TSTP Solution File: SET008-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n003.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 02:57:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of formulae : 214 ( 112 unt; 12 typ; 0 def)
% Number of atoms : 1167 ( 289 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2385 ( 247 ~; 387 |; 0 &;1751 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 590 ( 0 ^ 590 !; 0 ?; 590 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_aI_bDa,type,
aI_bDa: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bDa,type,
bDa: $i ).
thf(tp_difference,type,
difference: $i > $i > $i > $o ).
thf(tp_equal_sets,type,
equal_sets: $i > $i > $o ).
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(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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
thf(13,axiom,
! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
thf(14,axiom,
! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
thf(15,axiom,
! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
thf(16,axiom,
! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom2) ).
thf(17,axiom,
! [Subset: $i,Superset: $i] :
( ( subset @ Subset @ Superset )
| ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).
thf(18,axiom,
! [Element: $i,Subset: $i,Superset: $i] :
( ~ ( member @ Element @ Subset )
| ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).
thf(19,axiom,
difference @ b @ a @ bDa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_minus_a) ).
thf(20,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(21,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,negated_conjecture,
! [A: $i] :
~ ( member @ A @ aI_bDa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aI_bDa_is_empty) ).
thf(23,negated_conjecture,
~ ( intersection @ a @ bDa @ aI_bDa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bDa) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[21]) ).
thf(25,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(26,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(27,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(28,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(29,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(30,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(31,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(32,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(33,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(34,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(35,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(36,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(37,plain,
( ( ! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( subset @ Subset @ Superset )
| ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [Element: $i,Subset: $i,Superset: $i] :
( ~ ( member @ Element @ Subset )
| ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( difference @ b @ a @ bDa )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [A: $i] :
~ ( member @ A @ aI_bDa ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(45,plain,
( ( ~ ( intersection @ a @ bDa @ aI_bDa ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,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)],[25]) ).
thf(48,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)],[26]) ).
thf(49,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)],[28]) ).
thf(50,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)],[29]) ).
thf(51,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)],[30]) ).
thf(52,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)],[34]) ).
thf(53,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)],[35]) ).
thf(54,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)],[36]) ).
thf(55,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(56,plain,
( ( ! [Element: $i,Subset: $i] :
( ~ ( member @ Element @ Subset )
| ! [Superset: $i] :
( ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(57,plain,
( ( ~ ( intersection @ a @ bDa @ aI_bDa ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(58,plain,
( ( ! [A: $i] :
~ ( member @ A @ aI_bDa ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(59,plain,
( ( difference @ b @ a @ bDa )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(60,plain,
( ( ! [Element: $i,Subset: $i] :
( ~ ( member @ Element @ Subset )
| ! [Superset: $i] :
( ~ ( subset @ Subset @ Superset )
| ( member @ Element @ Superset ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(61,plain,
( ( ! [Subset: $i,Superset: $i] :
( ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(62,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ Subset @ Superset ) @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(63,plain,
( ( ! [Subset: $i,Superset: $i] :
( ~ ( equal_sets @ Subset @ Superset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(64,plain,
( ( ! [Superset: $i,Subset: $i] :
( ~ ( equal_sets @ Superset @ Subset )
| ( subset @ Subset @ Superset ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(65,plain,
( ( ! [Set1: $i,Set2: $i] :
( ~ ( subset @ Set1 @ Set2 )
| ~ ( subset @ Set2 @ Set1 )
| ( equal_sets @ Set2 @ Set1 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(66,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(67,plain,
( ( ! [Set1: $i,Set2: $i,Intersection: $i] :
( ~ ( intersection @ Set1 @ Set2 @ Intersection )
| ! [Element: $i] :
( ~ ( member @ Element @ Intersection )
| ( member @ Element @ Set2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
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(copy,[status(thm)],[52]) ).
thf(69,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)],[33]) ).
thf(70,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)],[32]) ).
thf(71,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)],[31]) ).
thf(72,plain,
( ( ! [Set1: $i,Set2: $i,Difference: $i] :
( ~ ( difference @ Set1 @ Set2 @ Difference )
| ! [Element: $i] :
( ~ ( member @ Element @ Difference )
| ( member @ Element @ Set1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(73,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)],[50]) ).
thf(74,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)],[49]) ).
thf(75,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)],[27]) ).
thf(76,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)],[48]) ).
thf(77,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)],[47]) ).
thf(78,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(79,plain,
( ( intersection @ a @ bDa @ aI_bDa )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(80,plain,
! [SV1: $i] :
( ( ~ ( member @ SV1 @ aI_bDa ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(81,plain,
! [SV2: $i] :
( ( ! [SY56: $i] :
( ~ ( member @ SV2 @ SY56 )
| ! [SY57: $i] :
( ~ ( subset @ SY56 @ SY57 )
| ( member @ SV2 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(82,plain,
! [SV3: $i] :
( ( ! [SY58: $i] :
( ( member @ ( member_of_1_not_of_2 @ SV3 @ SY58 ) @ SV3 )
| ( subset @ SV3 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV4: $i] :
( ( ! [SY59: $i] :
( ~ ( member @ ( member_of_1_not_of_2 @ SV4 @ SY59 ) @ SY59 )
| ( subset @ SV4 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(84,plain,
! [SV5: $i] :
( ( ! [SY60: $i] :
( ~ ( equal_sets @ SV5 @ SY60 )
| ( subset @ SV5 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(85,plain,
! [SV6: $i] :
( ( ! [SY61: $i] :
( ~ ( equal_sets @ SV6 @ SY61 )
| ( subset @ SY61 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
! [SV7: $i] :
( ( ! [SY62: $i] :
( ~ ( subset @ SV7 @ SY62 )
| ~ ( subset @ SY62 @ SV7 )
| ( equal_sets @ SY62 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV8: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ( intersection @ SV8 @ SY63 @ SY64 )
| ! [SY65: $i] :
( ~ ( member @ SY65 @ SY64 )
| ( member @ SY65 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV9: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( intersection @ SV9 @ SY66 @ SY67 )
| ! [Element: $i] :
( ~ ( member @ Element @ SY67 )
| ( member @ Element @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV10: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( intersection @ SV10 @ SY69 @ SY70 )
| ! [SY71: $i] :
( ~ ( member @ SY71 @ SY69 )
| ~ ( member @ SY71 @ SV10 )
| ( member @ SY71 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV11: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ( member @ ( h @ SV11 @ SY72 @ SY73 ) @ SY73 )
| ( intersection @ SV11 @ SY72 @ SY73 )
| ( member @ ( h @ SV11 @ SY72 @ SY73 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV12: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( member @ ( h @ SV12 @ SY74 @ SY75 ) @ SY75 )
| ( intersection @ SV12 @ SY74 @ SY75 )
| ( member @ ( h @ SV12 @ SY74 @ SY75 ) @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV13: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( member @ ( h @ SV13 @ SY76 @ SY77 ) @ SY77 )
| ~ ( member @ ( h @ SV13 @ SY76 @ SY77 ) @ SY76 )
| ~ ( member @ ( h @ SV13 @ SY76 @ SY77 ) @ SV13 )
| ( intersection @ SV13 @ SY76 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV14: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( difference @ SV14 @ SY78 @ SY79 )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SY79 )
| ( member @ SY80 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV15: $i] :
( ( ! [SY81: $i] :
( ~ ( member @ SV15 @ SY81 )
| ! [SY82: $i] :
( ~ ( member @ SV15 @ SY82 )
| ! [A_set: $i] :
~ ( difference @ A_set @ SY81 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV16: $i] :
( ( ! [SY84: $i] :
( ~ ( member @ SV16 @ SY84 )
| ! [SY85: $i,SY86: $i] :
( ~ ( difference @ SY84 @ SY85 @ SY86 )
| ( member @ SV16 @ SY86 )
| ( member @ SV16 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV17: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ( difference @ SV17 @ SY87 @ SY88 )
| ( member @ ( k @ SV17 @ SY87 @ SY88 ) @ SV17 )
| ( member @ ( k @ SV17 @ SY87 @ SY88 ) @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV18: $i] :
( ( ! [SY89: $i,SY90: $i] :
( ~ ( member @ ( k @ SV18 @ SY89 @ SY90 ) @ SY89 )
| ( difference @ SV18 @ SY89 @ SY90 )
| ( member @ ( k @ SV18 @ SY89 @ SY90 ) @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV19: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( member @ ( k @ SV19 @ SY91 @ SY92 ) @ SY92 )
| ~ ( member @ ( k @ SV19 @ SY91 @ SY92 ) @ SV19 )
| ( difference @ SV19 @ SY91 @ SY92 )
| ( member @ ( k @ SV19 @ SY91 @ SY92 ) @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV1: $i] :
( ( member @ SV1 @ aI_bDa )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(101,plain,
! [SV20: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ SV20 )
| ! [SY93: $i] :
( ~ ( subset @ SV20 @ SY93 )
| ( member @ SV2 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(102,plain,
! [SV21: $i,SV3: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV3 @ SV21 ) @ SV3 )
| ( subset @ SV3 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(103,plain,
! [SV22: $i,SV4: $i] :
( ( ~ ( member @ ( member_of_1_not_of_2 @ SV4 @ SV22 ) @ SV22 )
| ( subset @ SV4 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(104,plain,
! [SV23: $i,SV5: $i] :
( ( ~ ( equal_sets @ SV5 @ SV23 )
| ( subset @ SV5 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(105,plain,
! [SV24: $i,SV6: $i] :
( ( ~ ( equal_sets @ SV6 @ SV24 )
| ( subset @ SV24 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(106,plain,
! [SV25: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV25 )
| ~ ( subset @ SV25 @ SV7 )
| ( equal_sets @ SV25 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(107,plain,
! [SV26: $i,SV8: $i] :
( ( ! [SY94: $i] :
( ~ ( intersection @ SV8 @ SV26 @ SY94 )
| ! [SY65: $i] :
( ~ ( member @ SY65 @ SY94 )
| ( member @ SY65 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(108,plain,
! [SV27: $i,SV9: $i] :
( ( ! [SY96: $i] :
( ~ ( intersection @ SV9 @ SV27 @ SY96 )
| ! [SY97: $i] :
( ~ ( member @ SY97 @ SY96 )
| ( member @ SY97 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(109,plain,
! [SV28: $i,SV10: $i] :
( ( ! [SY98: $i] :
( ~ ( intersection @ SV10 @ SV28 @ SY98 )
| ! [SY99: $i] :
( ~ ( member @ SY99 @ SV28 )
| ~ ( member @ SY99 @ SV10 )
| ( member @ SY99 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(110,plain,
! [SV29: $i,SV11: $i] :
( ( ! [SY100: $i] :
( ( member @ ( h @ SV11 @ SV29 @ SY100 ) @ SY100 )
| ( intersection @ SV11 @ SV29 @ SY100 )
| ( member @ ( h @ SV11 @ SV29 @ SY100 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(111,plain,
! [SV30: $i,SV12: $i] :
( ( ! [SY101: $i] :
( ( member @ ( h @ SV12 @ SV30 @ SY101 ) @ SY101 )
| ( intersection @ SV12 @ SV30 @ SY101 )
| ( member @ ( h @ SV12 @ SV30 @ SY101 ) @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(112,plain,
! [SV31: $i,SV13: $i] :
( ( ! [SY102: $i] :
( ~ ( member @ ( h @ SV13 @ SV31 @ SY102 ) @ SY102 )
| ~ ( member @ ( h @ SV13 @ SV31 @ SY102 ) @ SV31 )
| ~ ( member @ ( h @ SV13 @ SV31 @ SY102 ) @ SV13 )
| ( intersection @ SV13 @ SV31 @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV32: $i,SV14: $i] :
( ( ! [SY103: $i] :
( ~ ( difference @ SV14 @ SV32 @ SY103 )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SY103 )
| ( member @ SY80 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV33: $i,SV15: $i] :
( ( ~ ( member @ SV15 @ SV33 )
| ! [SY105: $i] :
( ~ ( member @ SV15 @ SY105 )
| ! [SY106: $i] :
~ ( difference @ SY106 @ SV33 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(115,plain,
! [SV34: $i,SV16: $i] :
( ( ~ ( member @ SV16 @ SV34 )
| ! [SY107: $i,SY108: $i] :
( ~ ( difference @ SV34 @ SY107 @ SY108 )
| ( member @ SV16 @ SY108 )
| ( member @ SV16 @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(116,plain,
! [SV35: $i,SV17: $i] :
( ( ! [SY109: $i] :
( ( difference @ SV17 @ SV35 @ SY109 )
| ( member @ ( k @ SV17 @ SV35 @ SY109 ) @ SV17 )
| ( member @ ( k @ SV17 @ SV35 @ SY109 ) @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(117,plain,
! [SV36: $i,SV18: $i] :
( ( ! [SY110: $i] :
( ~ ( member @ ( k @ SV18 @ SV36 @ SY110 ) @ SV36 )
| ( difference @ SV18 @ SV36 @ SY110 )
| ( member @ ( k @ SV18 @ SV36 @ SY110 ) @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(118,plain,
! [SV37: $i,SV19: $i] :
( ( ! [SY111: $i] :
( ~ ( member @ ( k @ SV19 @ SV37 @ SY111 ) @ SY111 )
| ~ ( member @ ( k @ SV19 @ SV37 @ SY111 ) @ SV19 )
| ( difference @ SV19 @ SV37 @ SY111 )
| ( member @ ( k @ SV19 @ SV37 @ SY111 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(119,plain,
! [SV20: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV20 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( subset @ SV20 @ SY93 )
| ( member @ SV2 @ SY93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV21: $i,SV3: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV3 @ SV21 ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV22: $i,SV4: $i] :
( ( ( ~ ( member @ ( member_of_1_not_of_2 @ SV4 @ SV22 ) @ SV22 ) )
= $true )
| ( ( subset @ SV4 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV23: $i,SV5: $i] :
( ( ( ~ ( equal_sets @ SV5 @ SV23 ) )
= $true )
| ( ( subset @ SV5 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV24: $i,SV6: $i] :
( ( ( ~ ( equal_sets @ SV6 @ SV24 ) )
= $true )
| ( ( subset @ SV24 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV25: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV25 ) )
= $true )
| ( ( ~ ( subset @ SV25 @ SV7 )
| ( equal_sets @ SV25 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV38: $i,SV26: $i,SV8: $i] :
( ( ~ ( intersection @ SV8 @ SV26 @ SV38 )
| ! [SY112: $i] :
( ~ ( member @ SY112 @ SV38 )
| ( member @ SY112 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV39: $i,SV27: $i,SV9: $i] :
( ( ~ ( intersection @ SV9 @ SV27 @ SV39 )
| ! [SY113: $i] :
( ~ ( member @ SY113 @ SV39 )
| ( member @ SY113 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV40: $i,SV28: $i,SV10: $i] :
( ( ~ ( intersection @ SV10 @ SV28 @ SV40 )
| ! [SY114: $i] :
( ~ ( member @ SY114 @ SV28 )
| ~ ( member @ SY114 @ SV10 )
| ( member @ SY114 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV41: $i,SV29: $i,SV11: $i] :
( ( ( member @ ( h @ SV11 @ SV29 @ SV41 ) @ SV41 )
| ( intersection @ SV11 @ SV29 @ SV41 )
| ( member @ ( h @ SV11 @ SV29 @ SV41 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV42: $i,SV30: $i,SV12: $i] :
( ( ( member @ ( h @ SV12 @ SV30 @ SV42 ) @ SV42 )
| ( intersection @ SV12 @ SV30 @ SV42 )
| ( member @ ( h @ SV12 @ SV30 @ SV42 ) @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV43: $i,SV31: $i,SV13: $i] :
( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV43 )
| ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV31 )
| ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV13 )
| ( intersection @ SV13 @ SV31 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV44: $i,SV32: $i,SV14: $i] :
( ( ~ ( difference @ SV14 @ SV32 @ SV44 )
| ! [SY115: $i] :
( ~ ( member @ SY115 @ SV44 )
| ( member @ SY115 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV33: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV33 ) )
= $true )
| ( ( ! [SY105: $i] :
( ~ ( member @ SV15 @ SY105 )
| ! [SY106: $i] :
~ ( difference @ SY106 @ SV33 @ SY105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV34: $i,SV16: $i] :
( ( ( ~ ( member @ SV16 @ SV34 ) )
= $true )
| ( ( ! [SY107: $i,SY108: $i] :
( ~ ( difference @ SV34 @ SY107 @ SY108 )
| ( member @ SV16 @ SY108 )
| ( member @ SV16 @ SY107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV45: $i,SV35: $i,SV17: $i] :
( ( ( difference @ SV17 @ SV35 @ SV45 )
| ( member @ ( k @ SV17 @ SV35 @ SV45 ) @ SV17 )
| ( member @ ( k @ SV17 @ SV35 @ SV45 ) @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV46: $i,SV36: $i,SV18: $i] :
( ( ~ ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV36 )
| ( difference @ SV18 @ SV36 @ SV46 )
| ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV47: $i,SV37: $i,SV19: $i] :
( ( ~ ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV47 )
| ~ ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV19 )
| ( difference @ SV19 @ SV37 @ SV47 )
| ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(137,plain,
! [SV20: $i,SV2: $i] :
( ( ( member @ SV2 @ SV20 )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( subset @ SV20 @ SY93 )
| ( member @ SV2 @ SY93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(138,plain,
! [SV22: $i,SV4: $i] :
( ( ( member @ ( member_of_1_not_of_2 @ SV4 @ SV22 ) @ SV22 )
= $false )
| ( ( subset @ SV4 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV23: $i,SV5: $i] :
( ( ( equal_sets @ SV5 @ SV23 )
= $false )
| ( ( subset @ SV5 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV24: $i,SV6: $i] :
( ( ( equal_sets @ SV6 @ SV24 )
= $false )
| ( ( subset @ SV24 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(141,plain,
! [SV25: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV25 )
= $false )
| ( ( ~ ( subset @ SV25 @ SV7 )
| ( equal_sets @ SV25 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(142,plain,
! [SV38: $i,SV26: $i,SV8: $i] :
( ( ( ~ ( intersection @ SV8 @ SV26 @ SV38 ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( member @ SY112 @ SV38 )
| ( member @ SY112 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(143,plain,
! [SV39: $i,SV27: $i,SV9: $i] :
( ( ( ~ ( intersection @ SV9 @ SV27 @ SV39 ) )
= $true )
| ( ( ! [SY113: $i] :
( ~ ( member @ SY113 @ SV39 )
| ( member @ SY113 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(144,plain,
! [SV40: $i,SV28: $i,SV10: $i] :
( ( ( ~ ( intersection @ SV10 @ SV28 @ SV40 ) )
= $true )
| ( ( ! [SY114: $i] :
( ~ ( member @ SY114 @ SV28 )
| ~ ( member @ SY114 @ SV10 )
| ( member @ SY114 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(145,plain,
! [SV41: $i,SV29: $i,SV11: $i] :
( ( ( member @ ( h @ SV11 @ SV29 @ SV41 ) @ SV41 )
= $true )
| ( ( ( intersection @ SV11 @ SV29 @ SV41 )
| ( member @ ( h @ SV11 @ SV29 @ SV41 ) @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(146,plain,
! [SV42: $i,SV30: $i,SV12: $i] :
( ( ( member @ ( h @ SV12 @ SV30 @ SV42 ) @ SV42 )
= $true )
| ( ( ( intersection @ SV12 @ SV30 @ SV42 )
| ( member @ ( h @ SV12 @ SV30 @ SV42 ) @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(147,plain,
! [SV43: $i,SV31: $i,SV13: $i] :
( ( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV43 ) )
= $true )
| ( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV31 )
| ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV13 )
| ( intersection @ SV13 @ SV31 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV44: $i,SV32: $i,SV14: $i] :
( ( ( ~ ( difference @ SV14 @ SV32 @ SV44 ) )
= $true )
| ( ( ! [SY115: $i] :
( ~ ( member @ SY115 @ SV44 )
| ( member @ SY115 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(149,plain,
! [SV33: $i,SV15: $i] :
( ( ( member @ SV15 @ SV33 )
= $false )
| ( ( ! [SY105: $i] :
( ~ ( member @ SV15 @ SY105 )
| ! [SY106: $i] :
~ ( difference @ SY106 @ SV33 @ SY105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(150,plain,
! [SV34: $i,SV16: $i] :
( ( ( member @ SV16 @ SV34 )
= $false )
| ( ( ! [SY107: $i,SY108: $i] :
( ~ ( difference @ SV34 @ SY107 @ SY108 )
| ( member @ SV16 @ SY108 )
| ( member @ SV16 @ SY107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(151,plain,
! [SV45: $i,SV35: $i,SV17: $i] :
( ( ( difference @ SV17 @ SV35 @ SV45 )
= $true )
| ( ( ( member @ ( k @ SV17 @ SV35 @ SV45 ) @ SV17 )
| ( member @ ( k @ SV17 @ SV35 @ SV45 ) @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(152,plain,
! [SV46: $i,SV36: $i,SV18: $i] :
( ( ( ~ ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV36 ) )
= $true )
| ( ( ( difference @ SV18 @ SV36 @ SV46 )
| ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(153,plain,
! [SV47: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV19 )
| ( difference @ SV19 @ SV37 @ SV47 )
| ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(154,plain,
! [SV2: $i,SV48: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV48 )
| ( member @ SV2 @ SV48 ) )
= $true )
| ( ( member @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(155,plain,
! [SV7: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV7 ) )
= $true )
| ( ( equal_sets @ SV25 @ SV7 )
= $true )
| ( ( subset @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV38: $i,SV26: $i,SV8: $i] :
( ( ( intersection @ SV8 @ SV26 @ SV38 )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( member @ SY112 @ SV38 )
| ( member @ SY112 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV39: $i,SV27: $i,SV9: $i] :
( ( ( intersection @ SV9 @ SV27 @ SV39 )
= $false )
| ( ( ! [SY113: $i] :
( ~ ( member @ SY113 @ SV39 )
| ( member @ SY113 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV40: $i,SV28: $i,SV10: $i] :
( ( ( intersection @ SV10 @ SV28 @ SV40 )
= $false )
| ( ( ! [SY114: $i] :
( ~ ( member @ SY114 @ SV28 )
| ~ ( member @ SY114 @ SV10 )
| ( member @ SY114 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV41: $i,SV29: $i,SV11: $i] :
( ( ( intersection @ SV11 @ SV29 @ SV41 )
= $true )
| ( ( member @ ( h @ SV11 @ SV29 @ SV41 ) @ SV11 )
= $true )
| ( ( member @ ( h @ SV11 @ SV29 @ SV41 ) @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(160,plain,
! [SV42: $i,SV30: $i,SV12: $i] :
( ( ( intersection @ SV12 @ SV30 @ SV42 )
= $true )
| ( ( member @ ( h @ SV12 @ SV30 @ SV42 ) @ SV30 )
= $true )
| ( ( member @ ( h @ SV12 @ SV30 @ SV42 ) @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV43: $i,SV31: $i,SV13: $i] :
( ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV43 )
= $false )
| ( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV31 )
| ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV13 )
| ( intersection @ SV13 @ SV31 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(162,plain,
! [SV44: $i,SV32: $i,SV14: $i] :
( ( ( difference @ SV14 @ SV32 @ SV44 )
= $false )
| ( ( ! [SY115: $i] :
( ~ ( member @ SY115 @ SV44 )
| ( member @ SY115 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(163,plain,
! [SV33: $i,SV49: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV49 )
| ! [SY116: $i] :
~ ( difference @ SY116 @ SV33 @ SV49 ) )
= $true )
| ( ( member @ SV15 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV16: $i,SV50: $i,SV34: $i] :
( ( ( ! [SY117: $i] :
( ~ ( difference @ SV34 @ SV50 @ SY117 )
| ( member @ SV16 @ SY117 )
| ( member @ SV16 @ SV50 ) ) )
= $true )
| ( ( member @ SV16 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV45: $i,SV35: $i,SV17: $i] :
( ( ( member @ ( k @ SV17 @ SV35 @ SV45 ) @ SV17 )
= $true )
| ( ( member @ ( k @ SV17 @ SV35 @ SV45 ) @ SV45 )
= $true )
| ( ( difference @ SV17 @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(166,plain,
! [SV46: $i,SV36: $i,SV18: $i] :
( ( ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV36 )
= $false )
| ( ( ( difference @ SV18 @ SV36 @ SV46 )
| ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(167,plain,
! [SV47: $i,SV37: $i,SV19: $i] :
( ( ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV19 )
| ( difference @ SV19 @ SV37 @ SV47 )
| ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(168,plain,
! [SV2: $i,SV48: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV48 ) )
= $true )
| ( ( member @ SV2 @ SV48 )
= $true )
| ( ( member @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(169,plain,
! [SV7: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV7 )
= $false )
| ( ( equal_sets @ SV25 @ SV7 )
= $true )
| ( ( subset @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(170,plain,
! [SV26: $i,SV8: $i,SV38: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ SV38 )
| ( member @ SV51 @ SV8 ) )
= $true )
| ( ( intersection @ SV8 @ SV26 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(171,plain,
! [SV9: $i,SV27: $i,SV39: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ SV39 )
| ( member @ SV52 @ SV27 ) )
= $true )
| ( ( intersection @ SV9 @ SV27 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(172,plain,
! [SV40: $i,SV10: $i,SV28: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ SV28 )
| ~ ( member @ SV53 @ SV10 )
| ( member @ SV53 @ SV40 ) )
= $true )
| ( ( intersection @ SV10 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV43: $i,SV31: $i,SV13: $i] :
( ( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV31 ) )
= $true )
| ( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV13 )
| ( intersection @ SV13 @ SV31 @ SV43 ) )
= $true )
| ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV32: $i,SV14: $i,SV44: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ SV44 )
| ( member @ SV54 @ SV14 ) )
= $true )
| ( ( difference @ SV14 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV33: $i,SV49: $i,SV15: $i] :
( ( ( ~ ( member @ SV15 @ SV49 ) )
= $true )
| ( ( ! [SY116: $i] :
~ ( difference @ SY116 @ SV33 @ SV49 ) )
= $true )
| ( ( member @ SV15 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV16: $i,SV55: $i,SV50: $i,SV34: $i] :
( ( ( ~ ( difference @ SV34 @ SV50 @ SV55 )
| ( member @ SV16 @ SV55 )
| ( member @ SV16 @ SV50 ) )
= $true )
| ( ( member @ SV16 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV46: $i,SV36: $i,SV18: $i] :
( ( ( difference @ SV18 @ SV36 @ SV46 )
= $true )
| ( ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV46 )
= $true )
| ( ( member @ ( k @ SV18 @ SV36 @ SV46 ) @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(178,plain,
! [SV47: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV19 ) )
= $true )
| ( ( ( difference @ SV19 @ SV37 @ SV47 )
| ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV37 ) )
= $true )
| ( ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(179,plain,
! [SV2: $i,SV48: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV48 )
= $false )
| ( ( member @ SV2 @ SV48 )
= $true )
| ( ( member @ SV2 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(180,plain,
! [SV26: $i,SV8: $i,SV38: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ SV38 ) )
= $true )
| ( ( member @ SV51 @ SV8 )
= $true )
| ( ( intersection @ SV8 @ SV26 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV9: $i,SV27: $i,SV39: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ SV39 ) )
= $true )
| ( ( member @ SV52 @ SV27 )
= $true )
| ( ( intersection @ SV9 @ SV27 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV40: $i,SV10: $i,SV28: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ SV28 ) )
= $true )
| ( ( ~ ( member @ SV53 @ SV10 )
| ( member @ SV53 @ SV40 ) )
= $true )
| ( ( intersection @ SV10 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV43: $i,SV31: $i,SV13: $i] :
( ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV31 )
= $false )
| ( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV13 )
| ( intersection @ SV13 @ SV31 @ SV43 ) )
= $true )
| ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV32: $i,SV14: $i,SV44: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ SV44 ) )
= $true )
| ( ( member @ SV54 @ SV14 )
= $true )
| ( ( difference @ SV14 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV33: $i,SV49: $i,SV15: $i] :
( ( ( member @ SV15 @ SV49 )
= $false )
| ( ( ! [SY116: $i] :
~ ( difference @ SY116 @ SV33 @ SV49 ) )
= $true )
| ( ( member @ SV15 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV16: $i,SV55: $i,SV50: $i,SV34: $i] :
( ( ( ~ ( difference @ SV34 @ SV50 @ SV55 ) )
= $true )
| ( ( ( member @ SV16 @ SV55 )
| ( member @ SV16 @ SV50 ) )
= $true )
| ( ( member @ SV16 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV47: $i,SV37: $i,SV19: $i] :
( ( ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV19 )
= $false )
| ( ( ( difference @ SV19 @ SV37 @ SV47 )
| ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV37 ) )
= $true )
| ( ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV26: $i,SV8: $i,SV38: $i,SV51: $i] :
( ( ( member @ SV51 @ SV38 )
= $false )
| ( ( member @ SV51 @ SV8 )
= $true )
| ( ( intersection @ SV8 @ SV26 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV9: $i,SV27: $i,SV39: $i,SV52: $i] :
( ( ( member @ SV52 @ SV39 )
= $false )
| ( ( member @ SV52 @ SV27 )
= $true )
| ( ( intersection @ SV9 @ SV27 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV40: $i,SV10: $i,SV28: $i,SV53: $i] :
( ( ( member @ SV53 @ SV28 )
= $false )
| ( ( ~ ( member @ SV53 @ SV10 )
| ( member @ SV53 @ SV40 ) )
= $true )
| ( ( intersection @ SV10 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV43: $i,SV31: $i,SV13: $i] :
( ( ( ~ ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV13 ) )
= $true )
| ( ( intersection @ SV13 @ SV31 @ SV43 )
= $true )
| ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV31 )
= $false )
| ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV32: $i,SV14: $i,SV44: $i,SV54: $i] :
( ( ( member @ SV54 @ SV44 )
= $false )
| ( ( member @ SV54 @ SV14 )
= $true )
| ( ( difference @ SV14 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV15: $i,SV49: $i,SV33: $i,SV56: $i] :
( ( ( ~ ( difference @ SV56 @ SV33 @ SV49 ) )
= $true )
| ( ( member @ SV15 @ SV49 )
= $false )
| ( ( member @ SV15 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV16: $i,SV55: $i,SV50: $i,SV34: $i] :
( ( ( difference @ SV34 @ SV50 @ SV55 )
= $false )
| ( ( ( member @ SV16 @ SV55 )
| ( member @ SV16 @ SV50 ) )
= $true )
| ( ( member @ SV16 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV47: $i,SV37: $i,SV19: $i] :
( ( ( difference @ SV19 @ SV37 @ SV47 )
= $true )
| ( ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV37 )
= $true )
| ( ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV19 )
= $false )
| ( ( member @ ( k @ SV19 @ SV37 @ SV47 ) @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV28: $i,SV40: $i,SV10: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ SV10 ) )
= $true )
| ( ( member @ SV53 @ SV40 )
= $true )
| ( ( member @ SV53 @ SV28 )
= $false )
| ( ( intersection @ SV10 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(197,plain,
! [SV43: $i,SV31: $i,SV13: $i] :
( ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV13 )
= $false )
| ( ( intersection @ SV13 @ SV31 @ SV43 )
= $true )
| ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV31 )
= $false )
| ( ( member @ ( h @ SV13 @ SV31 @ SV43 ) @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(198,plain,
! [SV15: $i,SV49: $i,SV33: $i,SV56: $i] :
( ( ( difference @ SV56 @ SV33 @ SV49 )
= $false )
| ( ( member @ SV15 @ SV49 )
= $false )
| ( ( member @ SV15 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV34: $i,SV50: $i,SV55: $i,SV16: $i] :
( ( ( member @ SV16 @ SV55 )
= $true )
| ( ( member @ SV16 @ SV50 )
= $true )
| ( ( difference @ SV34 @ SV50 @ SV55 )
= $false )
| ( ( member @ SV16 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(200,plain,
! [SV28: $i,SV40: $i,SV10: $i,SV53: $i] :
( ( ( member @ SV53 @ SV10 )
= $false )
| ( ( member @ SV53 @ SV40 )
= $true )
| ( ( member @ SV53 @ SV28 )
= $false )
| ( ( intersection @ SV10 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(201,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,200,199,198,197,195,192,189,188,179,177,169,165,160,159,140,139,138,120,100,99,79]) ).
thf(202,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 20:20:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 21
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.38 (rf:0,axioms:21,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:23,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.19/0.49
% 0.19/0.49 ********************************
% 0.19/0.49 * All subproblems solved! *
% 0.19/0.49 ********************************
% 0.19/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:201,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.50
% 0.19/0.50 %**** Beginning of derivation protocol ****
% 0.19/0.50 % SZS output start CNFRefutation
% See solution above
% 0.19/0.50
% 0.19/0.50 %**** End of derivation protocol ****
% 0.19/0.50 %**** no. of clauses in derivation: 202 ****
% 0.19/0.50 %**** clause counter: 201 ****
% 0.19/0.50
% 0.19/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:201,loop_count:0,foatp_calls:1,translation:fof_full)
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