 ) ) )
= $true )
| ( ( member @ SV78 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(381,plain,
! [SV51: $i,SV58: $i] :
( ( ( member @ ( sK4_D @ SV58 @ SV51 ) @ SV58 )
= $false )
| ( ( subset @ SV51 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(382,plain,
! [SV59: $i,SV52: $i,SV72: $i] :
( ( ( member @ SV72 @ SV52 )
= $false )
| ( ( member @ SV72 @ SV59 )
= $true )
| ( ( subset @ SV52 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(383,plain,
! [SV53: $i,SV60: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 ) )
= $true )
| ( ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) )
= $true )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(384,plain,
! [SV53: $i,SV60: $i] :
( ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
= $true )
| ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 )
= $true )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(385,plain,
! [SV61: $i,SV54: $i] :
( ( ( ! [SY86: $i] :
( ~ ( member @ SY86 @ SV54 )
| ( member @ SY86 @ SV61 ) ) )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(386,plain,
! [SV54: $i,SV61: $i] :
( ( ( ! [SY87: $i] :
( ~ ( member @ SY87 @ SV61 )
| ( member @ SY87 @ SV54 ) ) )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(387,plain,
! [SV73: $i,SV66: $i] :
( ( ( SV66 = SV73 )
= $false )
| ( ( subset @ SV66 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(388,plain,
! [SV74: $i,SV67: $i] :
( ( ( SV67 = SV74 )
= $false )
| ( ( subset @ SV74 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(389,plain,
! [SV68: $i,SV44: $i,SV75: $i] :
( ( ( member @ SV75 @ ( difference @ SV44 @ SV68 ) )
= $false )
| ( ( member @ SV75 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(390,plain,
! [SV69: $i,SV44: $i,SV76: $i] :
( ( ( member @ SV76 @ ( difference @ SV44 @ SV69 ) )
= $false )
| ( ( ~ ( member @ SV76 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(391,plain,
! [SV70: $i,SV45: $i,SV77: $i] :
( ( ( member @ SV77 @ ( intersection @ SV45 @ SV70 ) )
= $false )
| ( ( member @ SV77 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(392,plain,
! [SV71: $i,SV45: $i,SV78: $i] :
( ( ( member @ SV78 @ ( intersection @ SV45 @ SV71 ) )
= $false )
| ( ( member @ SV78 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(393,plain,
! [SV53: $i,SV60: $i] :
( ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
= $false )
| ( ( ~ ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 ) )
= $true )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(394,plain,
! [SV61: $i,SV54: $i,SV79: $i] :
( ( ( ~ ( member @ SV79 @ SV54 )
| ( member @ SV79 @ SV61 ) )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(395,plain,
! [SV54: $i,SV61: $i,SV80: $i] :
( ( ( ~ ( member @ SV80 @ SV61 )
| ( member @ SV80 @ SV54 ) )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(396,plain,
! [SV44: $i,SV69: $i,SV76: $i] :
( ( ( member @ SV76 @ SV69 )
= $false )
| ( ( member @ SV76 @ ( difference @ SV44 @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(397,plain,
! [SV53: $i,SV60: $i] :
( ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV60 )
= $false )
| ( ( member @ ( sK5_D @ SV60 @ SV53 ) @ SV53 )
= $false )
| ( ( SV53 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(398,plain,
! [SV61: $i,SV54: $i,SV79: $i] :
( ( ( ~ ( member @ SV79 @ SV54 ) )
= $true )
| ( ( member @ SV79 @ SV61 )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(399,plain,
! [SV54: $i,SV61: $i,SV80: $i] :
( ( ( ~ ( member @ SV80 @ SV61 ) )
= $true )
| ( ( member @ SV80 @ SV54 )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(400,plain,
! [SV61: $i,SV54: $i,SV79: $i] :
( ( ( member @ SV79 @ SV54 )
= $false )
| ( ( member @ SV79 @ SV61 )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(401,plain,
! [SV54: $i,SV61: $i,SV80: $i] :
( ( ( member @ SV80 @ SV61 )
= $false )
| ( ( member @ SV80 @ SV54 )
= $true )
| ( ( SV54 = SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(402,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[242,401,400,397,396,392,391,389,388,387,384,382,381,378,375,372,365,359,342,341,295,293,278,252,251]) ).
thf(403,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[402,220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 14:16:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 10
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full)........................
% 31.99/32.36
% 31.99/32.36 ********************************
% 31.99/32.36 * All subproblems solved! *
% 31.99/32.36 ********************************
% 31.99/32.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:43,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:402,loop_count:0,foatp_calls:1,translation:fof_full)
% 32.22/32.42
% 32.22/32.42 %**** Beginning of derivation protocol ****
% 32.22/32.42 % SZS output start CNFRefutation
% See solution above
% 32.22/32.42
% 32.22/32.42 %**** End of derivation protocol ****
% 32.22/32.42 %**** no. of clauses in derivation: 403 ****
% 32.22/32.42 %**** clause counter: 402 ****
% 32.22/32.42
% 32.22/32.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:43,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:402,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------