TSTP Solution File: SET148+4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET148+4 : 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 : n028.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 03:00:18 EDT 2022
% Result : Theorem 13.61s 13.78s
% Output : CNFRefutation 13.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 28
% Syntax : Number of formulae : 291 ( 179 unt; 16 typ; 0 def)
% Number of atoms : 1579 ( 443 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 3331 ( 609 ~; 506 |; 44 &;2148 @)
% ( 20 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 859 ( 0 ^ 857 !; 2 ?; 859 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_set,type,
equal_set: $i > $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_Y,type,
sK2_Y: $i > $i > $i ).
thf(tp_sK3_Y,type,
sK3_Y: $i > $i > $i ).
thf(tp_sK4_X,type,
sK4_X: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(2,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(3,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(4,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(5,axiom,
! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(6,axiom,
! [X: $i] :
~ ( member @ X @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(7,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(8,axiom,
! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(9,axiom,
! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(12,conjecture,
! [A: $i] : ( equal_set @ ( intersection @ A @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI13) ).
thf(13,negated_conjecture,
( ( ! [A: $i] : ( equal_set @ ( intersection @ A @ A ) @ A ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i] : ( equal_set @ ( intersection @ A @ A ) @ A ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( product @ A ) )
<=> ! [Y: $i] :
( ( member @ Y @ A )
=> ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( sum @ A ) )
<=> ? [Y: $i] :
( ( member @ Y @ A )
& ( member @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( unordered_pair @ A @ B ) )
<=> ( ( X = A )
| ( X = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( singleton @ A ) )
<=> ( X = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( union @ A @ B ) )
<=> ( ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( member @ X @ ( intersection @ A @ B ) )
<=> ( ( member @ X @ A )
& ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [X: $i,A: $i] :
( ( member @ X @ ( power_set @ A ) )
<=> ( subset @ X @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( equal_set @ ( intersection @ sK1_A @ sK1_A ) @ sK1_A )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ~ ( equal_set @ ( intersection @ sK1_A @ sK1_A ) @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(28,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK2_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK2_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(29,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK3_Y @ A @ X ) @ A )
& ( member @ X @ ( sK3_Y @ A @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(30,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(31,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(32,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(33,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(34,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(35,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK4_X @ B @ A ) @ A )
& ~ ( member @ ( sK4_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( ( member @ ( sK4_X @ B @ A ) @ A )
& ~ ( member @ ( sK4_X @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [X: $i] :
( ~ ( member @ X @ A )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( equal_set @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( equal_set @ A @ B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(40,plain,
( ( ! [X: $i,A: $i] :
( ~ ( member @ X @ ( power_set @ A ) )
| ( subset @ X @ A ) )
& ! [X: $i,A: $i] :
( ~ ( subset @ X @ A )
| ( member @ X @ ( power_set @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(41,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ A )
| ~ ( member @ X @ B )
| ( member @ X @ ( intersection @ A @ B ) ) )
& ! [A: $i] :
( ! [B: $i] :
~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ A ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ ( intersection @ A @ B ) )
| ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(42,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( union @ A @ B ) )
| ( member @ X @ A )
| ( member @ X @ B ) )
& ! [A: $i] :
( ~ ( member @ X @ A )
| ! [B: $i] : ( member @ X @ ( union @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( member @ X @ B )
| ( member @ X @ ( union @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(43,plain,
( ( ! [X: $i] :
~ ( member @ X @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(44,plain,
( ( ! [B: $i] :
( ! [A: $i,E: $i] :
( ~ ( member @ B @ E )
| ( member @ B @ A )
| ( member @ B @ ( difference @ E @ A ) ) )
& ! [A: $i,E: $i] :
( ~ ( member @ B @ ( difference @ E @ A ) )
| ( member @ B @ E ) )
& ! [A: $i] :
( ! [E: $i] :
~ ( member @ B @ ( difference @ E @ A ) )
| ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(45,plain,
( ( ! [X: $i,A: $i] :
( ( X != A )
| ( member @ X @ ( singleton @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( singleton @ A ) )
| ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(46,plain,
( ( ! [X: $i] :
( ! [A: $i,B: $i] :
( ~ ( member @ X @ ( unordered_pair @ A @ B ) )
| ( X = A )
| ( X = B ) )
& ! [A: $i] :
( ( X != A )
| ! [B: $i] : ( member @ X @ ( unordered_pair @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( X != B )
| ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(47,plain,
( ( ! [X: $i,A: $i] :
( ! [Y: $i] :
( ~ ( member @ Y @ A )
| ~ ( member @ X @ Y ) )
| ( member @ X @ ( sum @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( sum @ A ) )
| ( ( member @ ( sK3_Y @ A @ X ) @ A )
& ( member @ X @ ( sK3_Y @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(48,plain,
( ( ! [X: $i,A: $i] :
( ( ( member @ ( sK2_Y @ A @ X ) @ A )
& ~ ( member @ X @ ( sK2_Y @ A @ X ) ) )
| ( member @ X @ ( product @ A ) ) )
& ! [X: $i,A: $i] :
( ~ ( member @ X @ ( product @ A ) )
| ! [Y: $i] :
( ~ ( member @ Y @ A )
| ( member @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(49,plain,
( ( ~ ( equal_set @ ( intersection @ sK1_A @ sK1_A ) @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(50,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(51,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 )
| ( SX0 = SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX0 != SX2 )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(52,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( member @ SX0 @ SX1 )
| ! [SX2: $i] : ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(53,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX1 )
| ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(54,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ SX2 )
| ( member @ SX0 @ SX1 )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ( member @ SX0 @ SX2 ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( member @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(55,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK3_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK3_Y @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(56,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(57,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK2_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK2_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(58,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_X @ 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)],[38]) ).
thf(59,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(60,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(61,plain,
( ( equal_set @ ( intersection @ sK1_A @ sK1_A ) @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(62,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(63,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY29: $i,SY30: $i] :
( ~ ( member @ SV2 @ ( unordered_pair @ SY29 @ SY30 ) )
| ( SV2 = SY29 )
| ( SV2 = SY30 ) )
| ~ ~ ( ~ ! [SY31: $i] :
( ( SV2 != SY31 )
| ! [SY32: $i] : ( member @ SV2 @ ( unordered_pair @ SY31 @ SY32 ) ) )
| ~ ! [SY33: $i,SY34: $i] :
( ( SV2 != SY34 )
| ( member @ SV2 @ ( unordered_pair @ SY33 @ SY34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(64,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( member @ SV3 @ ( union @ SY35 @ SY36 ) )
| ( member @ SV3 @ SY35 )
| ( member @ SV3 @ SY36 ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( member @ SV3 @ SY37 )
| ! [SY38: $i] : ( member @ SV3 @ ( union @ SY37 @ SY38 ) ) )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( union @ SY39 @ SY40 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(65,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( member @ SV4 @ SY41 )
| ~ ( member @ SV4 @ SY42 )
| ( member @ SV4 @ ( intersection @ SY41 @ SY42 ) ) )
| ~ ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i] :
~ ( member @ SV4 @ ( intersection @ SY43 @ SY44 ) )
| ( member @ SV4 @ SY43 ) )
| ~ ! [SY45: $i,SY46: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY45 @ SY46 ) )
| ( member @ SV4 @ SY46 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(66,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY47: $i,SY48: $i] :
( ~ ( member @ SV5 @ SY48 )
| ( member @ SV5 @ SY47 )
| ( member @ SV5 @ ( difference @ SY48 @ SY47 ) ) )
| ~ ~ ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SV5 @ ( difference @ SY50 @ SY49 ) )
| ( member @ SV5 @ SY50 ) )
| ~ ! [SY51: $i] :
( ! [SY52: $i] :
~ ( member @ SV5 @ ( difference @ SY52 @ SY51 ) )
| ~ ( member @ SV5 @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(67,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK3_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK3_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(68,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(69,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK2_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK2_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(70,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_X @ 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)],[58]) ).
thf(71,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(72,plain,
! [SV1: $i] :
( ( member @ SV1 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(73,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(74,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(75,plain,
! [SV2: $i] :
( ( ~ ! [SY29: $i,SY30: $i] :
( ~ ( member @ SV2 @ ( unordered_pair @ SY29 @ SY30 ) )
| ( SV2 = SY29 )
| ( SV2 = SY30 ) )
| ~ ~ ( ~ ! [SY31: $i] :
( ( SV2 != SY31 )
| ! [SY32: $i] : ( member @ SV2 @ ( unordered_pair @ SY31 @ SY32 ) ) )
| ~ ! [SY33: $i,SY34: $i] :
( ( SV2 != SY34 )
| ( member @ SV2 @ ( unordered_pair @ SY33 @ SY34 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(76,plain,
! [SV3: $i] :
( ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( member @ SV3 @ ( union @ SY35 @ SY36 ) )
| ( member @ SV3 @ SY35 )
| ( member @ SV3 @ SY36 ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( member @ SV3 @ SY37 )
| ! [SY38: $i] : ( member @ SV3 @ ( union @ SY37 @ SY38 ) ) )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( union @ SY39 @ SY40 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV4: $i] :
( ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( member @ SV4 @ SY41 )
| ~ ( member @ SV4 @ SY42 )
| ( member @ SV4 @ ( intersection @ SY41 @ SY42 ) ) )
| ~ ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i] :
~ ( member @ SV4 @ ( intersection @ SY43 @ SY44 ) )
| ( member @ SV4 @ SY43 ) )
| ~ ! [SY45: $i,SY46: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY45 @ SY46 ) )
| ( member @ SV4 @ SY46 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV5: $i] :
( ( ~ ! [SY47: $i,SY48: $i] :
( ~ ( member @ SV5 @ SY48 )
| ( member @ SV5 @ SY47 )
| ( member @ SV5 @ ( difference @ SY48 @ SY47 ) ) )
| ~ ~ ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SV5 @ ( difference @ SY50 @ SY49 ) )
| ( member @ SV5 @ SY50 ) )
| ~ ! [SY51: $i] :
( ! [SY52: $i] :
~ ( member @ SV5 @ ( difference @ SY52 @ SY51 ) )
| ~ ( member @ SV5 @ SY51 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(79,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(80,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK3_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK3_Y @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(81,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(82,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(83,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK2_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK2_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(84,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(85,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(86,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(87,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(88,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( equal_set @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(90,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(91,plain,
! [SV2: $i] :
( ( ~ ! [SY29: $i,SY30: $i] :
( ~ ( member @ SV2 @ ( unordered_pair @ SY29 @ SY30 ) )
| ( SV2 = SY29 )
| ( SV2 = SY30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(92,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ! [SY31: $i] :
( ( SV2 != SY31 )
| ! [SY32: $i] : ( member @ SV2 @ ( unordered_pair @ SY31 @ SY32 ) ) )
| ~ ! [SY33: $i,SY34: $i] :
( ( SV2 != SY34 )
| ( member @ SV2 @ ( unordered_pair @ SY33 @ SY34 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(93,plain,
! [SV3: $i] :
( ( ~ ! [SY35: $i,SY36: $i] :
( ~ ( member @ SV3 @ ( union @ SY35 @ SY36 ) )
| ( member @ SV3 @ SY35 )
| ( member @ SV3 @ SY36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(94,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ! [SY37: $i] :
( ~ ( member @ SV3 @ SY37 )
| ! [SY38: $i] : ( member @ SV3 @ ( union @ SY37 @ SY38 ) ) )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( union @ SY39 @ SY40 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(95,plain,
! [SV4: $i] :
( ( ~ ! [SY41: $i,SY42: $i] :
( ~ ( member @ SV4 @ SY41 )
| ~ ( member @ SV4 @ SY42 )
| ( member @ SV4 @ ( intersection @ SY41 @ SY42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(96,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i] :
~ ( member @ SV4 @ ( intersection @ SY43 @ SY44 ) )
| ( member @ SV4 @ SY43 ) )
| ~ ! [SY45: $i,SY46: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY45 @ SY46 ) )
| ( member @ SV4 @ SY46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(97,plain,
! [SV5: $i] :
( ( ~ ! [SY47: $i,SY48: $i] :
( ~ ( member @ SV5 @ SY48 )
| ( member @ SV5 @ SY47 )
| ( member @ SV5 @ ( difference @ SY48 @ SY47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(98,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SV5 @ ( difference @ SY50 @ SY49 ) )
| ( member @ SV5 @ SY50 ) )
| ~ ! [SY51: $i] :
( ! [SY52: $i] :
~ ( member @ SV5 @ ( difference @ SY52 @ SY51 ) )
| ~ ( member @ SV5 @ SY51 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ~ ( member @ SX0 @ SX2 ) )
| ( member @ SX0 @ ( sum @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( sum @ SX1 ) )
| ~ ( ~ ( member @ ( sK3_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ( member @ SX0 @ ( sK3_Y @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( member @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK2_Y @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( member @ SX0 @ ( sK2_Y @ SX1 @ SX0 ) ) )
| ( member @ SX0 @ ( product @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( product @ SX1 ) )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_X @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_X @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( member @ SX0 @ ( power_set @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( member @ SX0 @ ( power_set @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(109,plain,
! [SV6: $i] :
( ( ! [SY53: $i] :
( ~ ( subset @ SV6 @ SY53 )
| ~ ( subset @ SY53 @ SV6 )
| ( equal_set @ SV6 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(110,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(111,plain,
! [SV2: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( member @ SV2 @ ( unordered_pair @ SY29 @ SY30 ) )
| ( SV2 = SY29 )
| ( SV2 = SY30 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(112,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY31: $i] :
( ( SV2 != SY31 )
| ! [SY32: $i] : ( member @ SV2 @ ( unordered_pair @ SY31 @ SY32 ) ) )
| ~ ! [SY33: $i,SY34: $i] :
( ( SV2 != SY34 )
| ( member @ SV2 @ ( unordered_pair @ SY33 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(113,plain,
! [SV3: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ( member @ SV3 @ ( union @ SY35 @ SY36 ) )
| ( member @ SV3 @ SY35 )
| ( member @ SV3 @ SY36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(114,plain,
! [SV3: $i] :
( ( ~ ( ~ ! [SY37: $i] :
( ~ ( member @ SV3 @ SY37 )
| ! [SY38: $i] : ( member @ SV3 @ ( union @ SY37 @ SY38 ) ) )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( union @ SY39 @ SY40 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(115,plain,
! [SV4: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ~ ( member @ SV4 @ SY41 )
| ~ ( member @ SV4 @ SY42 )
| ( member @ SV4 @ ( intersection @ SY41 @ SY42 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(116,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i] :
~ ( member @ SV4 @ ( intersection @ SY43 @ SY44 ) )
| ( member @ SV4 @ SY43 ) )
| ~ ! [SY45: $i,SY46: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY45 @ SY46 ) )
| ( member @ SV4 @ SY46 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(117,plain,
! [SV5: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( member @ SV5 @ SY48 )
| ( member @ SV5 @ SY47 )
| ( member @ SV5 @ ( difference @ SY48 @ SY47 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(118,plain,
! [SV5: $i] :
( ( ~ ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SV5 @ ( difference @ SY50 @ SY49 ) )
| ( member @ SV5 @ SY50 ) )
| ~ ! [SY51: $i] :
( ! [SY52: $i] :
~ ( member @ SV5 @ ( difference @ SY52 @ SY51 ) )
| ~ ( member @ SV5 @ SY51 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(119,plain,
! [SV7: $i] :
( ( ! [SY54: $i] :
( ! [SY55: $i] :
( ~ ( member @ SY55 @ SY54 )
| ~ ( member @ SV7 @ SY55 ) )
| ( member @ SV7 @ ( sum @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(120,plain,
! [SV8: $i] :
( ( ! [SY56: $i] :
( ~ ( member @ SV8 @ ( sum @ SY56 ) )
| ~ ( ~ ( member @ ( sK3_Y @ SY56 @ SV8 ) @ SY56 )
| ~ ( member @ SV8 @ ( sK3_Y @ SY56 @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(121,plain,
! [SV9: $i] :
( ( ! [SY57: $i] :
( ( SV9 != SY57 )
| ( member @ SV9 @ ( singleton @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(122,plain,
! [SV10: $i] :
( ( ! [SY58: $i] :
( ~ ( member @ SV10 @ ( singleton @ SY58 ) )
| ( SV10 = SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(123,plain,
! [SV11: $i] :
( ( ! [SY59: $i] :
( ~ ( ~ ( member @ ( sK2_Y @ SY59 @ SV11 ) @ SY59 )
| ~ ~ ( member @ SV11 @ ( sK2_Y @ SY59 @ SV11 ) ) )
| ( member @ SV11 @ ( product @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(124,plain,
! [SV12: $i] :
( ( ! [SY60: $i] :
( ~ ( member @ SV12 @ ( product @ SY60 ) )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SY60 )
| ( member @ SV12 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(125,plain,
! [SV13: $i] :
( ( ! [SY62: $i] :
( ~ ( ~ ( member @ ( sK4_X @ SY62 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK4_X @ SY62 @ SV13 ) @ SY62 ) )
| ( subset @ SV13 @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(126,plain,
! [SV14: $i] :
( ( ! [SY63: $i] :
( ~ ( subset @ SV14 @ SY63 )
| ! [SY64: $i] :
( ~ ( member @ SY64 @ SV14 )
| ( member @ SY64 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(127,plain,
! [SV15: $i] :
( ( ! [SY65: $i] :
( ~ ( member @ SV15 @ ( power_set @ SY65 ) )
| ( subset @ SV15 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(128,plain,
! [SV16: $i] :
( ( ! [SY66: $i] :
( ~ ( subset @ SV16 @ SY66 )
| ( member @ SV16 @ ( power_set @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(129,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV17 )
| ~ ( subset @ SV17 @ SV6 )
| ( equal_set @ SV6 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(130,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(131,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(132,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY67: $i] :
( ~ ( member @ SV2 @ ( unordered_pair @ SV18 @ SY67 ) )
| ( SV2 = SV18 )
| ( SV2 = SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(133,plain,
! [SV2: $i] :
( ( ~ ! [SY31: $i] :
( ( SV2 != SY31 )
| ! [SY32: $i] : ( member @ SV2 @ ( unordered_pair @ SY31 @ SY32 ) ) )
| ~ ! [SY33: $i,SY34: $i] :
( ( SV2 != SY34 )
| ( member @ SV2 @ ( unordered_pair @ SY33 @ SY34 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(134,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY68: $i] :
( ~ ( member @ SV3 @ ( union @ SV19 @ SY68 ) )
| ( member @ SV3 @ SV19 )
| ( member @ SV3 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(135,plain,
! [SV3: $i] :
( ( ~ ! [SY37: $i] :
( ~ ( member @ SV3 @ SY37 )
| ! [SY38: $i] : ( member @ SV3 @ ( union @ SY37 @ SY38 ) ) )
| ~ ! [SY39: $i,SY40: $i] :
( ~ ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( union @ SY39 @ SY40 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(136,plain,
! [SV20: $i,SV4: $i] :
( ( ! [SY69: $i] :
( ~ ( member @ SV4 @ SV20 )
| ~ ( member @ SV4 @ SY69 )
| ( member @ SV4 @ ( intersection @ SV20 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(137,plain,
! [SV4: $i] :
( ( ~ ! [SY43: $i] :
( ! [SY44: $i] :
~ ( member @ SV4 @ ( intersection @ SY43 @ SY44 ) )
| ( member @ SV4 @ SY43 ) )
| ~ ! [SY45: $i,SY46: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY45 @ SY46 ) )
| ( member @ SV4 @ SY46 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(138,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY70: $i] :
( ~ ( member @ SV5 @ SY70 )
| ( member @ SV5 @ SV21 )
| ( member @ SV5 @ ( difference @ SY70 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(139,plain,
! [SV5: $i] :
( ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SV5 @ ( difference @ SY50 @ SY49 ) )
| ( member @ SV5 @ SY50 ) )
| ~ ! [SY51: $i] :
( ! [SY52: $i] :
~ ( member @ SV5 @ ( difference @ SY52 @ SY51 ) )
| ~ ( member @ SV5 @ SY51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(140,plain,
! [SV7: $i,SV22: $i] :
( ( ! [SY71: $i] :
( ~ ( member @ SY71 @ SV22 )
| ~ ( member @ SV7 @ SY71 ) )
| ( member @ SV7 @ ( sum @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(141,plain,
! [SV23: $i,SV8: $i] :
( ( ~ ( member @ SV8 @ ( sum @ SV23 ) )
| ~ ( ~ ( member @ ( sK3_Y @ SV23 @ SV8 ) @ SV23 )
| ~ ( member @ SV8 @ ( sK3_Y @ SV23 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(142,plain,
! [SV24: $i,SV9: $i] :
( ( ( SV9 != SV24 )
| ( member @ SV9 @ ( singleton @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(143,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( member @ SV10 @ ( singleton @ SV25 ) )
| ( SV10 = SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(144,plain,
! [SV11: $i,SV26: $i] :
( ( ~ ( ~ ( member @ ( sK2_Y @ SV26 @ SV11 ) @ SV26 )
| ~ ~ ( member @ SV11 @ ( sK2_Y @ SV26 @ SV11 ) ) )
| ( member @ SV11 @ ( product @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(145,plain,
! [SV27: $i,SV12: $i] :
( ( ~ ( member @ SV12 @ ( product @ SV27 ) )
| ! [SY72: $i] :
( ~ ( member @ SY72 @ SV27 )
| ( member @ SV12 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(146,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ( ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV28 ) )
| ( subset @ SV13 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(147,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV29 )
| ! [SY73: $i] :
( ~ ( member @ SY73 @ SV14 )
| ( member @ SY73 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV30: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ ( power_set @ SV30 ) )
| ( subset @ SV15 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV31 )
| ( member @ SV16 @ ( power_set @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV17 )
| ~ ( subset @ SV17 @ SV6 ) )
= $true )
| ( ( equal_set @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( equal_set @ SX0 @ SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(153,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ ( unordered_pair @ SV18 @ SV32 ) )
| ( SV2 = SV18 )
| ( SV2 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV2: $i] :
( ( ~ ! [SY31: $i] :
( ( SV2 != SY31 )
| ! [SY32: $i] : ( member @ SV2 @ ( unordered_pair @ SY31 @ SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(155,plain,
! [SV2: $i] :
( ( ~ ! [SY33: $i,SY34: $i] :
( ( SV2 != SY34 )
| ( member @ SV2 @ ( unordered_pair @ SY33 @ SY34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(156,plain,
! [SV33: $i,SV19: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ ( union @ SV19 @ SV33 ) )
| ( member @ SV3 @ SV19 )
| ( member @ SV3 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(157,plain,
! [SV3: $i] :
( ( ~ ! [SY37: $i] :
( ~ ( member @ SV3 @ SY37 )
| ! [SY38: $i] : ( member @ SV3 @ ( union @ SY37 @ SY38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(158,plain,
! [SV3: $i] :
( ( ~ ! [SY39: $i,SY40: $i] :
( ~ ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( union @ SY39 @ SY40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(159,plain,
! [SV34: $i,SV20: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ SV20 )
| ~ ( member @ SV4 @ SV34 )
| ( member @ SV4 @ ( intersection @ SV20 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(160,plain,
! [SV4: $i] :
( ( ~ ! [SY43: $i] :
( ! [SY44: $i] :
~ ( member @ SV4 @ ( intersection @ SY43 @ SY44 ) )
| ( member @ SV4 @ SY43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(161,plain,
! [SV4: $i] :
( ( ~ ! [SY45: $i,SY46: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY45 @ SY46 ) )
| ( member @ SV4 @ SY46 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(162,plain,
! [SV21: $i,SV35: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ SV35 )
| ( member @ SV5 @ SV21 )
| ( member @ SV5 @ ( difference @ SV35 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(163,plain,
! [SV5: $i] :
( ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SV5 @ ( difference @ SY50 @ SY49 ) )
| ( member @ SV5 @ SY50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(164,plain,
! [SV5: $i] :
( ( ~ ! [SY51: $i] :
( ! [SY52: $i] :
~ ( member @ SV5 @ ( difference @ SY52 @ SY51 ) )
| ~ ( member @ SV5 @ SY51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(165,plain,
! [SV7: $i,SV22: $i] :
( ( ( ! [SY71: $i] :
( ~ ( member @ SY71 @ SV22 )
| ~ ( member @ SV7 @ SY71 ) ) )
= $true )
| ( ( member @ SV7 @ ( sum @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(166,plain,
! [SV23: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ ( sum @ SV23 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ ( sK3_Y @ SV23 @ SV8 ) @ SV23 )
| ~ ( member @ SV8 @ ( sK3_Y @ SV23 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(167,plain,
! [SV24: $i,SV9: $i] :
( ( ( ( SV9 != SV24 ) )
= $true )
| ( ( member @ SV9 @ ( singleton @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(168,plain,
! [SV25: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( singleton @ SV25 ) ) )
= $true )
| ( ( SV10 = SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(169,plain,
! [SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( member @ ( sK2_Y @ SV26 @ SV11 ) @ SV26 )
| ~ ~ ( member @ SV11 @ ( sK2_Y @ SV26 @ SV11 ) ) ) )
= $true )
| ( ( member @ SV11 @ ( product @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(170,plain,
! [SV27: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ ( product @ SV27 ) ) )
= $true )
| ( ( ! [SY72: $i] :
( ~ ( member @ SY72 @ SV27 )
| ( member @ SV12 @ SY72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(171,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV28 ) ) )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(172,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV29 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( member @ SY73 @ SV14 )
| ( member @ SY73 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(173,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ ( power_set @ SV30 ) ) )
= $true )
| ( ( subset @ SV15 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(174,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV31 ) )
= $true )
| ( ( member @ SV16 @ ( power_set @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(175,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV17 ) )
= $true )
| ( ( ~ ( subset @ SV17 @ SV6 ) )
= $true )
| ( ( equal_set @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(176,plain,
! [SV36: $i] :
( ( ! [SY74: $i] :
( ~ ( equal_set @ SV36 @ SY74 )
| ( subset @ SV36 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(177,plain,
! [SV37: $i] :
( ( ! [SY75: $i] :
( ~ ( equal_set @ SV37 @ SY75 )
| ( subset @ SY75 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(178,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ ( unordered_pair @ SV18 @ SV32 ) ) )
= $true )
| ( ( ( SV2 = SV18 )
| ( SV2 = SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(179,plain,
! [SV2: $i] :
( ( ! [SY31: $i] :
( ( SV2 != SY31 )
| ! [SY32: $i] : ( member @ SV2 @ ( unordered_pair @ SY31 @ SY32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(180,plain,
! [SV2: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( SV2 != SY34 )
| ( member @ SV2 @ ( unordered_pair @ SY33 @ SY34 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(181,plain,
! [SV33: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ ( union @ SV19 @ SV33 ) ) )
= $true )
| ( ( ( member @ SV3 @ SV19 )
| ( member @ SV3 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(182,plain,
! [SV3: $i] :
( ( ! [SY37: $i] :
( ~ ( member @ SV3 @ SY37 )
| ! [SY38: $i] : ( member @ SV3 @ ( union @ SY37 @ SY38 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(183,plain,
! [SV3: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ~ ( member @ SV3 @ SY40 )
| ( member @ SV3 @ ( union @ SY39 @ SY40 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(184,plain,
! [SV34: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ SV20 )
| ~ ( member @ SV4 @ SV34 ) )
= $true )
| ( ( member @ SV4 @ ( intersection @ SV20 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(185,plain,
! [SV4: $i] :
( ( ! [SY43: $i] :
( ! [SY44: $i] :
~ ( member @ SV4 @ ( intersection @ SY43 @ SY44 ) )
| ( member @ SV4 @ SY43 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(186,plain,
! [SV4: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ( member @ SV4 @ ( intersection @ SY45 @ SY46 ) )
| ( member @ SV4 @ SY46 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(187,plain,
! [SV21: $i,SV35: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV35 )
| ( member @ SV5 @ SV21 ) )
= $true )
| ( ( member @ SV5 @ ( difference @ SV35 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(188,plain,
! [SV5: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( member @ SV5 @ ( difference @ SY50 @ SY49 ) )
| ( member @ SV5 @ SY50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(189,plain,
! [SV5: $i] :
( ( ! [SY51: $i] :
( ! [SY52: $i] :
~ ( member @ SV5 @ ( difference @ SY52 @ SY51 ) )
| ~ ( member @ SV5 @ SY51 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(190,plain,
! [SV7: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ SV22 )
| ~ ( member @ SV7 @ SV38 ) )
= $true )
| ( ( member @ SV7 @ ( sum @ SV22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(191,plain,
! [SV23: $i,SV8: $i] :
( ( ( member @ SV8 @ ( sum @ SV23 ) )
= $false )
| ( ( ~ ( ~ ( member @ ( sK3_Y @ SV23 @ SV8 ) @ SV23 )
| ~ ( member @ SV8 @ ( sK3_Y @ SV23 @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(192,plain,
! [SV24: $i,SV9: $i] :
( ( ( SV9 = SV24 )
= $false )
| ( ( member @ SV9 @ ( singleton @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(193,plain,
! [SV25: $i,SV10: $i] :
( ( ( member @ SV10 @ ( singleton @ SV25 ) )
= $false )
| ( ( SV10 = SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(194,plain,
! [SV11: $i,SV26: $i] :
( ( ( ~ ( member @ ( sK2_Y @ SV26 @ SV11 ) @ SV26 )
| ~ ~ ( member @ SV11 @ ( sK2_Y @ SV26 @ SV11 ) ) )
= $false )
| ( ( member @ SV11 @ ( product @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(195,plain,
! [SV27: $i,SV12: $i] :
( ( ( member @ SV12 @ ( product @ SV27 ) )
= $false )
| ( ( ! [SY72: $i] :
( ~ ( member @ SY72 @ SV27 )
| ( member @ SV12 @ SY72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(196,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV13 )
| ~ ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV28 ) )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(197,plain,
! [SV29: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV29 )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( member @ SY73 @ SV14 )
| ( member @ SY73 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(198,plain,
! [SV30: $i,SV15: $i] :
( ( ( member @ SV15 @ ( power_set @ SV30 ) )
= $false )
| ( ( subset @ SV15 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(199,plain,
! [SV31: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( member @ SV16 @ ( power_set @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(200,plain,
! [SV17: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV17 )
= $false )
| ( ( ~ ( subset @ SV17 @ SV6 ) )
= $true )
| ( ( equal_set @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(201,plain,
! [SV39: $i,SV36: $i] :
( ( ~ ( equal_set @ SV36 @ SV39 )
| ( subset @ SV36 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(202,plain,
! [SV40: $i,SV37: $i] :
( ( ~ ( equal_set @ SV37 @ SV40 )
| ( subset @ SV40 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(203,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( member @ SV2 @ ( unordered_pair @ SV18 @ SV32 ) )
= $false )
| ( ( ( SV2 = SV18 )
| ( SV2 = SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(204,plain,
! [SV41: $i,SV2: $i] :
( ( ( SV2 != SV41 )
| ! [SY76: $i] : ( member @ SV2 @ ( unordered_pair @ SV41 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(205,plain,
! [SV42: $i,SV2: $i] :
( ( ! [SY77: $i] :
( ( SV2 != SY77 )
| ( member @ SV2 @ ( unordered_pair @ SV42 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(206,plain,
! [SV33: $i,SV19: $i,SV3: $i] :
( ( ( member @ SV3 @ ( union @ SV19 @ SV33 ) )
= $false )
| ( ( ( member @ SV3 @ SV19 )
| ( member @ SV3 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(207,plain,
! [SV43: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ SV43 )
| ! [SY78: $i] : ( member @ SV3 @ ( union @ SV43 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(208,plain,
! [SV44: $i,SV3: $i] :
( ( ! [SY79: $i] :
( ~ ( member @ SV3 @ SY79 )
| ( member @ SV3 @ ( union @ SV44 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(209,plain,
! [SV34: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ SV20 ) )
= $true )
| ( ( ~ ( member @ SV4 @ SV34 ) )
= $true )
| ( ( member @ SV4 @ ( intersection @ SV20 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(210,plain,
! [SV45: $i,SV4: $i] :
( ( ! [SY80: $i] :
~ ( member @ SV4 @ ( intersection @ SV45 @ SY80 ) )
| ( member @ SV4 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(211,plain,
! [SV46: $i,SV4: $i] :
( ( ! [SY81: $i] :
( ~ ( member @ SV4 @ ( intersection @ SV46 @ SY81 ) )
| ( member @ SV4 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(212,plain,
! [SV21: $i,SV35: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ SV35 ) )
= $true )
| ( ( member @ SV5 @ SV21 )
= $true )
| ( ( member @ SV5 @ ( difference @ SV35 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(213,plain,
! [SV47: $i,SV5: $i] :
( ( ! [SY82: $i] :
( ~ ( member @ SV5 @ ( difference @ SY82 @ SV47 ) )
| ( member @ SV5 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(214,plain,
! [SV48: $i,SV5: $i] :
( ( ! [SY83: $i] :
~ ( member @ SV5 @ ( difference @ SY83 @ SV48 ) )
| ~ ( member @ SV5 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(215,plain,
! [SV7: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ SV22 ) )
= $true )
| ( ( ~ ( member @ SV7 @ SV38 ) )
= $true )
| ( ( member @ SV7 @ ( sum @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(216,plain,
! [SV8: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK3_Y @ SV23 @ SV8 ) @ SV23 )
| ~ ( member @ SV8 @ ( sK3_Y @ SV23 @ SV8 ) ) )
= $false )
| ( ( member @ SV8 @ ( sum @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(217,plain,
! [SV11: $i,SV26: $i] :
( ( ( ~ ( member @ ( sK2_Y @ SV26 @ SV11 ) @ SV26 ) )
= $false )
| ( ( member @ SV11 @ ( product @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(218,plain,
! [SV26: $i,SV11: $i] :
( ( ( ~ ~ ( member @ SV11 @ ( sK2_Y @ SV26 @ SV11 ) ) )
= $false )
| ( ( member @ SV11 @ ( product @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(219,plain,
! [SV12: $i,SV27: $i,SV49: $i] :
( ( ( ~ ( member @ SV49 @ SV27 )
| ( member @ SV12 @ SV49 ) )
= $true )
| ( ( member @ SV12 @ ( product @ SV27 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(220,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV13 ) )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(221,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV28 ) )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(222,plain,
! [SV29: $i,SV14: $i,SV50: $i] :
( ( ( ~ ( member @ SV50 @ SV14 )
| ( member @ SV50 @ SV29 ) )
= $true )
| ( ( subset @ SV14 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(223,plain,
! [SV6: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV6 )
= $false )
| ( ( subset @ SV6 @ SV17 )
= $false )
| ( ( equal_set @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(224,plain,
! [SV39: $i,SV36: $i] :
( ( ( ~ ( equal_set @ SV36 @ SV39 ) )
= $true )
| ( ( subset @ SV36 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(225,plain,
! [SV40: $i,SV37: $i] :
( ( ( ~ ( equal_set @ SV37 @ SV40 ) )
= $true )
| ( ( subset @ SV40 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(226,plain,
! [SV32: $i,SV18: $i,SV2: $i] :
( ( ( SV2 = SV18 )
= $true )
| ( ( SV2 = SV32 )
= $true )
| ( ( member @ SV2 @ ( unordered_pair @ SV18 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(227,plain,
! [SV41: $i,SV2: $i] :
( ( ( ( SV2 != SV41 ) )
= $true )
| ( ( ! [SY76: $i] : ( member @ SV2 @ ( unordered_pair @ SV41 @ SY76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(228,plain,
! [SV42: $i,SV51: $i,SV2: $i] :
( ( ( SV2 != SV51 )
| ( member @ SV2 @ ( unordered_pair @ SV42 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(229,plain,
! [SV33: $i,SV19: $i,SV3: $i] :
( ( ( member @ SV3 @ SV19 )
= $true )
| ( ( member @ SV3 @ SV33 )
= $true )
| ( ( member @ SV3 @ ( union @ SV19 @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(230,plain,
! [SV43: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ SV43 ) )
= $true )
| ( ( ! [SY78: $i] : ( member @ SV3 @ ( union @ SV43 @ SY78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(231,plain,
! [SV44: $i,SV52: $i,SV3: $i] :
( ( ~ ( member @ SV3 @ SV52 )
| ( member @ SV3 @ ( union @ SV44 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(232,plain,
! [SV34: $i,SV20: $i,SV4: $i] :
( ( ( member @ SV4 @ SV20 )
= $false )
| ( ( ~ ( member @ SV4 @ SV34 ) )
= $true )
| ( ( member @ SV4 @ ( intersection @ SV20 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(233,plain,
! [SV45: $i,SV4: $i] :
( ( ( ! [SY80: $i] :
~ ( member @ SV4 @ ( intersection @ SV45 @ SY80 ) ) )
= $true )
| ( ( member @ SV4 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(234,plain,
! [SV53: $i,SV46: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ ( intersection @ SV46 @ SV53 ) )
| ( member @ SV4 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(235,plain,
! [SV21: $i,SV35: $i,SV5: $i] :
( ( ( member @ SV5 @ SV35 )
= $false )
| ( ( member @ SV5 @ SV21 )
= $true )
| ( ( member @ SV5 @ ( difference @ SV35 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(236,plain,
! [SV47: $i,SV54: $i,SV5: $i] :
( ( ~ ( member @ SV5 @ ( difference @ SV54 @ SV47 ) )
| ( member @ SV5 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(237,plain,
! [SV48: $i,SV5: $i] :
( ( ( ! [SY83: $i] :
~ ( member @ SV5 @ ( difference @ SY83 @ SV48 ) ) )
= $true )
| ( ( ~ ( member @ SV5 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(238,plain,
! [SV7: $i,SV22: $i,SV38: $i] :
( ( ( member @ SV38 @ SV22 )
= $false )
| ( ( ~ ( member @ SV7 @ SV38 ) )
= $true )
| ( ( member @ SV7 @ ( sum @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(239,plain,
! [SV8: $i,SV23: $i] :
( ( ( ~ ( member @ ( sK3_Y @ SV23 @ SV8 ) @ SV23 ) )
= $false )
| ( ( member @ SV8 @ ( sum @ SV23 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(240,plain,
! [SV23: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ ( sK3_Y @ SV23 @ SV8 ) ) )
= $false )
| ( ( member @ SV8 @ ( sum @ SV23 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(241,plain,
! [SV11: $i,SV26: $i] :
( ( ( member @ ( sK2_Y @ SV26 @ SV11 ) @ SV26 )
= $true )
| ( ( member @ SV11 @ ( product @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(242,plain,
! [SV26: $i,SV11: $i] :
( ( ( ~ ( member @ SV11 @ ( sK2_Y @ SV26 @ SV11 ) ) )
= $true )
| ( ( member @ SV11 @ ( product @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(243,plain,
! [SV12: $i,SV27: $i,SV49: $i] :
( ( ( ~ ( member @ SV49 @ SV27 ) )
= $true )
| ( ( member @ SV12 @ SV49 )
= $true )
| ( ( member @ SV12 @ ( product @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(244,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV13 )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(245,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV28 ) )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(246,plain,
! [SV29: $i,SV14: $i,SV50: $i] :
( ( ( ~ ( member @ SV50 @ SV14 ) )
= $true )
| ( ( member @ SV50 @ SV29 )
= $true )
| ( ( subset @ SV14 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(247,plain,
! [SV39: $i,SV36: $i] :
( ( ( equal_set @ SV36 @ SV39 )
= $false )
| ( ( subset @ SV36 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(248,plain,
! [SV40: $i,SV37: $i] :
( ( ( equal_set @ SV37 @ SV40 )
= $false )
| ( ( subset @ SV40 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(249,plain,
! [SV41: $i,SV2: $i] :
( ( ( SV2 = SV41 )
= $false )
| ( ( ! [SY76: $i] : ( member @ SV2 @ ( unordered_pair @ SV41 @ SY76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(250,plain,
! [SV42: $i,SV51: $i,SV2: $i] :
( ( ( ( SV2 != SV51 ) )
= $true )
| ( ( member @ SV2 @ ( unordered_pair @ SV42 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(251,plain,
! [SV43: $i,SV3: $i] :
( ( ( member @ SV3 @ SV43 )
= $false )
| ( ( ! [SY78: $i] : ( member @ SV3 @ ( union @ SV43 @ SY78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(252,plain,
! [SV44: $i,SV52: $i,SV3: $i] :
( ( ( ~ ( member @ SV3 @ SV52 ) )
= $true )
| ( ( member @ SV3 @ ( union @ SV44 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(253,plain,
! [SV20: $i,SV34: $i,SV4: $i] :
( ( ( member @ SV4 @ SV34 )
= $false )
| ( ( member @ SV4 @ SV20 )
= $false )
| ( ( member @ SV4 @ ( intersection @ SV20 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(254,plain,
! [SV55: $i,SV45: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( intersection @ SV45 @ SV55 ) ) )
= $true )
| ( ( member @ SV4 @ SV45 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(255,plain,
! [SV53: $i,SV46: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( intersection @ SV46 @ SV53 ) ) )
= $true )
| ( ( member @ SV4 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(256,plain,
! [SV47: $i,SV54: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( difference @ SV54 @ SV47 ) ) )
= $true )
| ( ( member @ SV5 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(257,plain,
! [SV48: $i,SV56: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( difference @ SV56 @ SV48 ) ) )
= $true )
| ( ( ~ ( member @ SV5 @ SV48 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(258,plain,
! [SV22: $i,SV38: $i,SV7: $i] :
( ( ( member @ SV7 @ SV38 )
= $false )
| ( ( member @ SV38 @ SV22 )
= $false )
| ( ( member @ SV7 @ ( sum @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(259,plain,
! [SV8: $i,SV23: $i] :
( ( ( member @ ( sK3_Y @ SV23 @ SV8 ) @ SV23 )
= $true )
| ( ( member @ SV8 @ ( sum @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(260,plain,
! [SV23: $i,SV8: $i] :
( ( ( member @ SV8 @ ( sK3_Y @ SV23 @ SV8 ) )
= $true )
| ( ( member @ SV8 @ ( sum @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(261,plain,
! [SV26: $i,SV11: $i] :
( ( ( member @ SV11 @ ( sK2_Y @ SV26 @ SV11 ) )
= $false )
| ( ( member @ SV11 @ ( product @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(262,plain,
! [SV12: $i,SV27: $i,SV49: $i] :
( ( ( member @ SV49 @ SV27 )
= $false )
| ( ( member @ SV12 @ SV49 )
= $true )
| ( ( member @ SV12 @ ( product @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(263,plain,
! [SV13: $i,SV28: $i] :
( ( ( member @ ( sK4_X @ SV28 @ SV13 ) @ SV28 )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(264,plain,
! [SV29: $i,SV14: $i,SV50: $i] :
( ( ( member @ SV50 @ SV14 )
= $false )
| ( ( member @ SV50 @ SV29 )
= $true )
| ( ( subset @ SV14 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(265,plain,
! [SV57: $i,SV41: $i,SV2: $i] :
( ( ( member @ SV2 @ ( unordered_pair @ SV41 @ SV57 ) )
= $true )
| ( ( SV2 = SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(266,plain,
! [SV42: $i,SV51: $i,SV2: $i] :
( ( ( SV2 = SV51 )
= $false )
| ( ( member @ SV2 @ ( unordered_pair @ SV42 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(267,plain,
! [SV58: $i,SV43: $i,SV3: $i] :
( ( ( member @ SV3 @ ( union @ SV43 @ SV58 ) )
= $true )
| ( ( member @ SV3 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(268,plain,
! [SV44: $i,SV52: $i,SV3: $i] :
( ( ( member @ SV3 @ SV52 )
= $false )
| ( ( member @ SV3 @ ( union @ SV44 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(269,plain,
! [SV55: $i,SV45: $i,SV4: $i] :
( ( ( member @ SV4 @ ( intersection @ SV45 @ SV55 ) )
= $false )
| ( ( member @ SV4 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(270,plain,
! [SV53: $i,SV46: $i,SV4: $i] :
( ( ( member @ SV4 @ ( intersection @ SV46 @ SV53 ) )
= $false )
| ( ( member @ SV4 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(271,plain,
! [SV47: $i,SV54: $i,SV5: $i] :
( ( ( member @ SV5 @ ( difference @ SV54 @ SV47 ) )
= $false )
| ( ( member @ SV5 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(272,plain,
! [SV48: $i,SV56: $i,SV5: $i] :
( ( ( member @ SV5 @ ( difference @ SV56 @ SV48 ) )
= $false )
| ( ( ~ ( member @ SV5 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(273,plain,
! [SV56: $i,SV48: $i,SV5: $i] :
( ( ( member @ SV5 @ SV48 )
= $false )
| ( ( member @ SV5 @ ( difference @ SV56 @ SV48 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(274,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[61,273,271,270,269,268,267,266,265,264,263,262,261,260,259,258,253,248,247,244,241,235,229,226,223,199,198,193,192,72]) ).
thf(275,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET148+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 04:32:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 11
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:11,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:13,loop_count:0,foatp_calls:0,translation:fof_full)....................
% 13.61/13.78
% 13.61/13.78 ********************************
% 13.61/13.78 * All subproblems solved! *
% 13.61/13.78 ********************************
% 13.61/13.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:274,loop_count:0,foatp_calls:1,translation:fof_full)
% 13.64/13.82
% 13.64/13.82 %**** Beginning of derivation protocol ****
% 13.64/13.82 % SZS output start CNFRefutation
% See solution above
% 13.64/13.82
% 13.64/13.82 %**** End of derivation protocol ****
% 13.64/13.82 %**** no. of clauses in derivation: 275 ****
% 13.64/13.82 %**** clause counter: 274 ****
% 13.64/13.82
% 13.64/13.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:274,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------