TSTP Solution File: SET635+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET635+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 : n016.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 03:03:48 EDT 2022
% Result : Theorem 1.95s 2.15s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of formulae : 251 ( 163 unt; 13 typ; 0 def)
% Number of atoms : 1296 ( 445 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 2626 ( 477 ~; 394 |; 32 &;1705 @)
% ( 16 <=>; 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 : 16 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 672 ( 0 ^ 672 !; 0 ?; 672 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_sK1_B,type,
sK1_B: $i ).
thf(tp_sK2_SY36,type,
sK2_SY36: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(1,axiom,
! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
thf(2,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(3,axiom,
! [B: $i] : ( subset @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(4,axiom,
! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
thf(5,axiom,
! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(6,axiom,
! [B: $i] :
~ ( member @ B @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
thf(7,axiom,
! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(8,axiom,
! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
thf(9,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( difference @ B @ C ) )
<=> ( ( member @ D @ B )
& ~ ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(10,axiom,
! [B: $i,C: $i,D: $i] :
( ( member @ D @ ( intersection @ B @ C ) )
<=> ( ( member @ D @ B )
& ( member @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
thf(11,axiom,
! [B: $i,C: $i,D: $i] :
( ( intersection @ B @ ( difference @ C @ D ) )
= ( difference @ ( intersection @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).
thf(12,axiom,
! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( intersection @ C @ D ) )
= ( union @ ( difference @ B @ C ) @ ( difference @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
thf(13,axiom,
! [B: $i] :
( ( union @ B @ empty_set )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
thf(14,axiom,
! [B: $i,C: $i] :
( ( ( difference @ B @ C )
= empty_set )
<=> ( subset @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
thf(15,axiom,
! [B: $i,C: $i] : ( subset @ ( intersection @ B @ C ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
thf(16,conjecture,
! [B: $i,C: $i,D: $i] :
( ( intersection @ B @ ( difference @ C @ D ) )
= ( difference @ ( intersection @ B @ C ) @ ( intersection @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).
thf(17,negated_conjecture,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersection @ B @ ( difference @ C @ D ) )
= ( difference @ ( intersection @ B @ C ) @ ( intersection @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersection @ B @ ( difference @ C @ D ) )
= ( difference @ ( intersection @ B @ C ) @ ( intersection @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [B: $i] :
( ( empty @ B )
<=> ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ! [D: $i] :
( ( member @ D @ B )
<=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [B: $i,C: $i] :
( ( subset @ B @ C )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( member @ D @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [B: $i,C: $i] :
( ( B = C )
<=> ( ( subset @ B @ C )
& ( subset @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,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(28,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(29,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersection @ B @ ( difference @ C @ D ) )
= ( difference @ ( intersection @ B @ C ) @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(30,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( intersection @ C @ D ) )
= ( union @ ( difference @ B @ C ) @ ( difference @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(31,plain,
( ( ! [B: $i] :
( ( union @ B @ empty_set )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(32,plain,
( ( ! [B: $i,C: $i] :
( ( ( difference @ B @ C )
= empty_set )
<=> ( subset @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(33,plain,
( ( ! [B: $i,C: $i] : ( subset @ ( intersection @ B @ C ) @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [SY36: $i,SY37: $i] :
( ( intersection @ sK1_B @ ( difference @ SY36 @ SY37 ) )
= ( difference @ ( intersection @ sK1_B @ SY36 ) @ ( intersection @ sK1_B @ SY37 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(35,plain,
( ( ! [SY38: $i] :
( ( intersection @ sK1_B @ ( difference @ sK2_SY36 @ SY38 ) )
= ( difference @ ( intersection @ sK1_B @ sK2_SY36 ) @ ( intersection @ sK1_B @ SY38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(36,plain,
( ( ( intersection @ sK1_B @ ( difference @ sK2_SY36 @ sK3_SY38 ) )
= ( difference @ ( intersection @ sK1_B @ sK2_SY36 ) @ ( intersection @ sK1_B @ sK3_SY38 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(37,plain,
( ( ( ( intersection @ sK1_B @ ( difference @ sK2_SY36 @ sK3_SY38 ) )
!= ( difference @ ( intersection @ sK1_B @ sK2_SY36 ) @ ( intersection @ sK1_B @ sK3_SY38 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [B: $i] :
( ( member @ ( sK4_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(39,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(40,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK6_D @ C @ B ) @ B )
& ~ ( member @ ( sK6_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)],[22]) ).
thf(41,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)],[26]) ).
thf(42,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)],[27]) ).
thf(43,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)],[28]) ).
thf(44,plain,
( ( ! [B: $i,C: $i] :
( ( ( difference @ B @ C )
!= empty_set )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ( ( difference @ B @ C )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(45,plain,
( ( ! [B: $i,C: $i] : ( subset @ ( intersection @ B @ C ) @ B ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(46,plain,
( ( ! [B: $i,C: $i] :
( ( ( difference @ B @ C )
!= empty_set )
| ( subset @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ B @ C )
| ( ( difference @ B @ C )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(47,plain,
( ( ! [B: $i] :
( ( union @ B @ empty_set )
= B ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(48,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( difference @ B @ ( intersection @ C @ D ) )
= ( union @ ( difference @ B @ C ) @ ( difference @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(49,plain,
( ( ! [B: $i,C: $i,D: $i] :
( ( intersection @ B @ ( difference @ C @ D ) )
= ( difference @ ( intersection @ B @ C ) @ D ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(50,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)],[43]) ).
thf(51,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)],[42]) ).
thf(52,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)],[41]) ).
thf(53,plain,
( ( ! [B: $i,C: $i] :
( ( union @ B @ C )
= ( union @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(54,plain,
( ( ! [B: $i] :
~ ( member @ B @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(55,plain,
( ( ! [B: $i,C: $i] :
( ( intersection @ B @ C )
= ( intersection @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(56,plain,
( ( ! [B: $i,C: $i] :
( ( ( member @ ( sK6_D @ C @ B ) @ B )
& ~ ( member @ ( sK6_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)],[40]) ).
thf(57,plain,
( ( ! [B: $i] : ( subset @ B @ B ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(58,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)],[39]) ).
thf(59,plain,
( ( ! [B: $i] :
( ( member @ ( sK4_C @ B ) @ B )
| ( empty @ B ) )
& ! [B: $i] :
( ~ ( empty @ B )
| ! [C: $i] :
~ ( member @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(60,plain,
( ( ( ( intersection @ sK1_B @ ( difference @ sK2_SY36 @ sK3_SY38 ) )
!= ( difference @ ( intersection @ sK1_B @ sK2_SY36 ) @ ( intersection @ sK1_B @ sK3_SY38 ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(61,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)],[51]) ).
thf(62,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(63,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)],[58]) ).
thf(64,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_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)],[56]) ).
thf(65,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(66,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)],[52]) ).
thf(67,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)],[50]) ).
thf(68,plain,
! [SV1: $i] :
( ( ! [SY39: $i] : ( subset @ ( intersection @ SV1 @ SY39 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(69,plain,
! [SV2: $i] :
( ( ( union @ SV2 @ empty_set )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(70,plain,
! [SV3: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( difference @ SV3 @ ( intersection @ SY40 @ SY41 ) )
= ( union @ ( difference @ SV3 @ SY40 ) @ ( difference @ SV3 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(71,plain,
! [SV4: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( intersection @ SV4 @ ( difference @ SY42 @ SY43 ) )
= ( difference @ ( intersection @ SV4 @ SY42 ) @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(72,plain,
! [SV5: $i] :
( ( ! [SY44: $i] :
( ( union @ SV5 @ SY44 )
= ( union @ SY44 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(73,plain,
! [SV6: $i] :
( ( ~ ( member @ SV6 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(74,plain,
! [SV7: $i] :
( ( ! [SY45: $i] :
( ( intersection @ SV7 @ SY45 )
= ( intersection @ SY45 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(75,plain,
! [SV8: $i] :
( ( subset @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(76,plain,
( ( ( intersection @ sK1_B @ ( difference @ sK2_SY36 @ sK3_SY38 ) )
= ( difference @ ( intersection @ sK1_B @ sK2_SY36 ) @ ( intersection @ sK1_B @ sK3_SY38 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SV9 )
| ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( difference @ SV9 @ SY46 ) ) )
| ~ ~ ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV9 @ SY48 ) )
| ( member @ SY49 @ SV9 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( member @ SY51 @ ( difference @ SV9 @ SY50 ) )
| ~ ( member @ SY51 @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(79,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)],[63]) ).
thf(80,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_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)],[64]) ).
thf(81,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(82,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)],[66]) ).
thf(83,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( member @ SY53 @ SV10 )
| ~ ( member @ SY53 @ SY52 )
| ( member @ SY53 @ ( intersection @ SV10 @ SY52 ) ) )
| ~ ~ ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( member @ SY55 @ ( intersection @ SV10 @ SY54 ) )
| ( member @ SY55 @ SV10 ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SY57 @ ( intersection @ SV10 @ SY56 ) )
| ( member @ SY57 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(84,plain,
! [SV11: $i,SV1: $i] :
( ( subset @ ( intersection @ SV1 @ SV11 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(85,plain,
! [SV12: $i,SV3: $i] :
( ( ! [SY58: $i] :
( ( difference @ SV3 @ ( intersection @ SV12 @ SY58 ) )
= ( union @ ( difference @ SV3 @ SV12 ) @ ( difference @ SV3 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV13: $i,SV4: $i] :
( ( ! [SY59: $i] :
( ( intersection @ SV4 @ ( difference @ SV13 @ SY59 ) )
= ( difference @ ( intersection @ SV4 @ SV13 ) @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV14: $i,SV5: $i] :
( ( ( union @ SV5 @ SV14 )
= ( union @ SV14 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV6: $i] :
( ( member @ SV6 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV15: $i,SV7: $i] :
( ( ( intersection @ SV7 @ SV15 )
= ( intersection @ SV15 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
! [SV9: $i] :
( ( ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SV9 )
| ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( difference @ SV9 @ SY46 ) ) )
| ~ ~ ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV9 @ SY48 ) )
| ( member @ SY49 @ SV9 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( member @ SY51 @ ( difference @ SV9 @ SY50 ) )
| ~ ( member @ SY51 @ SY50 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(91,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(92,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(93,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)],[79]) ).
thf(94,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)],[79]) ).
thf(95,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(96,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(97,plain,
( ( ~ ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(98,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(99,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(100,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)],[82]) ).
thf(101,plain,
! [SV10: $i] :
( ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( member @ SY53 @ SV10 )
| ~ ( member @ SY53 @ SY52 )
| ( member @ SY53 @ ( intersection @ SV10 @ SY52 ) ) )
| ~ ~ ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( member @ SY55 @ ( intersection @ SV10 @ SY54 ) )
| ( member @ SY55 @ SV10 ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SY57 @ ( intersection @ SV10 @ SY56 ) )
| ( member @ SY57 @ SY56 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(102,plain,
! [SV16: $i,SV12: $i,SV3: $i] :
( ( ( difference @ SV3 @ ( intersection @ SV12 @ SV16 ) )
= ( union @ ( difference @ SV3 @ SV12 ) @ ( difference @ SV3 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV17: $i,SV13: $i,SV4: $i] :
( ( ( intersection @ SV4 @ ( difference @ SV13 @ SV17 ) )
= ( difference @ ( intersection @ SV4 @ SV13 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
! [SV9: $i] :
( ( ~ ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SV9 )
| ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( difference @ SV9 @ SY46 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(105,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV9 @ SY48 ) )
| ( member @ SY49 @ SV9 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( member @ SY51 @ ( difference @ SV9 @ SY50 ) )
| ~ ( member @ SY51 @ SY50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(108,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)],[93]) ).
thf(109,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)],[94]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( member @ ( sK6_D @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( ( member @ ( sK4_C @ SX0 ) @ SX0 )
| ( empty @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(113,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
~ ( member @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(115,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)],[100]) ).
thf(116,plain,
! [SV10: $i] :
( ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( member @ SY53 @ SV10 )
| ~ ( member @ SY53 @ SY52 )
| ( member @ SY53 @ ( intersection @ SV10 @ SY52 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(117,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( member @ SY55 @ ( intersection @ SV10 @ SY54 ) )
| ( member @ SY55 @ SV10 ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SY57 @ ( intersection @ SV10 @ SY56 ) )
| ( member @ SY57 @ SY56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(118,plain,
! [SV9: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( member @ SY47 @ SV9 )
| ( member @ SY47 @ SY46 )
| ( member @ SY47 @ ( difference @ SV9 @ SY46 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(119,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV9 @ SY48 ) )
| ( member @ SY49 @ SV9 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( member @ SY51 @ ( difference @ SV9 @ SY50 ) )
| ~ ( member @ SY51 @ SY50 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(120,plain,
! [SV18: $i] :
( ( ! [SY60: $i] :
( ( ( difference @ SV18 @ SY60 )
!= empty_set )
| ( subset @ SV18 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV19: $i] :
( ( ! [SY61: $i] :
( ~ ( subset @ SV19 @ SY61 )
| ( ( difference @ SV19 @ SY61 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(122,plain,
! [SV20: $i] :
( ( ! [SY62: $i] :
( ~ ( ~ ( ~ ( member @ ( sK5_D @ SY62 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK5_D @ SY62 @ SV20 ) @ SY62 ) )
| ~ ( ( member @ ( sK5_D @ SY62 @ SV20 ) @ SV20 )
| ( member @ ( sK5_D @ SY62 @ SV20 ) @ SY62 ) ) )
| ( SV20 = SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV21: $i] :
( ( ! [SY63: $i] :
( ( SV21 != SY63 )
| ~ ( ~ ! [SY64: $i] :
( ~ ( member @ SY64 @ SV21 )
| ( member @ SY64 @ SY63 ) )
| ~ ! [SY65: $i] :
( ~ ( member @ SY65 @ SY63 )
| ( member @ SY65 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV22: $i] :
( ( ! [SY66: $i] :
( ~ ( ~ ( member @ ( sK6_D @ SY66 @ SV22 ) @ SV22 )
| ~ ~ ( member @ ( sK6_D @ SY66 @ SV22 ) @ SY66 ) )
| ( subset @ SV22 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV23: $i] :
( ( ! [SY67: $i] :
( ~ ( subset @ SV23 @ SY67 )
| ! [SY68: $i] :
( ~ ( member @ SY68 @ SV23 )
| ( member @ SY68 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV24: $i] :
( ( ( member @ ( sK4_C @ SV24 ) @ SV24 )
| ( empty @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV25: $i] :
( ( ~ ( empty @ SV25 )
| ! [SY69: $i] :
~ ( member @ SY69 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV26: $i] :
( ( ! [SY70: $i] :
( ~ ( subset @ SV26 @ SY70 )
| ~ ( subset @ SY70 @ SV26 )
| ( SV26 = SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(129,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)],[115]) ).
thf(130,plain,
! [SV10: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( member @ SY53 @ SV10 )
| ~ ( member @ SY53 @ SY52 )
| ( member @ SY53 @ ( intersection @ SV10 @ SY52 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(131,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( member @ SY55 @ ( intersection @ SV10 @ SY54 ) )
| ( member @ SY55 @ SV10 ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SY57 @ ( intersection @ SV10 @ SY56 ) )
| ( member @ SY57 @ SY56 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(132,plain,
! [SV27: $i,SV9: $i] :
( ( ! [SY71: $i] :
( ~ ( member @ SY71 @ SV9 )
| ( member @ SY71 @ SV27 )
| ( member @ SY71 @ ( difference @ SV9 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV9: $i] :
( ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV9 @ SY48 ) )
| ( member @ SY49 @ SV9 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( member @ SY51 @ ( difference @ SV9 @ SY50 ) )
| ~ ( member @ SY51 @ SY50 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV28: $i,SV18: $i] :
( ( ( ( difference @ SV18 @ SV28 )
!= empty_set )
| ( subset @ SV18 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV29: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV29 )
| ( ( difference @ SV19 @ SV29 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV20: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) )
| ~ ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) ) )
| ( SV20 = SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV31: $i,SV21: $i] :
( ( ( SV21 != SV31 )
| ~ ( ~ ! [SY72: $i] :
( ~ ( member @ SY72 @ SV21 )
| ( member @ SY72 @ SV31 ) )
| ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV31 )
| ( member @ SY73 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV22: $i,SV32: $i] :
( ( ~ ( ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV22 )
| ~ ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV32 ) )
| ( subset @ SV22 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV33: $i,SV23: $i] :
( ( ~ ( subset @ SV23 @ SV33 )
| ! [SY74: $i] :
( ~ ( member @ SY74 @ SV23 )
| ( member @ SY74 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV24: $i] :
( ( ( member @ ( sK4_C @ SV24 ) @ SV24 )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV25: $i] :
( ( ( ~ ( empty @ SV25 ) )
= $true )
| ( ( ! [SY69: $i] :
~ ( member @ SY69 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( subset @ SV26 @ SV34 )
| ~ ( subset @ SV34 @ SV26 )
| ( SV26 = SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(143,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(144,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(145,plain,
! [SV35: $i,SV10: $i] :
( ( ! [SY75: $i] :
( ~ ( member @ SY75 @ SV10 )
| ~ ( member @ SY75 @ SV35 )
| ( member @ SY75 @ ( intersection @ SV10 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV10: $i] :
( ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( member @ SY55 @ ( intersection @ SV10 @ SY54 ) )
| ( member @ SY55 @ SV10 ) )
| ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SY57 @ ( intersection @ SV10 @ SY56 ) )
| ( member @ SY57 @ SY56 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(147,plain,
! [SV27: $i,SV9: $i,SV36: $i] :
( ( ~ ( member @ SV36 @ SV9 )
| ( member @ SV36 @ SV27 )
| ( member @ SV36 @ ( difference @ SV9 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV9: $i] :
( ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV9 @ SY48 ) )
| ( member @ SY49 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(149,plain,
! [SV9: $i] :
( ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( member @ SY51 @ ( difference @ SV9 @ SY50 ) )
| ~ ( member @ SY51 @ SY50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(150,plain,
! [SV28: $i,SV18: $i] :
( ( ( ( ( difference @ SV18 @ SV28 )
!= empty_set ) )
= $true )
| ( ( subset @ SV18 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV29: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV29 ) )
= $true )
| ( ( ( difference @ SV19 @ SV29 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV20: $i,SV30: $i] :
( ( ( ~ ( ~ ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) )
| ~ ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) ) ) )
= $true )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV31: $i,SV21: $i] :
( ( ( ( SV21 != SV31 ) )
= $true )
| ( ( ~ ( ~ ! [SY72: $i] :
( ~ ( member @ SY72 @ SV21 )
| ( member @ SY72 @ SV31 ) )
| ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV31 )
| ( member @ SY73 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(154,plain,
! [SV22: $i,SV32: $i] :
( ( ( ~ ( ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV22 )
| ~ ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV32 ) ) )
= $true )
| ( ( subset @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV33: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV33 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( member @ SY74 @ SV23 )
| ( member @ SY74 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV25: $i] :
( ( ( empty @ SV25 )
= $false )
| ( ( ! [SY69: $i] :
~ ( member @ SY69 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV34: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV34 )
| ~ ( subset @ SV34 @ SV26 ) )
= $true )
| ( ( SV26 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(160,plain,
! [SV35: $i,SV10: $i,SV37: $i] :
( ( ~ ( member @ SV37 @ SV10 )
| ~ ( member @ SV37 @ SV35 )
| ( member @ SV37 @ ( intersection @ SV10 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV10: $i] :
( ( ~ ! [SY54: $i,SY55: $i] :
( ~ ( member @ SY55 @ ( intersection @ SV10 @ SY54 ) )
| ( member @ SY55 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(162,plain,
! [SV10: $i] :
( ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( member @ SY57 @ ( intersection @ SV10 @ SY56 ) )
| ( member @ SY57 @ SY56 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(163,plain,
! [SV27: $i,SV9: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV9 )
| ( member @ SV36 @ SV27 ) )
= $true )
| ( ( member @ SV36 @ ( difference @ SV9 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV9: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ( member @ SY49 @ ( difference @ SV9 @ SY48 ) )
| ( member @ SY49 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(165,plain,
! [SV9: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( member @ SY51 @ ( difference @ SV9 @ SY50 ) )
| ~ ( member @ SY51 @ SY50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(166,plain,
! [SV28: $i,SV18: $i] :
( ( ( ( difference @ SV18 @ SV28 )
= empty_set )
= $false )
| ( ( subset @ SV18 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(167,plain,
! [SV29: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV29 )
= $false )
| ( ( ( difference @ SV19 @ SV29 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(168,plain,
! [SV20: $i,SV30: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) )
| ~ ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) ) )
= $false )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(169,plain,
! [SV31: $i,SV21: $i] :
( ( ( SV21 = SV31 )
= $false )
| ( ( ~ ( ~ ! [SY72: $i] :
( ~ ( member @ SY72 @ SV21 )
| ( member @ SY72 @ SV31 ) )
| ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV31 )
| ( member @ SY73 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV22: $i,SV32: $i] :
( ( ( ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV22 )
| ~ ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV32 ) )
= $false )
| ( ( subset @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV33: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV33 )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( member @ SY74 @ SV23 )
| ( member @ SY74 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV25: $i,SV38: $i] :
( ( ( ~ ( member @ SV38 @ SV25 ) )
= $true )
| ( ( empty @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(173,plain,
! [SV34: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV34 ) )
= $true )
| ( ( ~ ( subset @ SV34 @ SV26 ) )
= $true )
| ( ( SV26 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(174,plain,
! [SV39: $i] :
( ( ! [SY76: $i] :
( ( SV39 != SY76 )
| ( subset @ SV39 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(175,plain,
! [SV40: $i] :
( ( ! [SY77: $i] :
( ( SV40 != SY77 )
| ( subset @ SY77 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(176,plain,
! [SV35: $i,SV10: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV10 )
| ~ ( member @ SV37 @ SV35 ) )
= $true )
| ( ( member @ SV37 @ ( intersection @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(177,plain,
! [SV10: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( member @ SY55 @ ( intersection @ SV10 @ SY54 ) )
| ( member @ SY55 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(178,plain,
! [SV10: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( member @ SY57 @ ( intersection @ SV10 @ SY56 ) )
| ( member @ SY57 @ SY56 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(179,plain,
! [SV27: $i,SV9: $i,SV36: $i] :
( ( ( ~ ( member @ SV36 @ SV9 ) )
= $true )
| ( ( member @ SV36 @ SV27 )
= $true )
| ( ( member @ SV36 @ ( difference @ SV9 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(180,plain,
! [SV41: $i,SV9: $i] :
( ( ! [SY78: $i] :
( ~ ( member @ SY78 @ ( difference @ SV9 @ SV41 ) )
| ( member @ SY78 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV42: $i,SV9: $i] :
( ( ! [SY79: $i] :
( ~ ( member @ SY79 @ ( difference @ SV9 @ SV42 ) )
| ~ ( member @ SY79 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV20: $i,SV30: $i] :
( ( ( ~ ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) ) )
= $false )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(183,plain,
! [SV20: $i,SV30: $i] :
( ( ( ~ ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) ) )
= $false )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(184,plain,
! [SV31: $i,SV21: $i] :
( ( ( ~ ! [SY72: $i] :
( ~ ( member @ SY72 @ SV21 )
| ( member @ SY72 @ SV31 ) )
| ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV31 )
| ( member @ SY73 @ SV21 ) ) )
= $false )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(185,plain,
! [SV22: $i,SV32: $i] :
( ( ( ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV22 ) )
= $false )
| ( ( subset @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(186,plain,
! [SV22: $i,SV32: $i] :
( ( ( ~ ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV32 ) )
= $false )
| ( ( subset @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(187,plain,
! [SV33: $i,SV23: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV23 )
| ( member @ SV43 @ SV33 ) )
= $true )
| ( ( subset @ SV23 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(188,plain,
! [SV25: $i,SV38: $i] :
( ( ( member @ SV38 @ SV25 )
= $false )
| ( ( empty @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV34: $i,SV26: $i] :
( ( ( subset @ SV26 @ SV34 )
= $false )
| ( ( ~ ( subset @ SV34 @ SV26 ) )
= $true )
| ( ( SV26 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV44: $i,SV39: $i] :
( ( ( SV39 != SV44 )
| ( subset @ SV39 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV45: $i,SV40: $i] :
( ( ( SV40 != SV45 )
| ( subset @ SV45 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV35: $i,SV10: $i,SV37: $i] :
( ( ( ~ ( member @ SV37 @ SV10 ) )
= $true )
| ( ( ~ ( member @ SV37 @ SV35 ) )
= $true )
| ( ( member @ SV37 @ ( intersection @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV46: $i,SV10: $i] :
( ( ! [SY80: $i] :
( ~ ( member @ SY80 @ ( intersection @ SV10 @ SV46 ) )
| ( member @ SY80 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV47: $i,SV10: $i] :
( ( ! [SY81: $i] :
( ~ ( member @ SY81 @ ( intersection @ SV10 @ SV47 ) )
| ( member @ SY81 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV27: $i,SV9: $i,SV36: $i] :
( ( ( member @ SV36 @ SV9 )
= $false )
| ( ( member @ SV36 @ SV27 )
= $true )
| ( ( member @ SV36 @ ( difference @ SV9 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV41: $i,SV9: $i,SV48: $i] :
( ( ~ ( member @ SV48 @ ( difference @ SV9 @ SV41 ) )
| ( member @ SV48 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV42: $i,SV9: $i,SV49: $i] :
( ( ~ ( member @ SV49 @ ( difference @ SV9 @ SV42 ) )
| ~ ( member @ SV49 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(198,plain,
! [SV20: $i,SV30: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) )
= $true )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(199,plain,
! [SV20: $i,SV30: $i] :
( ( ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
| ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) )
= $true )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(200,plain,
! [SV31: $i,SV21: $i] :
( ( ( ~ ! [SY72: $i] :
( ~ ( member @ SY72 @ SV21 )
| ( member @ SY72 @ SV31 ) ) )
= $false )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(201,plain,
! [SV21: $i,SV31: $i] :
( ( ( ~ ! [SY73: $i] :
( ~ ( member @ SY73 @ SV31 )
| ( member @ SY73 @ SV21 ) ) )
= $false )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(202,plain,
! [SV22: $i,SV32: $i] :
( ( ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV22 )
= $true )
| ( ( subset @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(203,plain,
! [SV22: $i,SV32: $i] :
( ( ( ~ ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV32 ) )
= $true )
| ( ( subset @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(204,plain,
! [SV33: $i,SV23: $i,SV43: $i] :
( ( ( ~ ( member @ SV43 @ SV23 ) )
= $true )
| ( ( member @ SV43 @ SV33 )
= $true )
| ( ( subset @ SV23 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(205,plain,
! [SV26: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV26 )
= $false )
| ( ( subset @ SV26 @ SV34 )
= $false )
| ( ( SV26 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(206,plain,
! [SV44: $i,SV39: $i] :
( ( ( ( SV39 != SV44 ) )
= $true )
| ( ( subset @ SV39 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(207,plain,
! [SV45: $i,SV40: $i] :
( ( ( ( SV40 != SV45 ) )
= $true )
| ( ( subset @ SV45 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(208,plain,
! [SV35: $i,SV10: $i,SV37: $i] :
( ( ( member @ SV37 @ SV10 )
= $false )
| ( ( ~ ( member @ SV37 @ SV35 ) )
= $true )
| ( ( member @ SV37 @ ( intersection @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(209,plain,
! [SV46: $i,SV10: $i,SV50: $i] :
( ( ~ ( member @ SV50 @ ( intersection @ SV10 @ SV46 ) )
| ( member @ SV50 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(210,plain,
! [SV47: $i,SV10: $i,SV51: $i] :
( ( ~ ( member @ SV51 @ ( intersection @ SV10 @ SV47 ) )
| ( member @ SV51 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(211,plain,
! [SV41: $i,SV9: $i,SV48: $i] :
( ( ( ~ ( member @ SV48 @ ( difference @ SV9 @ SV41 ) ) )
= $true )
| ( ( member @ SV48 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(212,plain,
! [SV42: $i,SV9: $i,SV49: $i] :
( ( ( ~ ( member @ SV49 @ ( difference @ SV9 @ SV42 ) ) )
= $true )
| ( ( ~ ( member @ SV49 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(213,plain,
! [SV20: $i,SV30: $i] :
( ( ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 ) )
= $true )
| ( ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) )
= $true )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(214,plain,
! [SV20: $i,SV30: $i] :
( ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
= $true )
| ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 )
= $true )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(215,plain,
! [SV31: $i,SV21: $i] :
( ( ( ! [SY72: $i] :
( ~ ( member @ SY72 @ SV21 )
| ( member @ SY72 @ SV31 ) ) )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(216,plain,
! [SV21: $i,SV31: $i] :
( ( ( ! [SY73: $i] :
( ~ ( member @ SY73 @ SV31 )
| ( member @ SY73 @ SV21 ) ) )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(217,plain,
! [SV22: $i,SV32: $i] :
( ( ( member @ ( sK6_D @ SV32 @ SV22 ) @ SV32 )
= $false )
| ( ( subset @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(218,plain,
! [SV33: $i,SV23: $i,SV43: $i] :
( ( ( member @ SV43 @ SV23 )
= $false )
| ( ( member @ SV43 @ SV33 )
= $true )
| ( ( subset @ SV23 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(219,plain,
! [SV44: $i,SV39: $i] :
( ( ( SV39 = SV44 )
= $false )
| ( ( subset @ SV39 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(220,plain,
! [SV45: $i,SV40: $i] :
( ( ( SV40 = SV45 )
= $false )
| ( ( subset @ SV45 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(221,plain,
! [SV10: $i,SV35: $i,SV37: $i] :
( ( ( member @ SV37 @ SV35 )
= $false )
| ( ( member @ SV37 @ SV10 )
= $false )
| ( ( member @ SV37 @ ( intersection @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(222,plain,
! [SV46: $i,SV10: $i,SV50: $i] :
( ( ( ~ ( member @ SV50 @ ( intersection @ SV10 @ SV46 ) ) )
= $true )
| ( ( member @ SV50 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(223,plain,
! [SV47: $i,SV10: $i,SV51: $i] :
( ( ( ~ ( member @ SV51 @ ( intersection @ SV10 @ SV47 ) ) )
= $true )
| ( ( member @ SV51 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(224,plain,
! [SV41: $i,SV9: $i,SV48: $i] :
( ( ( member @ SV48 @ ( difference @ SV9 @ SV41 ) )
= $false )
| ( ( member @ SV48 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(225,plain,
! [SV42: $i,SV9: $i,SV49: $i] :
( ( ( member @ SV49 @ ( difference @ SV9 @ SV42 ) )
= $false )
| ( ( ~ ( member @ SV49 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(226,plain,
! [SV20: $i,SV30: $i] :
( ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
= $false )
| ( ( ~ ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 ) )
= $true )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(227,plain,
! [SV31: $i,SV21: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ SV21 )
| ( member @ SV52 @ SV31 ) )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(228,plain,
! [SV21: $i,SV31: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ SV31 )
| ( member @ SV53 @ SV21 ) )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(229,plain,
! [SV46: $i,SV10: $i,SV50: $i] :
( ( ( member @ SV50 @ ( intersection @ SV10 @ SV46 ) )
= $false )
| ( ( member @ SV50 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(230,plain,
! [SV47: $i,SV10: $i,SV51: $i] :
( ( ( member @ SV51 @ ( intersection @ SV10 @ SV47 ) )
= $false )
| ( ( member @ SV51 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(231,plain,
! [SV9: $i,SV42: $i,SV49: $i] :
( ( ( member @ SV49 @ SV42 )
= $false )
| ( ( member @ SV49 @ ( difference @ SV9 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV20: $i,SV30: $i] :
( ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV30 )
= $false )
| ( ( member @ ( sK5_D @ SV30 @ SV20 ) @ SV20 )
= $false )
| ( ( SV20 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(233,plain,
! [SV31: $i,SV21: $i,SV52: $i] :
( ( ( ~ ( member @ SV52 @ SV21 ) )
= $true )
| ( ( member @ SV52 @ SV31 )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(234,plain,
! [SV21: $i,SV31: $i,SV53: $i] :
( ( ( ~ ( member @ SV53 @ SV31 ) )
= $true )
| ( ( member @ SV53 @ SV21 )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(235,plain,
! [SV31: $i,SV21: $i,SV52: $i] :
( ( ( member @ SV52 @ SV21 )
= $false )
| ( ( member @ SV52 @ SV31 )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(236,plain,
! [SV21: $i,SV31: $i,SV53: $i] :
( ( ( member @ SV53 @ SV31 )
= $false )
| ( ( member @ SV53 @ SV21 )
= $true )
| ( ( SV21 = SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(237,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[69,236,235,232,231,230,229,224,221,220,219,218,217,214,205,202,195,188,167,166,140,103,102,89,88,87,84,76,75]) ).
thf(238,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n016.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 13:54:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 15
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:15,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:17,loop_count:0,foatp_calls:0,translation:fof_full)................
% 1.95/2.15
% 1.95/2.15 ********************************
% 1.95/2.15 * All subproblems solved! *
% 1.95/2.15 ********************************
% 1.95/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:237,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.95/2.16
% 1.95/2.16 %**** Beginning of derivation protocol ****
% 1.95/2.16 % SZS output start CNFRefutation
% See solution above
% 1.95/2.16
% 1.95/2.16 %**** End of derivation protocol ****
% 1.95/2.16 %**** no. of clauses in derivation: 238 ****
% 1.95/2.16 %**** clause counter: 237 ****
% 1.95/2.16
% 1.95/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:237,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------