TSTP Solution File: SET622+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:03:36 EDT 2022
% Result : Theorem 0.76s 0.94s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 244 ( 161 unt; 11 typ; 0 def)
% Number of atoms : 1299 ( 429 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 2872 ( 486 ~; 414 |; 32 &;1924 @)
% ( 14 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 718 ( 0 ^ 718 !; 0 ?; 718 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY37,type,
sK2_SY37: $i ).
thf(tp_sK3_SY39,type,
sK3_SY39: $i ).
thf(tp_sK4_D,type,
sK4_D: $i > $i > $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_symmetric_difference,type,
symmetric_difference: $i > $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(1,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(2,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(3,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(6,axiom,
! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(7,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(8,axiom,
! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(9,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
thf(10,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
thf(11,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(12,axiom,
! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( difference @ ( union @ B @ C ) @ ( intersection @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
thf(13,axiom,
! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( difference @ C @ D ) )
= ( union @ ( difference @ B @ C ) @ ( intersection @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_difference_union2) ).
thf(14,axiom,
! [B: $i,C: $i,D: $i] :
( ( intersection @ ( intersection @ B @ C ) @ D )
= ( intersection @ B @ ( intersection @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_intersection) ).
thf(15,conjecture,
! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( symmetric_difference @ C @ D ) )
= ( union @ ( difference @ B @ ( union @ C @ D ) ) @ ( intersection @ ( intersection @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th98) ).
thf(16,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( symmetric_difference @ C @ D ) )
= ( union @ ( difference @ B @ ( union @ C @ D ) ) @ ( intersection @ ( intersection @ B @ C ) @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( symmetric_difference @ C @ D ) )
= ( union @ ( difference @ B @ ( union @ C @ D ) ) @ ( intersection @ ( intersection @ B @ C ) @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( union @ B @ C ) )
<=> ( ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( difference @ ( union @ B @ C ) @ ( intersection @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( difference @ C @ D ) )
= ( union @ ( difference @ B @ C ) @ ( intersection @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersection @ ( intersection @ B @ C ) @ D )
= ( intersection @ B @ ( intersection @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(32,plain,
( ( ! [SY37: $i,SY38: $i] :
( ( difference @ sK1_B @ ( symmetric_difference @ SY37 @ SY38 ) )
= ( union @ ( difference @ sK1_B @ ( union @ SY37 @ SY38 ) ) @ ( intersection @ ( intersection @ sK1_B @ SY37 ) @ SY38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(33,plain,
( ( ! [SY39: $i] :
( ( difference @ sK1_B @ ( symmetric_difference @ sK2_SY37 @ SY39 ) )
= ( union @ ( difference @ sK1_B @ ( union @ sK2_SY37 @ SY39 ) ) @ ( intersection @ ( intersection @ sK1_B @ sK2_SY37 ) @ SY39 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[32]) ).
thf(34,plain,
( ( ( difference @ sK1_B @ ( symmetric_difference @ sK2_SY37 @ sK3_SY39 ) )
= ( union @ ( difference @ sK1_B @ ( union @ sK2_SY37 @ sK3_SY39 ) ) @ ( intersection @ ( intersection @ sK1_B @ sK2_SY37 ) @ sK3_SY39 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(35,plain,
( ( ( ( difference @ sK1_B @ ( symmetric_difference @ sK2_SY37 @ sK3_SY39 ) )
!= ( union @ ( difference @ sK1_B @ ( union @ sK2_SY37 @ sK3_SY39 ) ) @ ( intersection @ ( intersection @ sK1_B @ sK2_SY37 ) @ sK3_SY39 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(36,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK4_D @ C @ B ) @ B )
& ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(37,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK5_D @ C @ B ) @ B )
| ~ ( member @ ( sK5_D @ C @ B ) @ C ) )
& ( ( member @ ( sK5_D @ C @ B ) @ B )
| ( member @ ( sK5_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(38,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ C @ B )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(39,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C )
| ( member @ D @ ( difference @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ~ ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(40,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C )
| ( member @ D @ ( intersection @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(41,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ ( union @ B @ C ) )
| ( member @ D @ B )
| ( member @ D @ C ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ ( union @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ ( union @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(42,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersection @ ( intersection @ B @ C ) @ D )
= ( intersection @ B @ ( intersection @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( difference @ C @ D ) )
= ( union @ ( difference @ B @ C ) @ ( intersection @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( difference @ ( union @ B @ C ) @ ( intersection @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ ( union @ B @ C ) )
| ( member @ D @ B )
| ( member @ D @ C ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ ( union @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ ( union @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(46,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ~ ( member @ D @ C )
| ( member @ D @ ( intersection @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( intersection @ B @ C ) )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(47,plain,
( ( ! [B: $i] :
( ! [C: $i,D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C )
| ( member @ D @ ( difference @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ( member @ D @ B ) )
& ! [C: $i,D: $i] :
( ~ ( member @ D @ ( difference @ B @ C ) )
| ~ ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(48,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( union @ ( difference @ B @ C ) @ ( difference @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ~ ( subset @ C @ B )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( subset @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(50,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [B: $i,C: $i] :
( ( symmetric_difference @ B @ C )
= ( symmetric_difference @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [B: $i,C: $i] :
( ( ( ~ ( member @ ( sK5_D @ C @ B ) @ B )
| ~ ( member @ ( sK5_D @ C @ B ) @ C ) )
& ( ( member @ ( sK5_D @ C @ B ) @ B )
| ( member @ ( sK5_D @ C @ B ) @ C ) ) )
| ( B = C ) )
& ! [B: $i,C: $i] :
( ( B != C )
| ( ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) )
& ! [D: $i] :
( ~ ( member @ D @ C )
| ( member @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(54,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK4_D @ C @ B ) @ B )
& ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ! [D: $i] :
( ~ ( member @ D @ B )
| ( member @ D @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(55,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(56,plain,
( ( ( ( difference @ sK1_B @ ( symmetric_difference @ sK2_SY37 @ sK3_SY39 ) )
!= ( union @ ( difference @ sK1_B @ ( union @ sK2_SY37 @ sK3_SY39 ) ) @ ( intersection @ ( intersection @ sK1_B @ sK2_SY37 ) @ sK3_SY39 ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(57,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( intersection @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(58,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( difference @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
| ~ ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(59,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(60,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(61,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ ( union @ SX0 @ SX1 ) )
| ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ ( union @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(62,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(63,plain,
! [SV1: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( intersection @ ( intersection @ SV1 @ SY40 ) @ SY41 )
= ( intersection @ SV1 @ ( intersection @ SY40 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(64,plain,
! [SV2: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( difference @ SV2 @ ( difference @ SY42 @ SY43 ) )
= ( union @ ( difference @ SV2 @ SY42 ) @ ( intersection @ SV2 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(65,plain,
! [SV3: $i] :
( ( ! [SY44: $i] :
( ( symmetric_difference @ SV3 @ SY44 )
= ( difference @ ( union @ SV3 @ SY44 ) @ ( intersection @ SV3 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(66,plain,
! [SV4: $i] :
( ( ! [SY45: $i] :
( ( symmetric_difference @ SV4 @ SY45 )
= ( union @ ( difference @ SV4 @ SY45 ) @ ( difference @ SY45 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(67,plain,
! [SV5: $i] :
( ( ! [SY46: $i] :
( ( union @ SV5 @ SY46 )
= ( union @ SY46 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV6: $i] :
( ( ! [SY47: $i] :
( ( intersection @ SV6 @ SY47 )
= ( intersection @ SY47 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV7: $i] :
( ( ! [SY48: $i] :
( ( symmetric_difference @ SV7 @ SY48 )
= ( symmetric_difference @ SY48 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV8: $i] :
( ( subset @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(71,plain,
( ( ( difference @ sK1_B @ ( symmetric_difference @ sK2_SY37 @ sK3_SY39 ) )
= ( union @ ( difference @ sK1_B @ ( union @ sK2_SY37 @ sK3_SY39 ) ) @ ( intersection @ ( intersection @ sK1_B @ sK2_SY37 ) @ sK3_SY39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(72,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SY50 @ SV9 )
| ~ ( member @ SY50 @ SY49 )
| ( member @ SY50 @ ( intersection @ SV9 @ SY49 ) ) )
| ~ ~ ( ~ ! [SY51: $i,SY52: $i] :
( ~ ( member @ SY52 @ ( intersection @ SV9 @ SY51 ) )
| ( member @ SY52 @ SV9 ) )
| ~ ! [SY53: $i,SY54: $i] :
( ~ ( member @ SY54 @ ( intersection @ SV9 @ SY53 ) )
| ( member @ SY54 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(73,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY55: $i,SY56: $i] :
( ~ ( member @ SY56 @ SV10 )
| ( member @ SY56 @ SY55 )
| ( member @ SY56 @ ( difference @ SV10 @ SY55 ) ) )
| ~ ~ ( ~ ! [SY57: $i,SY58: $i] :
( ~ ( member @ SY58 @ ( difference @ SV10 @ SY57 ) )
| ( member @ SY58 @ SV10 ) )
| ~ ! [SY59: $i,SY60: $i] :
( ~ ( member @ SY60 @ ( difference @ SV10 @ SY59 ) )
| ~ ( member @ SY60 @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(75,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(76,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ ( union @ SV11 @ SY61 ) )
| ( member @ SY62 @ SV11 )
| ( member @ SY62 @ SY61 ) )
| ~ ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ( member @ SY64 @ ( union @ SV11 @ SY63 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SY66 @ ( union @ SV11 @ SY65 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(77,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(78,plain,
! [SV12: $i,SV1: $i] :
( ( ! [SY67: $i] :
( ( intersection @ ( intersection @ SV1 @ SV12 ) @ SY67 )
= ( intersection @ SV1 @ ( intersection @ SV12 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV13: $i,SV2: $i] :
( ( ! [SY68: $i] :
( ( difference @ SV2 @ ( difference @ SV13 @ SY68 ) )
= ( union @ ( difference @ SV2 @ SV13 ) @ ( intersection @ SV2 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV14: $i,SV3: $i] :
( ( ( symmetric_difference @ SV3 @ SV14 )
= ( difference @ ( union @ SV3 @ SV14 ) @ ( intersection @ SV3 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV15: $i,SV4: $i] :
( ( ( symmetric_difference @ SV4 @ SV15 )
= ( union @ ( difference @ SV4 @ SV15 ) @ ( difference @ SV15 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV16: $i,SV5: $i] :
( ( ( union @ SV5 @ SV16 )
= ( union @ SV16 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV17: $i,SV6: $i] :
( ( ( intersection @ SV6 @ SV17 )
= ( intersection @ SV17 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(84,plain,
! [SV18: $i,SV7: $i] :
( ( ( symmetric_difference @ SV7 @ SV18 )
= ( symmetric_difference @ SV18 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(85,plain,
! [SV9: $i] :
( ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SY50 @ SV9 )
| ~ ( member @ SY50 @ SY49 )
| ( member @ SY50 @ ( intersection @ SV9 @ SY49 ) ) )
| ~ ~ ( ~ ! [SY51: $i,SY52: $i] :
( ~ ( member @ SY52 @ ( intersection @ SV9 @ SY51 ) )
| ( member @ SY52 @ SV9 ) )
| ~ ! [SY53: $i,SY54: $i] :
( ~ ( member @ SY54 @ ( intersection @ SV9 @ SY53 ) )
| ( member @ SY54 @ SY53 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV10: $i] :
( ( ~ ! [SY55: $i,SY56: $i] :
( ~ ( member @ SY56 @ SV10 )
| ( member @ SY56 @ SY55 )
| ( member @ SY56 @ ( difference @ SV10 @ SY55 ) ) )
| ~ ~ ( ~ ! [SY57: $i,SY58: $i] :
( ~ ( member @ SY58 @ ( difference @ SV10 @ SY57 ) )
| ( member @ SY58 @ SV10 ) )
| ~ ! [SY59: $i,SY60: $i] :
( ~ ( member @ SY60 @ ( difference @ SV10 @ SY59 ) )
| ~ ( member @ SY60 @ SY59 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(87,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(88,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(89,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(90,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(91,plain,
! [SV11: $i] :
( ( ~ ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ ( union @ SV11 @ SY61 ) )
| ( member @ SY62 @ SV11 )
| ( member @ SY62 @ SY61 ) )
| ~ ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ( member @ SY64 @ ( union @ SV11 @ SY63 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SY66 @ ( union @ SV11 @ SY65 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(92,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(93,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(94,plain,
! [SV19: $i,SV12: $i,SV1: $i] :
( ( ( intersection @ ( intersection @ SV1 @ SV12 ) @ SV19 )
= ( intersection @ SV1 @ ( intersection @ SV12 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(95,plain,
! [SV20: $i,SV13: $i,SV2: $i] :
( ( ( difference @ SV2 @ ( difference @ SV13 @ SV20 ) )
= ( union @ ( difference @ SV2 @ SV13 ) @ ( intersection @ SV2 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(96,plain,
! [SV9: $i] :
( ( ~ ! [SY49: $i,SY50: $i] :
( ~ ( member @ SY50 @ SV9 )
| ~ ( member @ SY50 @ SY49 )
| ( member @ SY50 @ ( intersection @ SV9 @ SY49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(97,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ! [SY51: $i,SY52: $i] :
( ~ ( member @ SY52 @ ( intersection @ SV9 @ SY51 ) )
| ( member @ SY52 @ SV9 ) )
| ~ ! [SY53: $i,SY54: $i] :
( ~ ( member @ SY54 @ ( intersection @ SV9 @ SY53 ) )
| ( member @ SY54 @ SY53 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(98,plain,
! [SV10: $i] :
( ( ~ ! [SY55: $i,SY56: $i] :
( ~ ( member @ SY56 @ SV10 )
| ( member @ SY56 @ SY55 )
| ( member @ SY56 @ ( difference @ SV10 @ SY55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(99,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ! [SY57: $i,SY58: $i] :
( ~ ( member @ SY58 @ ( difference @ SV10 @ SY57 ) )
| ( member @ SY58 @ SV10 ) )
| ~ ! [SY59: $i,SY60: $i] :
( ~ ( member @ SY60 @ ( difference @ SV10 @ SY59 ) )
| ~ ( member @ SY60 @ SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ~ ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX0 )
| ( member @ ( sK5_D @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 )
| ( member @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(104,plain,
! [SV11: $i] :
( ( ~ ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ ( union @ SV11 @ SY61 ) )
| ( member @ SY62 @ SV11 )
| ( member @ SY62 @ SY61 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(105,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ( member @ SY64 @ ( union @ SV11 @ SY63 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SY66 @ ( union @ SV11 @ SY65 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(107,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(108,plain,
! [SV9: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( member @ SY50 @ SV9 )
| ~ ( member @ SY50 @ SY49 )
| ( member @ SY50 @ ( intersection @ SV9 @ SY49 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(109,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY51: $i,SY52: $i] :
( ~ ( member @ SY52 @ ( intersection @ SV9 @ SY51 ) )
| ( member @ SY52 @ SV9 ) )
| ~ ! [SY53: $i,SY54: $i] :
( ~ ( member @ SY54 @ ( intersection @ SV9 @ SY53 ) )
| ( member @ SY54 @ SY53 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(110,plain,
! [SV10: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( member @ SY56 @ SV10 )
| ( member @ SY56 @ SY55 )
| ( member @ SY56 @ ( difference @ SV10 @ SY55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(111,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY57: $i,SY58: $i] :
( ~ ( member @ SY58 @ ( difference @ SV10 @ SY57 ) )
| ( member @ SY58 @ SV10 ) )
| ~ ! [SY59: $i,SY60: $i] :
( ~ ( member @ SY60 @ ( difference @ SV10 @ SY59 ) )
| ~ ( member @ SY60 @ SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(112,plain,
! [SV21: $i] :
( ( ! [SY69: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SY69 @ SV21 ) @ SV21 )
| ~ ( member @ ( sK5_D @ SY69 @ SV21 ) @ SY69 ) )
| ~ ( ( member @ ( sK5_D @ SY69 @ SV21 ) @ SV21 )
| ( member @ ( sK5_D @ SY69 @ SV21 ) @ SY69 ) ) )
| ( SV21 = SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV22: $i] :
( ( ! [SY70: $i] :
( ( SV22 != SY70 )
| ~ ( ~ ! [SY71: $i] :
( ~ ( member @ SY71 @ SV22 )
| ( member @ SY71 @ SY70 ) )
| ~ ! [SY72: $i] :
( ~ ( member @ SY72 @ SY70 )
| ( member @ SY72 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV23: $i] :
( ( ! [SY73: $i] :
( ~ ( ~ ( member @ ( sK4_D @ SY73 @ SV23 ) @ SV23 )
| ~ ~ ( member @ ( sK4_D @ SY73 @ SV23 ) @ SY73 ) )
| ( subset @ SV23 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV24: $i] :
( ( ! [SY74: $i] :
( ~ ( subset @ SV24 @ SY74 )
| ! [SY75: $i] :
( ~ ( member @ SY75 @ SV24 )
| ( member @ SY75 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV11: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ~ ( member @ SY62 @ ( union @ SV11 @ SY61 ) )
| ( member @ SY62 @ SV11 )
| ( member @ SY62 @ SY61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(117,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ( member @ SY64 @ ( union @ SV11 @ SY63 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SY66 @ ( union @ SV11 @ SY65 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(118,plain,
! [SV25: $i] :
( ( ! [SY76: $i] :
( ~ ( subset @ SV25 @ SY76 )
| ~ ( subset @ SY76 @ SV25 )
| ( SV25 = SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(119,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV26: $i,SV9: $i] :
( ( ! [SY77: $i] :
( ~ ( member @ SY77 @ SV9 )
| ~ ( member @ SY77 @ SV26 )
| ( member @ SY77 @ ( intersection @ SV9 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV9: $i] :
( ( ~ ! [SY51: $i,SY52: $i] :
( ~ ( member @ SY52 @ ( intersection @ SV9 @ SY51 ) )
| ( member @ SY52 @ SV9 ) )
| ~ ! [SY53: $i,SY54: $i] :
( ~ ( member @ SY54 @ ( intersection @ SV9 @ SY53 ) )
| ( member @ SY54 @ SY53 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV27: $i,SV10: $i] :
( ( ! [SY78: $i] :
( ~ ( member @ SY78 @ SV10 )
| ( member @ SY78 @ SV27 )
| ( member @ SY78 @ ( difference @ SV10 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV10: $i] :
( ( ~ ! [SY57: $i,SY58: $i] :
( ~ ( member @ SY58 @ ( difference @ SV10 @ SY57 ) )
| ( member @ SY58 @ SV10 ) )
| ~ ! [SY59: $i,SY60: $i] :
( ~ ( member @ SY60 @ ( difference @ SV10 @ SY59 ) )
| ~ ( member @ SY60 @ SY59 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV21: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) )
| ~ ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) ) )
| ( SV21 = SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV29: $i,SV22: $i] :
( ( ( SV22 != SV29 )
| ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV22 )
| ( member @ SY79 @ SV29 ) )
| ~ ! [SY80: $i] :
( ~ ( member @ SY80 @ SV29 )
| ( member @ SY80 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV23: $i,SV30: $i] :
( ( ~ ( ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV23 )
| ~ ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV30 ) )
| ( subset @ SV23 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV31: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV31 )
| ! [SY81: $i] :
( ~ ( member @ SY81 @ SV24 )
| ( member @ SY81 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV32: $i,SV11: $i] :
( ( ! [SY82: $i] :
( ~ ( member @ SY82 @ ( union @ SV11 @ SV32 ) )
| ( member @ SY82 @ SV11 )
| ( member @ SY82 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV11: $i] :
( ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ( member @ SY64 @ ( union @ SV11 @ SY63 ) ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SY66 @ ( union @ SV11 @ SY65 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV33: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV33 )
| ~ ( subset @ SV33 @ SV25 )
| ( SV25 = SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(131,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(132,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(133,plain,
! [SV26: $i,SV9: $i,SV34: $i] :
( ( ~ ( member @ SV34 @ SV9 )
| ~ ( member @ SV34 @ SV26 )
| ( member @ SV34 @ ( intersection @ SV9 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV9: $i] :
( ( ~ ! [SY51: $i,SY52: $i] :
( ~ ( member @ SY52 @ ( intersection @ SV9 @ SY51 ) )
| ( member @ SY52 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(135,plain,
! [SV9: $i] :
( ( ~ ! [SY53: $i,SY54: $i] :
( ~ ( member @ SY54 @ ( intersection @ SV9 @ SY53 ) )
| ( member @ SY54 @ SY53 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(136,plain,
! [SV27: $i,SV10: $i,SV35: $i] :
( ( ~ ( member @ SV35 @ SV10 )
| ( member @ SV35 @ SV27 )
| ( member @ SV35 @ ( difference @ SV10 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV10: $i] :
( ( ~ ! [SY57: $i,SY58: $i] :
( ~ ( member @ SY58 @ ( difference @ SV10 @ SY57 ) )
| ( member @ SY58 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(138,plain,
! [SV10: $i] :
( ( ~ ! [SY59: $i,SY60: $i] :
( ~ ( member @ SY60 @ ( difference @ SV10 @ SY59 ) )
| ~ ( member @ SY60 @ SY59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(139,plain,
! [SV21: $i,SV28: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) )
| ~ ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) ) ) )
= $true )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(140,plain,
! [SV29: $i,SV22: $i] :
( ( ( ( SV22 != SV29 ) )
= $true )
| ( ( ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV22 )
| ( member @ SY79 @ SV29 ) )
| ~ ! [SY80: $i] :
( ~ ( member @ SY80 @ SV29 )
| ( member @ SY80 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(141,plain,
! [SV23: $i,SV30: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV23 )
| ~ ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV30 ) ) )
= $true )
| ( ( subset @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(142,plain,
! [SV31: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV31 ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( member @ SY81 @ SV24 )
| ( member @ SY81 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(143,plain,
! [SV32: $i,SV11: $i,SV36: $i] :
( ( ~ ( member @ SV36 @ ( union @ SV11 @ SV32 ) )
| ( member @ SV36 @ SV11 )
| ( member @ SV36 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(144,plain,
! [SV11: $i] :
( ( ~ ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ( member @ SY64 @ ( union @ SV11 @ SY63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(145,plain,
! [SV11: $i] :
( ( ~ ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SY66 @ ( union @ SV11 @ SY65 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(146,plain,
! [SV33: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV33 )
| ~ ( subset @ SV33 @ SV25 ) )
= $true )
| ( ( SV25 = SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(149,plain,
! [SV26: $i,SV9: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV9 )
| ~ ( member @ SV34 @ SV26 ) )
= $true )
| ( ( member @ SV34 @ ( intersection @ SV9 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(150,plain,
! [SV9: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ( member @ SY52 @ ( intersection @ SV9 @ SY51 ) )
| ( member @ SY52 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(151,plain,
! [SV9: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ( member @ SY54 @ ( intersection @ SV9 @ SY53 ) )
| ( member @ SY54 @ SY53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(152,plain,
! [SV27: $i,SV10: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ SV10 )
| ( member @ SV35 @ SV27 ) )
= $true )
| ( ( member @ SV35 @ ( difference @ SV10 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV10: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( member @ SY58 @ ( difference @ SV10 @ SY57 ) )
| ( member @ SY58 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(154,plain,
! [SV10: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( member @ SY60 @ ( difference @ SV10 @ SY59 ) )
| ~ ( member @ SY60 @ SY59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(155,plain,
! [SV21: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) )
| ~ ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) ) )
= $false )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV29: $i,SV22: $i] :
( ( ( SV22 = SV29 )
= $false )
| ( ( ~ ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV22 )
| ( member @ SY79 @ SV29 ) )
| ~ ! [SY80: $i] :
( ~ ( member @ SY80 @ SV29 )
| ( member @ SY80 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV23: $i,SV30: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV23 )
| ~ ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV30 ) )
= $false )
| ( ( subset @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(158,plain,
! [SV31: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV31 )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( member @ SY81 @ SV24 )
| ( member @ SY81 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV32: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ ( union @ SV11 @ SV32 ) ) )
= $true )
| ( ( ( member @ SV36 @ SV11 )
| ( member @ SV36 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV11: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ( member @ SY64 @ SV11 )
| ( member @ SY64 @ ( union @ SV11 @ SY63 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(161,plain,
! [SV11: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ~ ( member @ SY66 @ SY65 )
| ( member @ SY66 @ ( union @ SV11 @ SY65 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(162,plain,
! [SV33: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV33 ) )
= $true )
| ( ( ~ ( subset @ SV33 @ SV25 ) )
= $true )
| ( ( SV25 = SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(163,plain,
! [SV37: $i] :
( ( ! [SY83: $i] :
( ( SV37 != SY83 )
| ( subset @ SV37 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV38: $i] :
( ( ! [SY84: $i] :
( ( SV38 != SY84 )
| ( subset @ SY84 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(165,plain,
! [SV26: $i,SV9: $i,SV34: $i] :
( ( ( ~ ( member @ SV34 @ SV9 ) )
= $true )
| ( ( ~ ( member @ SV34 @ SV26 ) )
= $true )
| ( ( member @ SV34 @ ( intersection @ SV9 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(166,plain,
! [SV39: $i,SV9: $i] :
( ( ! [SY85: $i] :
( ~ ( member @ SY85 @ ( intersection @ SV9 @ SV39 ) )
| ( member @ SY85 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(167,plain,
! [SV40: $i,SV9: $i] :
( ( ! [SY86: $i] :
( ~ ( member @ SY86 @ ( intersection @ SV9 @ SV40 ) )
| ( member @ SY86 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(168,plain,
! [SV27: $i,SV10: $i,SV35: $i] :
( ( ( ~ ( member @ SV35 @ SV10 ) )
= $true )
| ( ( member @ SV35 @ SV27 )
= $true )
| ( ( member @ SV35 @ ( difference @ SV10 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV41: $i,SV10: $i] :
( ( ! [SY87: $i] :
( ~ ( member @ SY87 @ ( difference @ SV10 @ SV41 ) )
| ( member @ SY87 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV42: $i,SV10: $i] :
( ( ! [SY88: $i] :
( ~ ( member @ SY88 @ ( difference @ SV10 @ SV42 ) )
| ~ ( member @ SY88 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV21: $i,SV28: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) ) )
= $false )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(172,plain,
! [SV21: $i,SV28: $i] :
( ( ( ~ ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) ) )
= $false )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(173,plain,
! [SV29: $i,SV22: $i] :
( ( ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV22 )
| ( member @ SY79 @ SV29 ) )
| ~ ! [SY80: $i] :
( ~ ( member @ SY80 @ SV29 )
| ( member @ SY80 @ SV22 ) ) )
= $false )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(174,plain,
! [SV23: $i,SV30: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV23 ) )
= $false )
| ( ( subset @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(175,plain,
! [SV23: $i,SV30: $i] :
( ( ( ~ ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV30 ) )
= $false )
| ( ( subset @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(176,plain,
! [SV31: $i,SV24: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV24 )
| ( member @ SV43 @ SV31 ) )
= $true )
| ( ( subset @ SV24 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(177,plain,
! [SV32: $i,SV11: $i,SV36: $i] :
( ( ( member @ SV36 @ ( union @ SV11 @ SV32 ) )
= $false )
| ( ( ( member @ SV36 @ SV11 )
| ( member @ SV36 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(178,plain,
! [SV44: $i,SV11: $i] :
( ( ! [SY89: $i] :
( ~ ( member @ SY89 @ SV11 )
| ( member @ SY89 @ ( union @ SV11 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(179,plain,
! [SV11: $i,SV45: $i] :
( ( ! [SY90: $i] :
( ~ ( member @ SY90 @ SV45 )
| ( member @ SY90 @ ( union @ SV11 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(180,plain,
! [SV33: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV33 )
= $false )
| ( ( ~ ( subset @ SV33 @ SV25 ) )
= $true )
| ( ( SV25 = SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(181,plain,
! [SV46: $i,SV37: $i] :
( ( ( SV37 != SV46 )
| ( subset @ SV37 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(182,plain,
! [SV47: $i,SV38: $i] :
( ( ( SV38 != SV47 )
| ( subset @ SV47 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(183,plain,
! [SV26: $i,SV9: $i,SV34: $i] :
( ( ( member @ SV34 @ SV9 )
= $false )
| ( ( ~ ( member @ SV34 @ SV26 ) )
= $true )
| ( ( member @ SV34 @ ( intersection @ SV9 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(184,plain,
! [SV39: $i,SV9: $i,SV48: $i] :
( ( ~ ( member @ SV48 @ ( intersection @ SV9 @ SV39 ) )
| ( member @ SV48 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(185,plain,
! [SV40: $i,SV9: $i,SV49: $i] :
( ( ~ ( member @ SV49 @ ( intersection @ SV9 @ SV40 ) )
| ( member @ SV49 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(186,plain,
! [SV27: $i,SV10: $i,SV35: $i] :
( ( ( member @ SV35 @ SV10 )
= $false )
| ( ( member @ SV35 @ SV27 )
= $true )
| ( ( member @ SV35 @ ( difference @ SV10 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(187,plain,
! [SV41: $i,SV10: $i,SV50: $i] :
( ( ~ ( member @ SV50 @ ( difference @ SV10 @ SV41 ) )
| ( member @ SV50 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(188,plain,
! [SV42: $i,SV10: $i,SV51: $i] :
( ( ~ ( member @ SV51 @ ( difference @ SV10 @ SV42 ) )
| ~ ( member @ SV51 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(189,plain,
! [SV21: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) )
= $true )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(190,plain,
! [SV21: $i,SV28: $i] :
( ( ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
| ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) )
= $true )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(191,plain,
! [SV29: $i,SV22: $i] :
( ( ( ~ ! [SY79: $i] :
( ~ ( member @ SY79 @ SV22 )
| ( member @ SY79 @ SV29 ) ) )
= $false )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(192,plain,
! [SV22: $i,SV29: $i] :
( ( ( ~ ! [SY80: $i] :
( ~ ( member @ SY80 @ SV29 )
| ( member @ SY80 @ SV22 ) ) )
= $false )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(193,plain,
! [SV23: $i,SV30: $i] :
( ( ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV23 )
= $true )
| ( ( subset @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(194,plain,
! [SV23: $i,SV30: $i] :
( ( ( ~ ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV30 ) )
= $true )
| ( ( subset @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(195,plain,
! [SV31: $i,SV24: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV24 ) )
= $true )
| ( ( member @ SV43 @ SV31 )
= $true )
| ( ( subset @ SV24 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(196,plain,
! [SV32: $i,SV11: $i,SV36: $i] :
( ( ( member @ SV36 @ SV11 )
= $true )
| ( ( member @ SV36 @ SV32 )
= $true )
| ( ( member @ SV36 @ ( union @ SV11 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(197,plain,
! [SV44: $i,SV11: $i,SV52: $i] :
( ( ~ ( member @ SV52 @ SV11 )
| ( member @ SV52 @ ( union @ SV11 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(198,plain,
! [SV11: $i,SV45: $i,SV53: $i] :
( ( ~ ( member @ SV53 @ SV45 )
| ( member @ SV53 @ ( union @ SV11 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(199,plain,
! [SV25: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV25 )
= $false )
| ( ( subset @ SV25 @ SV33 )
= $false )
| ( ( SV25 = SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(200,plain,
! [SV46: $i,SV37: $i] :
( ( ( ( SV37 != SV46 ) )
= $true )
| ( ( subset @ SV37 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(201,plain,
! [SV47: $i,SV38: $i] :
( ( ( ( SV38 != SV47 ) )
= $true )
| ( ( subset @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(202,plain,
! [SV9: $i,SV26: $i,SV34: $i] :
( ( ( member @ SV34 @ SV26 )
= $false )
| ( ( member @ SV34 @ SV9 )
= $false )
| ( ( member @ SV34 @ ( intersection @ SV9 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(203,plain,
! [SV39: $i,SV9: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ ( intersection @ SV9 @ SV39 ) ) )
= $true )
| ( ( member @ SV48 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(204,plain,
! [SV40: $i,SV9: $i,SV49: $i] :
( ( ( ~ ( member @ SV49 @ ( intersection @ SV9 @ SV40 ) ) )
= $true )
| ( ( member @ SV49 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(205,plain,
! [SV41: $i,SV10: $i,SV50: $i] :
( ( ( ~ ( member @ SV50 @ ( difference @ SV10 @ SV41 ) ) )
= $true )
| ( ( member @ SV50 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(206,plain,
! [SV42: $i,SV10: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ ( difference @ SV10 @ SV42 ) ) )
= $true )
| ( ( ~ ( member @ SV51 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(207,plain,
! [SV21: $i,SV28: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 ) )
= $true )
| ( ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) )
= $true )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(208,plain,
! [SV21: $i,SV28: $i] :
( ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
= $true )
| ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 )
= $true )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(209,plain,
! [SV29: $i,SV22: $i] :
( ( ( ! [SY79: $i] :
( ~ ( member @ SY79 @ SV22 )
| ( member @ SY79 @ SV29 ) ) )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(210,plain,
! [SV22: $i,SV29: $i] :
( ( ( ! [SY80: $i] :
( ~ ( member @ SY80 @ SV29 )
| ( member @ SY80 @ SV22 ) ) )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(211,plain,
! [SV23: $i,SV30: $i] :
( ( ( member @ ( sK4_D @ SV30 @ SV23 ) @ SV30 )
= $false )
| ( ( subset @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV31: $i,SV24: $i,SV43: $i] :
( ( ( member @ SV43 @ SV24 )
= $false )
| ( ( member @ SV43 @ SV31 )
= $true )
| ( ( subset @ SV24 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV44: $i,SV11: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ SV11 ) )
= $true )
| ( ( member @ SV52 @ ( union @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(214,plain,
! [SV11: $i,SV45: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ SV45 ) )
= $true )
| ( ( member @ SV53 @ ( union @ SV11 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(215,plain,
! [SV46: $i,SV37: $i] :
( ( ( SV37 = SV46 )
= $false )
| ( ( subset @ SV37 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(216,plain,
! [SV47: $i,SV38: $i] :
( ( ( SV38 = SV47 )
= $false )
| ( ( subset @ SV47 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV39: $i,SV9: $i,SV48: $i] :
( ( ( member @ SV48 @ ( intersection @ SV9 @ SV39 ) )
= $false )
| ( ( member @ SV48 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(218,plain,
! [SV40: $i,SV9: $i,SV49: $i] :
( ( ( member @ SV49 @ ( intersection @ SV9 @ SV40 ) )
= $false )
| ( ( member @ SV49 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(219,plain,
! [SV41: $i,SV10: $i,SV50: $i] :
( ( ( member @ SV50 @ ( difference @ SV10 @ SV41 ) )
= $false )
| ( ( member @ SV50 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(220,plain,
! [SV42: $i,SV10: $i,SV51: $i] :
( ( ( member @ SV51 @ ( difference @ SV10 @ SV42 ) )
= $false )
| ( ( ~ ( member @ SV51 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(221,plain,
! [SV21: $i,SV28: $i] :
( ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
= $false )
| ( ( ~ ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 ) )
= $true )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(222,plain,
! [SV29: $i,SV22: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ SV22 )
| ( member @ SV54 @ SV29 ) )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(223,plain,
! [SV22: $i,SV29: $i,SV55: $i] :
( ( ( ~ ( member @ SV55 @ SV29 )
| ( member @ SV55 @ SV22 ) )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(224,plain,
! [SV44: $i,SV11: $i,SV52: $i] :
( ( ( member @ SV52 @ SV11 )
= $false )
| ( ( member @ SV52 @ ( union @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(225,plain,
! [SV11: $i,SV45: $i,SV53: $i] :
( ( ( member @ SV53 @ SV45 )
= $false )
| ( ( member @ SV53 @ ( union @ SV11 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(226,plain,
! [SV10: $i,SV42: $i,SV51: $i] :
( ( ( member @ SV51 @ SV42 )
= $false )
| ( ( member @ SV51 @ ( difference @ SV10 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(227,plain,
! [SV21: $i,SV28: $i] :
( ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV28 )
= $false )
| ( ( member @ ( sK5_D @ SV28 @ SV21 ) @ SV21 )
= $false )
| ( ( SV21 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(228,plain,
! [SV29: $i,SV22: $i,SV54: $i] :
( ( ( ~ ( member @ SV54 @ SV22 ) )
= $true )
| ( ( member @ SV54 @ SV29 )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(229,plain,
! [SV22: $i,SV29: $i,SV55: $i] :
( ( ( ~ ( member @ SV55 @ SV29 ) )
= $true )
| ( ( member @ SV55 @ SV22 )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(230,plain,
! [SV29: $i,SV22: $i,SV54: $i] :
( ( ( member @ SV54 @ SV22 )
= $false )
| ( ( member @ SV54 @ SV29 )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(231,plain,
! [SV22: $i,SV29: $i,SV55: $i] :
( ( ( member @ SV55 @ SV29 )
= $false )
| ( ( member @ SV55 @ SV22 )
= $true )
| ( ( SV22 = SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(232,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[70,231,230,227,226,225,224,219,218,217,216,215,212,211,208,202,199,196,193,186,95,94,84,83,82,81,80,71]) ).
thf(233,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n026.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 00:40:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 14
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:14,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:16,loop_count:0,foatp_calls:0,translation:fof_full)................
% 0.76/0.94
% 0.76/0.94 ********************************
% 0.76/0.94 * All subproblems solved! *
% 0.76/0.94 ********************************
% 0.76/0.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:232,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.76/0.95
% 0.76/0.95 %**** Beginning of derivation protocol ****
% 0.76/0.95 % SZS output start CNFRefutation
% See solution above
% 0.76/0.95
% 0.76/0.95 %**** End of derivation protocol ****
% 0.76/0.95 %**** no. of clauses in derivation: 233 ****
% 0.76/0.95 %**** clause counter: 232 ****
% 0.76/0.95
% 0.76/0.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:232,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------