%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:38:50 AM UTC 2026
% Result : Unsatisfiable 16.22s 3.02s
% Output : CNFRefutation 16.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 272 ( 149 unt; 0 typ; 0 def)
% Number of atoms : 1599 ( 393 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 3348 ( 332 ~; 541 |; 0 &;2475 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 820 ( 0 ^; 820 !; 0 ?; 820 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_aIb,type,
aIb: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_cD_aIb,type,
cD_aIb: $i ).
thf(tp_cDa,type,
cDa: $i ).
thf(tp_cDb,type,
cDb: $i ).
thf(tp_difference,type,
difference: $i > $i > $i > $o ).
thf(tp_equal_sets,type,
equal_sets: $i > $i > $o ).
thf(tp_g,type,
g: $i > $i > $i > $i ).
thf(tp_h,type,
h: $i > $i > $i > $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i > $o ).
thf(tp_k,type,
k: $i > $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_member_of_1_not_of_2,type,
member_of_1_not_of_2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i > $i > $o ).
thf(1,axiom,
! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference )
| ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set1 )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 )
| ( difference @ Set1 @ Set2 @ Difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom3) ).
thf(2,axiom,
! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference )
| ( difference @ Set1 @ Set2 @ Difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom1) ).
thf(3,axiom,
! [Set1: $i,Set2: $i,Difference: $i] :
( ( difference @ Set1 @ Set2 @ Difference )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set1 )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_axiom2) ).
thf(4,axiom,
! [Element: $i,Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ Element @ Set1 )
| ~ ( difference @ Set1 @ Set2 @ Difference )
| ( member @ Element @ Difference )
| ( member @ Element @ Set2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
thf(5,axiom,
! [Element: $i,Set1: $i,Set2: $i,A_set: $i] :
( ~ ( member @ Element @ Set1 )
| ~ ( member @ Element @ Set2 )
| ~ ( difference @ A_set @ Set1 @ Set2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_difference) ).
thf(6,axiom,
! [Set1: $i,Set2: $i,Difference: $i,Element: $i] :
( ~ ( difference @ Set1 @ Set2 @ Difference )
| ~ ( member @ Element @ Difference )
| ( member @ Element @ Set1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference) ).
thf(7,axiom,
! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 )
| ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 )
| ( intersection @ Set1 @ Set2 @ Intersection ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom3) ).
thf(8,axiom,
! [Set1: $i,Set2: $i,Intersection: $i] :
( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ( intersection @ Set1 @ Set2 @ Intersection )
| ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom2) ).
thf(9,axiom,
! [Set1: $i,Set2: $i,Intersection: $i] :
( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ( intersection @ Set1 @ Set2 @ Intersection )
| ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom1) ).
thf(10,axiom,
! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ~ ( member @ Element @ Set2 )
| ~ ( member @ Element @ Set1 )
| ( member @ Element @ Intersection ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
thf(11,axiom,
! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
thf(12,axiom,
! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(13,axiom,
! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
| ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
| ( union @ Set1 @ Set2 @ Union ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom3) ).
thf(14,axiom,
! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
| ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
| ( union @ Set1 @ Set2 @ Union ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom2) ).
thf(15,axiom,
! [Set1: $i,Set2: $i,Union: $i] :
( ( union @ Set1 @ Set2 @ Union )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_axiom1) ).
thf(16,axiom,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ~ ( member @ Element @ Set2 )
| ( member @ Element @ Union ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
thf(17,axiom,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ~ ( member @ Element @ Set1 )
| ( member @ Element @ Union ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
thf(18,axiom,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ~ ( member @ Element @ Union )
| ( member @ Element @ Set1 )
| ( member @ Element @ Set2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
thf(19,axiom,
! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(20,axiom,
! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(21,axiom,
! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(22,axiom,
! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(23,axiom,
! [Subset: $i,Superset: $i] :
( ( subset @ Subset @ Superset )
| ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(24,axiom,
! [Element: $i,Subset: $i,Superset: $i] :
( ~ ( member @ Element @ Subset )
| ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(25,axiom,
difference @ c @ aIb @ cD_aIb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_aIb) ).
thf(26,axiom,
difference @ c @ b @ cDb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_b) ).
thf(27,axiom,
difference @ c @ a @ cDa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_minus_a) ).
thf(28,axiom,
intersection @ a @ b @ aIb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
thf(29,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(30,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,negated_conjecture,
~ ( union @ cDa @ cDb @ cD_aIb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
thf(32,plain,
$false = $false,
inference(unfold_def,[status(thm)],[30]) ).
thf(33,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference )
| ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set1 )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 )
| ( difference @ Set1 @ Set2 @ Difference ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(34,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference )
| ( difference @ Set1 @ Set2 @ Difference ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(35,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ( difference @ Set1 @ Set2 @ Difference )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set1 )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Element: $i,Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ Element @ Set1 )
| ~ ( difference @ Set1 @ Set2 @ Difference )
| ( member @ Element @ Difference )
| ( member @ Element @ Set2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(37,plain,
( ( ! [Element: $i,Set1: $i,Set2: $i,A_set: $i] :
( ~ ( member @ Element @ Set1 )
| ~ ( member @ Element @ Set2 )
| ~ ( difference @ A_set @ Set1 @ Set2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(38,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i,Element: $i] :
( ~ ( difference @ Set1 @ Set2 @ Difference )
| ~ ( member @ Element @ Difference )
| ( member @ Element @ Set1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(39,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 )
| ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 )
| ( intersection @ Set1 @ Set2 @ Intersection ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(40,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ( intersection @ Set1 @ Set2 @ Intersection )
| ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(41,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ( intersection @ Set1 @ Set2 @ Intersection )
| ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(42,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ~ ( member @ Element @ Set2 )
| ~ ( member @ Element @ Set1 )
| ( member @ Element @ Intersection ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(43,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(44,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i,Element: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(45,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
| ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
| ( union @ Set1 @ Set2 @ Union ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(46,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
| ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
| ( union @ Set1 @ Set2 @ Union ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(47,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ( union @ Set1 @ Set2 @ Union )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(48,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ~ ( member @ Element @ Set2 )
| ( member @ Element @ Union ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(49,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ~ ( member @ Element @ Set1 )
| ( member @ Element @ Union ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(50,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ~ ( member @ Element @ Union )
| ( member @ Element @ Set1 )
| ( member @ Element @ Set2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(51,plain,
( ( ! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(52,plain,
( ( ! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(53,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(54,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(55,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( subset @ Subset @ Superset )
| ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(56,plain,
( ( ! [Element: $i,Subset: $i,Superset: $i] :
( ~ ( member @ Element @ Subset )
| ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(57,plain,
( ( difference @ c @ aIb @ cD_aIb )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(58,plain,
( ( difference @ c @ b @ cDb )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(59,plain,
( ( difference @ c @ a @ cDa )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(60,plain,
( ( intersection @ a @ b @ aIb )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(61,plain,
( ( ~ ( union @ cDa @ cDb @ cD_aIb ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(62,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(63,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference )
| ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set1 )
| ( difference @ Set1 @ Set2 @ Difference )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(64,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 )
| ( difference @ Set1 @ Set2 @ Difference )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(65,plain,
( ( ! [Element: $i,Set1: $i] :
( ~ ( member @ Element @ Set1 )
| ! [Set2: $i,Difference: $i] :
( ~ ( difference @ Set1 @ Set2 @ Difference )
| ( member @ Element @ Difference )
| ( member @ Element @ Set2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(66,plain,
( ( ! [Element: $i,Set1: $i] :
( ~ ( member @ Element @ Set1 )
| ! [Set2: $i] :
( ~ ( member @ Element @ Set2 )
| ! [A_set: $i] :
~ ( difference @ A_set @ Set1 @ Set2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(67,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( difference @ Set1 @ Set2 @ Difference )
| ! [Element: $i] :
( ~ ( member @ Element @ Difference )
| ( member @ Element @ Set1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(68,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Set2 )
| ~ ( member @ Element @ Set1 )
| ( member @ Element @ Intersection ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(69,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(70,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(71,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ! [Element: $i] :
( ~ ( member @ Element @ Set2 )
| ( member @ Element @ Union ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(72,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ! [Element: $i] :
( ~ ( member @ Element @ Set1 )
| ( member @ Element @ Union ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(73,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ! [Element: $i] :
( ~ ( member @ Element @ Union )
| ( member @ Element @ Set1 )
| ( member @ Element @ Set2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(74,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(75,plain,
( ( ! [Element: $i,Subset: $i] :
( ~ ( member @ Element @ Subset )
| ! [Superset: $i] :
( ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(76,plain,
( ( ~ ( union @ cDa @ cDb @ cD_aIb ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(77,plain,
( ( intersection @ a @ b @ aIb )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(78,plain,
( ( difference @ c @ a @ cDa )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(79,plain,
( ( difference @ c @ b @ cDb )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(80,plain,
( ( difference @ c @ aIb @ cD_aIb )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(81,plain,
( ( ! [Element: $i,Subset: $i] :
( ~ ( member @ Element @ Subset )
| ! [Superset: $i] :
( ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(82,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(83,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(84,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(85,plain,
( ( ! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(86,plain,
( ( ! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(87,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ! [Element: $i] :
( ~ ( member @ Element @ Union )
| ( member @ Element @ Set1 )
| ( member @ Element @ Set2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(88,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ! [Element: $i] :
( ~ ( member @ Element @ Set1 )
| ( member @ Element @ Union ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(89,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( union @ Set1 @ Set2 @ Union )
| ! [Element: $i] :
( ~ ( member @ Element @ Set2 )
| ( member @ Element @ Union ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(90,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ( union @ Set1 @ Set2 @ Union )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
| ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(91,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set1 )
| ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
| ( union @ Set1 @ Set2 @ Union ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(92,plain,
( ( ! [Set1: $i,Set2: $i,Union: $i] :
( ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Set2 )
| ~ ( member @ ( g @ Set1 @ Set2 @ Union ) @ Union )
| ( union @ Set1 @ Set2 @ Union ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(93,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(94,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(95,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Set2 )
| ~ ( member @ Element @ Set1 )
| ( member @ Element @ Intersection ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(96,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ( intersection @ Set1 @ Set2 @ Intersection )
| ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(97,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ( intersection @ Set1 @ Set2 @ Intersection )
| ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(98,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Intersection )
| ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set2 )
| ~ ( member @ ( h @ Set1 @ Set2 @ Intersection ) @ Set1 )
| ( intersection @ Set1 @ Set2 @ Intersection ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(99,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( difference @ Set1 @ Set2 @ Difference )
| ! [Element: $i] :
( ~ ( member @ Element @ Difference )
| ( member @ Element @ Set1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(100,plain,
( ( ! [Element: $i,Set1: $i] :
( ~ ( member @ Element @ Set1 )
| ! [Set2: $i] :
( ~ ( member @ Element @ Set2 )
| ! [A_set: $i] :
~ ( difference @ A_set @ Set1 @ Set2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(101,plain,
( ( ! [Element: $i,Set1: $i] :
( ~ ( member @ Element @ Set1 )
| ! [Set2: $i,Difference: $i] :
( ~ ( difference @ Set1 @ Set2 @ Difference )
| ( member @ Element @ Difference )
| ( member @ Element @ Set2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(102,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ( difference @ Set1 @ Set2 @ Difference )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set1 )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(103,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 )
| ( difference @ Set1 @ Set2 @ Difference )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(104,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Difference )
| ~ ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set1 )
| ( difference @ Set1 @ Set2 @ Difference )
| ( member @ ( k @ Set1 @ Set2 @ Difference ) @ Set2 ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(105,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[62]) ).
thf(106,plain,
( ( union @ cDa @ cDb @ cD_aIb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(107,plain,
! [SV1: $i] :
( ( ! [SY76: $i] :
( ~ ( member @ SV1 @ SY76 )
| ! [SY77: $i] :
( ~ ( subset @ SY76 @ SY77 )
| ( member @ SV1 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(108,plain,
! [SV2: $i] :
( ( ! [SY78: $i] :
( ( member @ ( member_of_1_not_of_2 @ SV2 @ SY78 ) @ SV2 )
| ( subset @ SV2 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(109,plain,
! [SV3: $i] :
( ( ! [SY79: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SY79 ) @ SY79 )
| ( subset @ SV3 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(110,plain,
! [SV4: $i] :
( ( ! [SY80: $i] :
( ~ ( equal_sets @ SV4 @ SY80 )
| ( subset @ SV4 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(111,plain,
! [SV5: $i] :
( ( ! [SY81: $i] :
( ~ ( equal_sets @ SV5 @ SY81 )
| ( subset @ SY81 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(112,plain,
! [SV6: $i] :
( ( ! [SY82: $i] :
( ~ ( subset @ SV6 @ SY82 )
| ~ ( subset @ SY82 @ SV6 )
| ( equal_sets @ SY82 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(113,plain,
! [SV7: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ( union @ SV7 @ SY83 @ SY84 )
| ! [SY85: $i] :
( ~ ( member @ SY85 @ SY84 )
| ( member @ SY85 @ SV7 )
| ( member @ SY85 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(114,plain,
! [SV8: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( union @ SV8 @ SY86 @ SY87 )
| ! [SY88: $i] :
( ~ ( member @ SY88 @ SV8 )
| ( member @ SY88 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(115,plain,
! [SV9: $i] :
( ( ! [SY89: $i,SY90: $i] :
( ~ ( union @ SV9 @ SY89 @ SY90 )
| ! [Element: $i] :
( ~ ( member @ Element @ SY89 )
| ( member @ Element @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(116,plain,
! [SV10: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ( union @ SV10 @ SY92 @ SY93 )
| ( member @ ( g @ SV10 @ SY92 @ SY93 ) @ SV10 )
| ( member @ ( g @ SV10 @ SY92 @ SY93 ) @ SY92 )
| ( member @ ( g @ SV10 @ SY92 @ SY93 ) @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(117,plain,
! [SV11: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( member @ ( g @ SV11 @ SY94 @ SY95 ) @ SV11 )
| ~ ( member @ ( g @ SV11 @ SY94 @ SY95 ) @ SY95 )
| ( union @ SV11 @ SY94 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(118,plain,
! [SV12: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( member @ ( g @ SV12 @ SY96 @ SY97 ) @ SY96 )
| ~ ( member @ ( g @ SV12 @ SY96 @ SY97 ) @ SY97 )
| ( union @ SV12 @ SY96 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(119,plain,
! [SV13: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ( intersection @ SV13 @ SY98 @ SY99 )
| ! [SY100: $i] :
( ~ ( member @ SY100 @ SY99 )
| ( member @ SY100 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(120,plain,
! [SV14: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ( intersection @ SV14 @ SY101 @ SY102 )
| ! [Element: $i] :
( ~ ( member @ Element @ SY102 )
| ( member @ Element @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(121,plain,
! [SV15: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( intersection @ SV15 @ SY104 @ SY105 )
| ! [SY106: $i] :
( ~ ( member @ SY106 @ SY104 )
| ~ ( member @ SY106 @ SV15 )
| ( member @ SY106 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(122,plain,
! [SV16: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ( member @ ( h @ SV16 @ SY107 @ SY108 ) @ SY108 )
| ( intersection @ SV16 @ SY107 @ SY108 )
| ( member @ ( h @ SV16 @ SY107 @ SY108 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(123,plain,
! [SV17: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ( member @ ( h @ SV17 @ SY109 @ SY110 ) @ SY110 )
| ( intersection @ SV17 @ SY109 @ SY110 )
| ( member @ ( h @ SV17 @ SY109 @ SY110 ) @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(124,plain,
! [SV18: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( member @ ( h @ SV18 @ SY111 @ SY112 ) @ SY112 )
| ~ ( member @ ( h @ SV18 @ SY111 @ SY112 ) @ SY111 )
| ~ ( member @ ( h @ SV18 @ SY111 @ SY112 ) @ SV18 )
| ( intersection @ SV18 @ SY111 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(125,plain,
! [SV19: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( difference @ SV19 @ SY113 @ SY114 )
| ! [SY115: $i] :
( ~ ( member @ SY115 @ SY114 )
| ( member @ SY115 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(126,plain,
! [SV20: $i] :
( ( ! [SY116: $i] :
( ~ ( member @ SV20 @ SY116 )
| ! [SY117: $i] :
( ~ ( member @ SV20 @ SY117 )
| ! [A_set: $i] :
~ ( difference @ A_set @ SY116 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(127,plain,
! [SV21: $i] :
( ( ! [SY119: $i] :
( ~ ( member @ SV21 @ SY119 )
| ! [SY120: $i,SY121: $i] :
( ~ ( difference @ SY119 @ SY120 @ SY121 )
| ( member @ SV21 @ SY121 )
| ( member @ SV21 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(128,plain,
! [SV22: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ( difference @ SV22 @ SY122 @ SY123 )
| ( member @ ( k @ SV22 @ SY122 @ SY123 ) @ SV22 )
| ( member @ ( k @ SV22 @ SY122 @ SY123 ) @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(129,plain,
! [SV23: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ~ ( member @ ( k @ SV23 @ SY124 @ SY125 ) @ SY124 )
| ( difference @ SV23 @ SY124 @ SY125 )
| ( member @ ( k @ SV23 @ SY124 @ SY125 ) @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(130,plain,
! [SV24: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ~ ( member @ ( k @ SV24 @ SY126 @ SY127 ) @ SY127 )
| ~ ( member @ ( k @ SV24 @ SY126 @ SY127 ) @ SV24 )
| ( difference @ SV24 @ SY126 @ SY127 )
| ( member @ ( k @ SV24 @ SY126 @ SY127 ) @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(131,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(132,plain,
! [SV25: $i,SV1: $i] :
( ( ~ ( member @ SV1 @ SV25 )
| ! [SY128: $i] :
( ~ ( subset @ SV25 @ SY128 )
| ( member @ SV1 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(133,plain,
! [SV26: $i,SV2: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV2 @ SV26 ) @ SV2 )
| ( subset @ SV2 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(134,plain,
! [SV27: $i,SV3: $i] :
( ( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SV27 ) @ SV27 )
| ( subset @ SV3 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(135,plain,
! [SV28: $i,SV4: $i] :
( ( ~ ( equal_sets @ SV4 @ SV28 )
| ( subset @ SV4 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(136,plain,
! [SV29: $i,SV5: $i] :
( ( ~ ( equal_sets @ SV5 @ SV29 )
| ( subset @ SV29 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(137,plain,
! [SV30: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV30 )
| ~ ( subset @ SV30 @ SV6 )
| ( equal_sets @ SV30 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(138,plain,
! [SV31: $i,SV7: $i] :
( ( ! [SY129: $i] :
( ~ ( union @ SV7 @ SV31 @ SY129 )
| ! [SY130: $i] :
( ~ ( member @ SY130 @ SY129 )
| ( member @ SY130 @ SV7 )
| ( member @ SY130 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(139,plain,
! [SV32: $i,SV8: $i] :
( ( ! [SY131: $i] :
( ~ ( union @ SV8 @ SV32 @ SY131 )
| ! [SY88: $i] :
( ~ ( member @ SY88 @ SV8 )
| ( member @ SY88 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(140,plain,
! [SV33: $i,SV9: $i] :
( ( ! [SY133: $i] :
( ~ ( union @ SV9 @ SV33 @ SY133 )
| ! [SY134: $i] :
( ~ ( member @ SY134 @ SV33 )
| ( member @ SY134 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(141,plain,
! [SV34: $i,SV10: $i] :
( ( ! [SY135: $i] :
( ( union @ SV10 @ SV34 @ SY135 )
| ( member @ ( g @ SV10 @ SV34 @ SY135 ) @ SV10 )
| ( member @ ( g @ SV10 @ SV34 @ SY135 ) @ SV34 )
| ( member @ ( g @ SV10 @ SV34 @ SY135 ) @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(142,plain,
! [SV35: $i,SV11: $i] :
( ( ! [SY136: $i] :
( ~ ( member @ ( g @ SV11 @ SV35 @ SY136 ) @ SV11 )
| ~ ( member @ ( g @ SV11 @ SV35 @ SY136 ) @ SY136 )
| ( union @ SV11 @ SV35 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(143,plain,
! [SV36: $i,SV12: $i] :
( ( ! [SY137: $i] :
( ~ ( member @ ( g @ SV12 @ SV36 @ SY137 ) @ SV36 )
| ~ ( member @ ( g @ SV12 @ SV36 @ SY137 ) @ SY137 )
| ( union @ SV12 @ SV36 @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(144,plain,
! [SV37: $i,SV13: $i] :
( ( ! [SY138: $i] :
( ~ ( intersection @ SV13 @ SV37 @ SY138 )
| ! [SY100: $i] :
( ~ ( member @ SY100 @ SY138 )
| ( member @ SY100 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(145,plain,
! [SV38: $i,SV14: $i] :
( ( ! [SY140: $i] :
( ~ ( intersection @ SV14 @ SV38 @ SY140 )
| ! [SY141: $i] :
( ~ ( member @ SY141 @ SY140 )
| ( member @ SY141 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(146,plain,
! [SV39: $i,SV15: $i] :
( ( ! [SY142: $i] :
( ~ ( intersection @ SV15 @ SV39 @ SY142 )
| ! [SY143: $i] :
( ~ ( member @ SY143 @ SV39 )
| ~ ( member @ SY143 @ SV15 )
| ( member @ SY143 @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(147,plain,
! [SV40: $i,SV16: $i] :
( ( ! [SY144: $i] :
( ( member @ ( h @ SV16 @ SV40 @ SY144 ) @ SY144 )
| ( intersection @ SV16 @ SV40 @ SY144 )
| ( member @ ( h @ SV16 @ SV40 @ SY144 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(148,plain,
! [SV41: $i,SV17: $i] :
( ( ! [SY145: $i] :
( ( member @ ( h @ SV17 @ SV41 @ SY145 ) @ SY145 )
| ( intersection @ SV17 @ SV41 @ SY145 )
| ( member @ ( h @ SV17 @ SV41 @ SY145 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(149,plain,
! [SV42: $i,SV18: $i] :
( ( ! [SY146: $i] :
( ~ ( member @ ( h @ SV18 @ SV42 @ SY146 ) @ SY146 )
| ~ ( member @ ( h @ SV18 @ SV42 @ SY146 ) @ SV42 )
| ~ ( member @ ( h @ SV18 @ SV42 @ SY146 ) @ SV18 )
| ( intersection @ SV18 @ SV42 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(150,plain,
! [SV43: $i,SV19: $i] :
( ( ! [SY147: $i] :
( ~ ( difference @ SV19 @ SV43 @ SY147 )
| ! [SY115: $i] :
( ~ ( member @ SY115 @ SY147 )
| ( member @ SY115 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(151,plain,
! [SV44: $i,SV20: $i] :
( ( ~ ( member @ SV20 @ SV44 )
| ! [SY149: $i] :
( ~ ( member @ SV20 @ SY149 )
| ! [SY150: $i] :
~ ( difference @ SY150 @ SV44 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(152,plain,
! [SV45: $i,SV21: $i] :
( ( ~ ( member @ SV21 @ SV45 )
| ! [SY151: $i,SY152: $i] :
( ~ ( difference @ SV45 @ SY151 @ SY152 )
| ( member @ SV21 @ SY152 )
| ( member @ SV21 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(153,plain,
! [SV46: $i,SV22: $i] :
( ( ! [SY153: $i] :
( ( difference @ SV22 @ SV46 @ SY153 )
| ( member @ ( k @ SV22 @ SV46 @ SY153 ) @ SV22 )
| ( member @ ( k @ SV22 @ SV46 @ SY153 ) @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(154,plain,
! [SV47: $i,SV23: $i] :
( ( ! [SY154: $i] :
( ~ ( member @ ( k @ SV23 @ SV47 @ SY154 ) @ SV47 )
| ( difference @ SV23 @ SV47 @ SY154 )
| ( member @ ( k @ SV23 @ SV47 @ SY154 ) @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(155,plain,
! [SV48: $i,SV24: $i] :
( ( ! [SY155: $i] :
( ~ ( member @ ( k @ SV24 @ SV48 @ SY155 ) @ SY155 )
| ~ ( member @ ( k @ SV24 @ SV48 @ SY155 ) @ SV24 )
| ( difference @ SV24 @ SV48 @ SY155 )
| ( member @ ( k @ SV24 @ SV48 @ SY155 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(156,plain,
! [SV25: $i,SV1: $i] :
( ( ( ~ ( member @ SV1 @ SV25 ) )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( subset @ SV25 @ SY128 )
| ( member @ SV1 @ SY128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(157,plain,
! [SV26: $i,SV2: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV2 @ SV26 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(158,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( member @ ( member_of_1_not_of_2 @ SV3 @ SV27 ) @ SV27 ) )
= $true )
| ( ( subset @ SV3 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(159,plain,
! [SV28: $i,SV4: $i] :
( ( ( ~ ( equal_sets @ SV4 @ SV28 ) )
= $true )
| ( ( subset @ SV4 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(160,plain,
! [SV29: $i,SV5: $i] :
( ( ( ~ ( equal_sets @ SV5 @ SV29 ) )
= $true )
| ( ( subset @ SV29 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(161,plain,
! [SV30: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV30 ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV6 )
| ( equal_sets @ SV30 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(162,plain,
! [SV49: $i,SV31: $i,SV7: $i] :
( ( ~ ( union @ SV7 @ SV31 @ SV49 )
| ! [SY156: $i] :
( ~ ( member @ SY156 @ SV49 )
| ( member @ SY156 @ SV7 )
| ( member @ SY156 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(163,plain,
! [SV50: $i,SV32: $i,SV8: $i] :
( ( ~ ( union @ SV8 @ SV32 @ SV50 )
| ! [SY157: $i] :
( ~ ( member @ SY157 @ SV8 )
| ( member @ SY157 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(164,plain,
! [SV51: $i,SV33: $i,SV9: $i] :
( ( ~ ( union @ SV9 @ SV33 @ SV51 )
| ! [SY158: $i] :
( ~ ( member @ SY158 @ SV33 )
| ( member @ SY158 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(165,plain,
! [SV52: $i,SV34: $i,SV10: $i] :
( ( ( union @ SV10 @ SV34 @ SV52 )
| ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV10 )
| ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV34 )
| ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(166,plain,
! [SV53: $i,SV35: $i,SV11: $i] :
( ( ~ ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV11 )
| ~ ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV53 )
| ( union @ SV11 @ SV35 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(167,plain,
! [SV54: $i,SV36: $i,SV12: $i] :
( ( ~ ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV36 )
| ~ ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV54 )
| ( union @ SV12 @ SV36 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(168,plain,
! [SV55: $i,SV37: $i,SV13: $i] :
( ( ~ ( intersection @ SV13 @ SV37 @ SV55 )
| ! [SY159: $i] :
( ~ ( member @ SY159 @ SV55 )
| ( member @ SY159 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(169,plain,
! [SV56: $i,SV38: $i,SV14: $i] :
( ( ~ ( intersection @ SV14 @ SV38 @ SV56 )
| ! [SY160: $i] :
( ~ ( member @ SY160 @ SV56 )
| ( member @ SY160 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV57: $i,SV39: $i,SV15: $i] :
( ( ~ ( intersection @ SV15 @ SV39 @ SV57 )
| ! [SY161: $i] :
( ~ ( member @ SY161 @ SV39 )
| ~ ( member @ SY161 @ SV15 )
| ( member @ SY161 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(171,plain,
! [SV58: $i,SV40: $i,SV16: $i] :
( ( ( member @ ( h @ SV16 @ SV40 @ SV58 ) @ SV58 )
| ( intersection @ SV16 @ SV40 @ SV58 )
| ( member @ ( h @ SV16 @ SV40 @ SV58 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV59: $i,SV41: $i,SV17: $i] :
( ( ( member @ ( h @ SV17 @ SV41 @ SV59 ) @ SV59 )
| ( intersection @ SV17 @ SV41 @ SV59 )
| ( member @ ( h @ SV17 @ SV41 @ SV59 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(173,plain,
! [SV60: $i,SV42: $i,SV18: $i] :
( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV60 )
| ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV42 )
| ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV18 )
| ( intersection @ SV18 @ SV42 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(174,plain,
! [SV61: $i,SV43: $i,SV19: $i] :
( ( ~ ( difference @ SV19 @ SV43 @ SV61 )
| ! [SY162: $i] :
( ~ ( member @ SY162 @ SV61 )
| ( member @ SY162 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(175,plain,
! [SV44: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV44 ) )
= $true )
| ( ( ! [SY149: $i] :
( ~ ( member @ SV20 @ SY149 )
| ! [SY150: $i] :
~ ( difference @ SY150 @ SV44 @ SY149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(176,plain,
! [SV45: $i,SV21: $i] :
( ( ( ~ ( member @ SV21 @ SV45 ) )
= $true )
| ( ( ! [SY151: $i,SY152: $i] :
( ~ ( difference @ SV45 @ SY151 @ SY152 )
| ( member @ SV21 @ SY152 )
| ( member @ SV21 @ SY151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(177,plain,
! [SV62: $i,SV46: $i,SV22: $i] :
( ( ( difference @ SV22 @ SV46 @ SV62 )
| ( member @ ( k @ SV22 @ SV46 @ SV62 ) @ SV22 )
| ( member @ ( k @ SV22 @ SV46 @ SV62 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(178,plain,
! [SV63: $i,SV47: $i,SV23: $i] :
( ( ~ ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV47 )
| ( difference @ SV23 @ SV47 @ SV63 )
| ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(179,plain,
! [SV64: $i,SV48: $i,SV24: $i] :
( ( ~ ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV64 )
| ~ ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV24 )
| ( difference @ SV24 @ SV48 @ SV64 )
| ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(180,plain,
! [SV25: $i,SV1: $i] :
( ( ( member @ SV1 @ SV25 )
= $false )
| ( ( ! [SY128: $i] :
( ~ ( subset @ SV25 @ SY128 )
| ( member @ SV1 @ SY128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(181,plain,
! [SV27: $i,SV3: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV3 @ SV27 ) @ SV27 )
= $false )
| ( ( subset @ SV3 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(182,plain,
! [SV28: $i,SV4: $i] :
( ( ( equal_sets @ SV4 @ SV28 )
= $false )
| ( ( subset @ SV4 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(183,plain,
! [SV29: $i,SV5: $i] :
( ( ( equal_sets @ SV5 @ SV29 )
= $false )
| ( ( subset @ SV29 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(184,plain,
! [SV30: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV30 )
= $false )
| ( ( ~ ( subset @ SV30 @ SV6 )
| ( equal_sets @ SV30 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(185,plain,
! [SV49: $i,SV31: $i,SV7: $i] :
( ( ( ~ ( union @ SV7 @ SV31 @ SV49 ) )
= $true )
| ( ( ! [SY156: $i] :
( ~ ( member @ SY156 @ SV49 )
| ( member @ SY156 @ SV7 )
| ( member @ SY156 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV50: $i,SV32: $i,SV8: $i] :
( ( ( ~ ( union @ SV8 @ SV32 @ SV50 ) )
= $true )
| ( ( ! [SY157: $i] :
( ~ ( member @ SY157 @ SV8 )
| ( member @ SY157 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV51: $i,SV33: $i,SV9: $i] :
( ( ( ~ ( union @ SV9 @ SV33 @ SV51 ) )
= $true )
| ( ( ! [SY158: $i] :
( ~ ( member @ SY158 @ SV33 )
| ( member @ SY158 @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV52: $i,SV34: $i,SV10: $i] :
( ( ( union @ SV10 @ SV34 @ SV52 )
= $true )
| ( ( ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV10 )
| ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV34 )
| ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV53: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV11 ) )
= $true )
| ( ( ~ ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV53 )
| ( union @ SV11 @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(190,plain,
! [SV54: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV36 ) )
= $true )
| ( ( ~ ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV54 )
| ( union @ SV12 @ SV36 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(191,plain,
! [SV55: $i,SV37: $i,SV13: $i] :
( ( ( ~ ( intersection @ SV13 @ SV37 @ SV55 ) )
= $true )
| ( ( ! [SY159: $i] :
( ~ ( member @ SY159 @ SV55 )
| ( member @ SY159 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(192,plain,
! [SV56: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( intersection @ SV14 @ SV38 @ SV56 ) )
= $true )
| ( ( ! [SY160: $i] :
( ~ ( member @ SY160 @ SV56 )
| ( member @ SY160 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(193,plain,
! [SV57: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( intersection @ SV15 @ SV39 @ SV57 ) )
= $true )
| ( ( ! [SY161: $i] :
( ~ ( member @ SY161 @ SV39 )
| ~ ( member @ SY161 @ SV15 )
| ( member @ SY161 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(194,plain,
! [SV58: $i,SV40: $i,SV16: $i] :
( ( ( member @ ( h @ SV16 @ SV40 @ SV58 ) @ SV58 )
= $true )
| ( ( ( intersection @ SV16 @ SV40 @ SV58 )
| ( member @ ( h @ SV16 @ SV40 @ SV58 ) @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV59: $i,SV41: $i,SV17: $i] :
( ( ( member @ ( h @ SV17 @ SV41 @ SV59 ) @ SV59 )
= $true )
| ( ( ( intersection @ SV17 @ SV41 @ SV59 )
| ( member @ ( h @ SV17 @ SV41 @ SV59 ) @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV60: $i,SV42: $i,SV18: $i] :
( ( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV60 ) )
= $true )
| ( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV42 )
| ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV18 )
| ( intersection @ SV18 @ SV42 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV61: $i,SV43: $i,SV19: $i] :
( ( ( ~ ( difference @ SV19 @ SV43 @ SV61 ) )
= $true )
| ( ( ! [SY162: $i] :
( ~ ( member @ SY162 @ SV61 )
| ( member @ SY162 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV44: $i,SV20: $i] :
( ( ( member @ SV20 @ SV44 )
= $false )
| ( ( ! [SY149: $i] :
( ~ ( member @ SV20 @ SY149 )
| ! [SY150: $i] :
~ ( difference @ SY150 @ SV44 @ SY149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV45: $i,SV21: $i] :
( ( ( member @ SV21 @ SV45 )
= $false )
| ( ( ! [SY151: $i,SY152: $i] :
( ~ ( difference @ SV45 @ SY151 @ SY152 )
| ( member @ SV21 @ SY152 )
| ( member @ SV21 @ SY151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV62: $i,SV46: $i,SV22: $i] :
( ( ( difference @ SV22 @ SV46 @ SV62 )
= $true )
| ( ( ( member @ ( k @ SV22 @ SV46 @ SV62 ) @ SV22 )
| ( member @ ( k @ SV22 @ SV46 @ SV62 ) @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV63: $i,SV47: $i,SV23: $i] :
( ( ( ~ ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV47 ) )
= $true )
| ( ( ( difference @ SV23 @ SV47 @ SV63 )
| ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV64: $i,SV48: $i,SV24: $i] :
( ( ( ~ ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV64 ) )
= $true )
| ( ( ~ ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV24 )
| ( difference @ SV24 @ SV48 @ SV64 )
| ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(203,plain,
! [SV1: $i,SV65: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV65 )
| ( member @ SV1 @ SV65 ) )
= $true )
| ( ( member @ SV1 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(204,plain,
! [SV6: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV6 ) )
= $true )
| ( ( equal_sets @ SV30 @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(205,plain,
! [SV49: $i,SV31: $i,SV7: $i] :
( ( ( union @ SV7 @ SV31 @ SV49 )
= $false )
| ( ( ! [SY156: $i] :
( ~ ( member @ SY156 @ SV49 )
| ( member @ SY156 @ SV7 )
| ( member @ SY156 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(206,plain,
! [SV50: $i,SV32: $i,SV8: $i] :
( ( ( union @ SV8 @ SV32 @ SV50 )
= $false )
| ( ( ! [SY157: $i] :
( ~ ( member @ SY157 @ SV8 )
| ( member @ SY157 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(207,plain,
! [SV51: $i,SV33: $i,SV9: $i] :
( ( ( union @ SV9 @ SV33 @ SV51 )
= $false )
| ( ( ! [SY158: $i] :
( ~ ( member @ SY158 @ SV33 )
| ( member @ SY158 @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(208,plain,
! [SV52: $i,SV34: $i,SV10: $i] :
( ( ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV10 )
= $true )
| ( ( ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV34 )
| ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV52 ) )
= $true )
| ( ( union @ SV10 @ SV34 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(209,plain,
! [SV53: $i,SV35: $i,SV11: $i] :
( ( ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV11 )
= $false )
| ( ( ~ ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV53 )
| ( union @ SV11 @ SV35 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(210,plain,
! [SV54: $i,SV36: $i,SV12: $i] :
( ( ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV36 )
= $false )
| ( ( ~ ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV54 )
| ( union @ SV12 @ SV36 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV55: $i,SV37: $i,SV13: $i] :
( ( ( intersection @ SV13 @ SV37 @ SV55 )
= $false )
| ( ( ! [SY159: $i] :
( ~ ( member @ SY159 @ SV55 )
| ( member @ SY159 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(212,plain,
! [SV56: $i,SV38: $i,SV14: $i] :
( ( ( intersection @ SV14 @ SV38 @ SV56 )
= $false )
| ( ( ! [SY160: $i] :
( ~ ( member @ SY160 @ SV56 )
| ( member @ SY160 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(213,plain,
! [SV57: $i,SV39: $i,SV15: $i] :
( ( ( intersection @ SV15 @ SV39 @ SV57 )
= $false )
| ( ( ! [SY161: $i] :
( ~ ( member @ SY161 @ SV39 )
| ~ ( member @ SY161 @ SV15 )
| ( member @ SY161 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(214,plain,
! [SV58: $i,SV40: $i,SV16: $i] :
( ( ( intersection @ SV16 @ SV40 @ SV58 )
= $true )
| ( ( member @ ( h @ SV16 @ SV40 @ SV58 ) @ SV16 )
= $true )
| ( ( member @ ( h @ SV16 @ SV40 @ SV58 ) @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(215,plain,
! [SV59: $i,SV41: $i,SV17: $i] :
( ( ( intersection @ SV17 @ SV41 @ SV59 )
= $true )
| ( ( member @ ( h @ SV17 @ SV41 @ SV59 ) @ SV41 )
= $true )
| ( ( member @ ( h @ SV17 @ SV41 @ SV59 ) @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(216,plain,
! [SV60: $i,SV42: $i,SV18: $i] :
( ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV60 )
= $false )
| ( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV42 )
| ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV18 )
| ( intersection @ SV18 @ SV42 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(217,plain,
! [SV61: $i,SV43: $i,SV19: $i] :
( ( ( difference @ SV19 @ SV43 @ SV61 )
= $false )
| ( ( ! [SY162: $i] :
( ~ ( member @ SY162 @ SV61 )
| ( member @ SY162 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(218,plain,
! [SV44: $i,SV66: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV66 )
| ! [SY163: $i] :
~ ( difference @ SY163 @ SV44 @ SV66 ) )
= $true )
| ( ( member @ SV20 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(219,plain,
! [SV21: $i,SV67: $i,SV45: $i] :
( ( ( ! [SY164: $i] :
( ~ ( difference @ SV45 @ SV67 @ SY164 )
| ( member @ SV21 @ SY164 )
| ( member @ SV21 @ SV67 ) ) )
= $true )
| ( ( member @ SV21 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(220,plain,
! [SV62: $i,SV46: $i,SV22: $i] :
( ( ( member @ ( k @ SV22 @ SV46 @ SV62 ) @ SV22 )
= $true )
| ( ( member @ ( k @ SV22 @ SV46 @ SV62 ) @ SV62 )
= $true )
| ( ( difference @ SV22 @ SV46 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV63: $i,SV47: $i,SV23: $i] :
( ( ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV47 )
= $false )
| ( ( ( difference @ SV23 @ SV47 @ SV63 )
| ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV64: $i,SV48: $i,SV24: $i] :
( ( ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV64 )
= $false )
| ( ( ~ ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV24 )
| ( difference @ SV24 @ SV48 @ SV64 )
| ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(223,plain,
! [SV1: $i,SV65: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV65 ) )
= $true )
| ( ( member @ SV1 @ SV65 )
= $true )
| ( ( member @ SV1 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(224,plain,
! [SV6: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV6 )
= $false )
| ( ( equal_sets @ SV30 @ SV6 )
= $true )
| ( ( subset @ SV6 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(225,plain,
! [SV31: $i,SV7: $i,SV49: $i,SV68: $i] :
( ( ( ~ ( member @ SV68 @ SV49 )
| ( member @ SV68 @ SV7 )
| ( member @ SV68 @ SV31 ) )
= $true )
| ( ( union @ SV7 @ SV31 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(226,plain,
! [SV32: $i,SV50: $i,SV8: $i,SV69: $i] :
( ( ( ~ ( member @ SV69 @ SV8 )
| ( member @ SV69 @ SV50 ) )
= $true )
| ( ( union @ SV8 @ SV32 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(227,plain,
! [SV9: $i,SV51: $i,SV33: $i,SV70: $i] :
( ( ( ~ ( member @ SV70 @ SV33 )
| ( member @ SV70 @ SV51 ) )
= $true )
| ( ( union @ SV9 @ SV33 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(228,plain,
! [SV52: $i,SV34: $i,SV10: $i] :
( ( ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV34 )
= $true )
| ( ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV52 )
= $true )
| ( ( member @ ( g @ SV10 @ SV34 @ SV52 ) @ SV10 )
= $true )
| ( ( union @ SV10 @ SV34 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(229,plain,
! [SV53: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV53 ) )
= $true )
| ( ( union @ SV11 @ SV35 @ SV53 )
= $true )
| ( ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(230,plain,
! [SV54: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV54 ) )
= $true )
| ( ( union @ SV12 @ SV36 @ SV54 )
= $true )
| ( ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(231,plain,
! [SV37: $i,SV13: $i,SV55: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV55 )
| ( member @ SV71 @ SV13 ) )
= $true )
| ( ( intersection @ SV13 @ SV37 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(232,plain,
! [SV14: $i,SV38: $i,SV56: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV56 )
| ( member @ SV72 @ SV38 ) )
= $true )
| ( ( intersection @ SV14 @ SV38 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(233,plain,
! [SV57: $i,SV15: $i,SV39: $i,SV73: $i] :
( ( ( ~ ( member @ SV73 @ SV39 )
| ~ ( member @ SV73 @ SV15 )
| ( member @ SV73 @ SV57 ) )
= $true )
| ( ( intersection @ SV15 @ SV39 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(234,plain,
! [SV60: $i,SV42: $i,SV18: $i] :
( ( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV42 ) )
= $true )
| ( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV18 )
| ( intersection @ SV18 @ SV42 @ SV60 ) )
= $true )
| ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(235,plain,
! [SV43: $i,SV19: $i,SV61: $i,SV74: $i] :
( ( ( ~ ( member @ SV74 @ SV61 )
| ( member @ SV74 @ SV19 ) )
= $true )
| ( ( difference @ SV19 @ SV43 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(236,plain,
! [SV44: $i,SV66: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV66 ) )
= $true )
| ( ( ! [SY163: $i] :
~ ( difference @ SY163 @ SV44 @ SV66 ) )
= $true )
| ( ( member @ SV20 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(237,plain,
! [SV21: $i,SV75: $i,SV67: $i,SV45: $i] :
( ( ( ~ ( difference @ SV45 @ SV67 @ SV75 )
| ( member @ SV21 @ SV75 )
| ( member @ SV21 @ SV67 ) )
= $true )
| ( ( member @ SV21 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(238,plain,
! [SV63: $i,SV47: $i,SV23: $i] :
( ( ( difference @ SV23 @ SV47 @ SV63 )
= $true )
| ( ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV63 )
= $true )
| ( ( member @ ( k @ SV23 @ SV47 @ SV63 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(239,plain,
! [SV64: $i,SV48: $i,SV24: $i] :
( ( ( ~ ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV24 ) )
= $true )
| ( ( ( difference @ SV24 @ SV48 @ SV64 )
| ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV48 ) )
= $true )
| ( ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(240,plain,
! [SV1: $i,SV65: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV65 )
= $false )
| ( ( member @ SV1 @ SV65 )
= $true )
| ( ( member @ SV1 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(241,plain,
! [SV31: $i,SV7: $i,SV49: $i,SV68: $i] :
( ( ( ~ ( member @ SV68 @ SV49 ) )
= $true )
| ( ( ( member @ SV68 @ SV7 )
| ( member @ SV68 @ SV31 ) )
= $true )
| ( ( union @ SV7 @ SV31 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(242,plain,
! [SV32: $i,SV50: $i,SV8: $i,SV69: $i] :
( ( ( ~ ( member @ SV69 @ SV8 ) )
= $true )
| ( ( member @ SV69 @ SV50 )
= $true )
| ( ( union @ SV8 @ SV32 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(243,plain,
! [SV9: $i,SV51: $i,SV33: $i,SV70: $i] :
( ( ( ~ ( member @ SV70 @ SV33 ) )
= $true )
| ( ( member @ SV70 @ SV51 )
= $true )
| ( ( union @ SV9 @ SV33 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(244,plain,
! [SV53: $i,SV35: $i,SV11: $i] :
( ( ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV53 )
= $false )
| ( ( union @ SV11 @ SV35 @ SV53 )
= $true )
| ( ( member @ ( g @ SV11 @ SV35 @ SV53 ) @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV54: $i,SV36: $i,SV12: $i] :
( ( ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV54 )
= $false )
| ( ( union @ SV12 @ SV36 @ SV54 )
= $true )
| ( ( member @ ( g @ SV12 @ SV36 @ SV54 ) @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV37: $i,SV13: $i,SV55: $i,SV71: $i] :
( ( ( ~ ( member @ SV71 @ SV55 ) )
= $true )
| ( ( member @ SV71 @ SV13 )
= $true )
| ( ( intersection @ SV13 @ SV37 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(247,plain,
! [SV14: $i,SV38: $i,SV56: $i,SV72: $i] :
( ( ( ~ ( member @ SV72 @ SV56 ) )
= $true )
| ( ( member @ SV72 @ SV38 )
= $true )
| ( ( intersection @ SV14 @ SV38 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV57: $i,SV15: $i,SV39: $i,SV73: $i] :
( ( ( ~ ( member @ SV73 @ SV39 ) )
= $true )
| ( ( ~ ( member @ SV73 @ SV15 )
| ( member @ SV73 @ SV57 ) )
= $true )
| ( ( intersection @ SV15 @ SV39 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV60: $i,SV42: $i,SV18: $i] :
( ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV42 )
= $false )
| ( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV18 )
| ( intersection @ SV18 @ SV42 @ SV60 ) )
= $true )
| ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(250,plain,
! [SV43: $i,SV19: $i,SV61: $i,SV74: $i] :
( ( ( ~ ( member @ SV74 @ SV61 ) )
= $true )
| ( ( member @ SV74 @ SV19 )
= $true )
| ( ( difference @ SV19 @ SV43 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(251,plain,
! [SV44: $i,SV66: $i,SV20: $i] :
( ( ( member @ SV20 @ SV66 )
= $false )
| ( ( ! [SY163: $i] :
~ ( difference @ SY163 @ SV44 @ SV66 ) )
= $true )
| ( ( member @ SV20 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(252,plain,
! [SV21: $i,SV75: $i,SV67: $i,SV45: $i] :
( ( ( ~ ( difference @ SV45 @ SV67 @ SV75 ) )
= $true )
| ( ( ( member @ SV21 @ SV75 )
| ( member @ SV21 @ SV67 ) )
= $true )
| ( ( member @ SV21 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(253,plain,
! [SV64: $i,SV48: $i,SV24: $i] :
( ( ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV24 )
= $false )
| ( ( ( difference @ SV24 @ SV48 @ SV64 )
| ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV48 ) )
= $true )
| ( ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(254,plain,
! [SV31: $i,SV7: $i,SV49: $i,SV68: $i] :
( ( ( member @ SV68 @ SV49 )
= $false )
| ( ( ( member @ SV68 @ SV7 )
| ( member @ SV68 @ SV31 ) )
= $true )
| ( ( union @ SV7 @ SV31 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(255,plain,
! [SV32: $i,SV50: $i,SV8: $i,SV69: $i] :
( ( ( member @ SV69 @ SV8 )
= $false )
| ( ( member @ SV69 @ SV50 )
= $true )
| ( ( union @ SV8 @ SV32 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(256,plain,
! [SV9: $i,SV51: $i,SV33: $i,SV70: $i] :
( ( ( member @ SV70 @ SV33 )
= $false )
| ( ( member @ SV70 @ SV51 )
= $true )
| ( ( union @ SV9 @ SV33 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(257,plain,
! [SV37: $i,SV13: $i,SV55: $i,SV71: $i] :
( ( ( member @ SV71 @ SV55 )
= $false )
| ( ( member @ SV71 @ SV13 )
= $true )
| ( ( intersection @ SV13 @ SV37 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(258,plain,
! [SV14: $i,SV38: $i,SV56: $i,SV72: $i] :
( ( ( member @ SV72 @ SV56 )
= $false )
| ( ( member @ SV72 @ SV38 )
= $true )
| ( ( intersection @ SV14 @ SV38 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(259,plain,
! [SV57: $i,SV15: $i,SV39: $i,SV73: $i] :
( ( ( member @ SV73 @ SV39 )
= $false )
| ( ( ~ ( member @ SV73 @ SV15 )
| ( member @ SV73 @ SV57 ) )
= $true )
| ( ( intersection @ SV15 @ SV39 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(260,plain,
! [SV60: $i,SV42: $i,SV18: $i] :
( ( ( ~ ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV18 ) )
= $true )
| ( ( intersection @ SV18 @ SV42 @ SV60 )
= $true )
| ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV42 )
= $false )
| ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(261,plain,
! [SV43: $i,SV19: $i,SV61: $i,SV74: $i] :
( ( ( member @ SV74 @ SV61 )
= $false )
| ( ( member @ SV74 @ SV19 )
= $true )
| ( ( difference @ SV19 @ SV43 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(262,plain,
! [SV20: $i,SV66: $i,SV44: $i,SV76: $i] :
( ( ( ~ ( difference @ SV76 @ SV44 @ SV66 ) )
= $true )
| ( ( member @ SV20 @ SV66 )
= $false )
| ( ( member @ SV20 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(263,plain,
! [SV21: $i,SV75: $i,SV67: $i,SV45: $i] :
( ( ( difference @ SV45 @ SV67 @ SV75 )
= $false )
| ( ( ( member @ SV21 @ SV75 )
| ( member @ SV21 @ SV67 ) )
= $true )
| ( ( member @ SV21 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV64: $i,SV48: $i,SV24: $i] :
( ( ( difference @ SV24 @ SV48 @ SV64 )
= $true )
| ( ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV48 )
= $true )
| ( ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV24 )
= $false )
| ( ( member @ ( k @ SV24 @ SV48 @ SV64 ) @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV49: $i,SV31: $i,SV7: $i,SV68: $i] :
( ( ( member @ SV68 @ SV7 )
= $true )
| ( ( member @ SV68 @ SV31 )
= $true )
| ( ( member @ SV68 @ SV49 )
= $false )
| ( ( union @ SV7 @ SV31 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV39: $i,SV57: $i,SV15: $i,SV73: $i] :
( ( ( ~ ( member @ SV73 @ SV15 ) )
= $true )
| ( ( member @ SV73 @ SV57 )
= $true )
| ( ( member @ SV73 @ SV39 )
= $false )
| ( ( intersection @ SV15 @ SV39 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(267,plain,
! [SV60: $i,SV42: $i,SV18: $i] :
( ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV18 )
= $false )
| ( ( intersection @ SV18 @ SV42 @ SV60 )
= $true )
| ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV42 )
= $false )
| ( ( member @ ( h @ SV18 @ SV42 @ SV60 ) @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(268,plain,
! [SV20: $i,SV66: $i,SV44: $i,SV76: $i] :
( ( ( difference @ SV76 @ SV44 @ SV66 )
= $false )
| ( ( member @ SV20 @ SV66 )
= $false )
| ( ( member @ SV20 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(269,plain,
! [SV45: $i,SV67: $i,SV75: $i,SV21: $i] :
( ( ( member @ SV21 @ SV75 )
= $true )
| ( ( member @ SV21 @ SV67 )
= $true )
| ( ( difference @ SV45 @ SV67 @ SV75 )
= $false )
| ( ( member @ SV21 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV39: $i,SV57: $i,SV15: $i,SV73: $i] :
( ( ( member @ SV73 @ SV15 )
= $false )
| ( ( member @ SV73 @ SV57 )
= $true )
| ( ( member @ SV73 @ SV39 )
= $false )
| ( ( intersection @ SV15 @ SV39 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(271,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[77,270,269,268,267,265,264,261,258,257,256,255,245,244,240,238,228,224,220,215,214,183,182,181,157,131,106,80,79,78]) ).
thf(272,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n009.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:26:02 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.22/3.02
% 16.22/3.02 No.of.Axioms: 29
% 16.22/3.02
% 16.22/3.02 Length.of.Defs: 0
% 16.22/3.02
% 16.22/3.02 Contains.Choice.Funs: false
% 16.22/3.02 ........
% 16.22/3.02
% 16.22/3.02 ********************************
% 16.22/3.02 * All subproblems solved! *
% 16.22/3.02 ********************************
% 16.22/3.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:29,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 16.22/3.02
% 16.22/3.02 %**** Beginning of derivation protocol ****
% 16.22/3.02 % SZS output start CNFRefutation
% See solution above
% 16.22/3.02
% 16.22/3.02 %**** End of derivation protocol ****
% 16.22/3.02 %**** no. of clauses in derivation: 272 ****
% 16.22/3.02 %**** clause counter: 271 ****
% 16.22/3.02
% 16.22/3.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:29,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------