%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET063^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:39:16 AM UTC 2026
% Result : Theorem 1.23s 0.44s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 45
% Syntax : Number of formulae : 466 ( 254 unt; 0 typ; 10 def)
% Number of atoms : 2750 ( 651 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 6390 ( 941 ~; 687 |; 27 &;4665 @)
% ( 21 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 5 con; 0-3 aty)
% Number of variables : 1248 ( 109 ^;1135 !; 4 ?;1248 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_set,type,
equal_set: $i > $i > mworld > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_member,type,
member: $i > $i > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mexists_di,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mforall_di,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(tp_sK1_SY3,type,
sK1_SY3: $i ).
thf(tp_sK2_SY862,type,
sK2_SY862: $i > $i > $i ).
thf(tp_sK3_SY868,type,
sK3_SY868: $i > $i > $i ).
thf(tp_sK4_SY879,type,
sK4_SY879: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > mworld > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor_def) ).
thf(1,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] :
( mequiv @ ( member @ X @ ( product @ A ) )
@ ( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_0) ).
thf(2,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] :
( mequiv @ ( member @ X @ ( sum @ A ) )
@ ( mexists_di
@ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_0) ).
thf(3,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_0) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_0) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_0) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_0) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_0) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_0) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set_0) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_0) ).
thf(11,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_di
@ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_0) ).
thf(12,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(14,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(15,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(16,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_2) ).
thf(17,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_1) ).
thf(18,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(19,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(20,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(21,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(22,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution_1) ).
thf(23,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(24,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution_1) ).
thf(25,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set_substitution_1) ).
thf(26,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_2) ).
thf(27,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_1) ).
thf(28,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_2) ).
thf(29,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_1) ).
thf(30,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mforall_di
@ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(31,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(32,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(33,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(34,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(35,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( equal_set @ ( intersection @ A @ empty_set ) @ empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI17) ).
thf(36,negated_conjecture,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( equal_set @ ( intersection @ A @ empty_set ) @ empty_set ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[35]) ).
thf(37,plain,
( ( ! [SY3: $i] : ( equal_set @ ( intersection @ SY3 @ empty_set ) @ empty_set @ mactual ) )
= $false ),
inference(unfold_def,[status(thm)],[36,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(38,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( member @ SY30 @ ( product @ SY31 ) @ mactual )
<=> ! [SY32: $i] :
( ( member @ SY32 @ SY31 @ mactual )
=> ( member @ SY30 @ SY32 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(39,plain,
( ( ! [SY61: $i,SY62: $i] :
( ( member @ SY61 @ ( sum @ SY62 ) @ mactual )
<=> ? [SY63: $i] :
( ( member @ SY63 @ SY62 @ mactual )
& ( member @ SY61 @ SY63 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(40,plain,
( ( ! [SY91: $i,SY92: $i,SY93: $i] :
( ( member @ SY91 @ ( unordered_pair @ SY92 @ SY93 ) @ mactual )
<=> ( ( qmltpeq @ SY91 @ SY92 @ mactual )
| ( qmltpeq @ SY91 @ SY93 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(41,plain,
( ( ! [SY110: $i,SY111: $i] :
( ( member @ SY110 @ ( singleton @ SY111 ) @ mactual )
<=> ( qmltpeq @ SY110 @ SY111 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(42,plain,
( ( ! [SY139: $i,SY140: $i,SY141: $i] :
( ( member @ SY139 @ ( difference @ SY141 @ SY140 ) @ mactual )
<=> ( ( member @ SY139 @ SY141 @ mactual )
& ~ ( member @ SY139 @ SY140 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(43,plain,
( ( ! [SY150: $i] :
~ ( member @ SY150 @ empty_set @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(44,plain,
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ( member @ SY176 @ ( union @ SY177 @ SY178 ) @ mactual )
<=> ( ( member @ SY176 @ SY177 @ mactual )
| ( member @ SY176 @ SY178 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(45,plain,
( ( ! [SY206: $i,SY207: $i,SY208: $i] :
( ( member @ SY206 @ ( intersection @ SY207 @ SY208 ) @ mactual )
<=> ( ( member @ SY206 @ SY207 @ mactual )
& ( member @ SY206 @ SY208 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(46,plain,
( ( ! [SY225: $i,SY226: $i] :
( ( member @ SY225 @ ( power_set @ SY226 ) @ mactual )
<=> ( subset @ SY225 @ SY226 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(47,plain,
( ( ! [SY245: $i,SY246: $i] :
( ( equal_set @ SY245 @ SY246 @ mactual )
<=> ( ( subset @ SY245 @ SY246 @ mactual )
& ( subset @ SY246 @ SY245 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(48,plain,
( ( ! [SY274: $i,SY275: $i] :
( ( subset @ SY274 @ SY275 @ mactual )
<=> ! [SY276: $i] :
( ( member @ SY276 @ SY274 @ mactual )
=> ( member @ SY276 @ SY275 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(49,plain,
( ( ! [SY304: $i,SY305: $i,SY306: $i] :
( ( ( qmltpeq @ SY304 @ SY305 @ mactual )
& ( subset @ SY306 @ SY304 @ mactual ) )
=> ( subset @ SY306 @ SY305 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(50,plain,
( ( ! [SY334: $i,SY335: $i,SY336: $i] :
( ( ( qmltpeq @ SY334 @ SY335 @ mactual )
& ( subset @ SY334 @ SY336 @ mactual ) )
=> ( subset @ SY335 @ SY336 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(51,plain,
( ( ! [SY364: $i,SY365: $i,SY366: $i] :
( ( ( qmltpeq @ SY364 @ SY365 @ mactual )
& ( member @ SY366 @ SY364 @ mactual ) )
=> ( member @ SY366 @ SY365 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(52,plain,
( ( ! [SY394: $i,SY395: $i,SY396: $i] :
( ( ( qmltpeq @ SY394 @ SY395 @ mactual )
& ( member @ SY394 @ SY396 @ mactual ) )
=> ( member @ SY395 @ SY396 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(53,plain,
( ( ! [SY424: $i,SY425: $i,SY426: $i] :
( ( ( qmltpeq @ SY424 @ SY425 @ mactual )
& ( equal_set @ SY426 @ SY424 @ mactual ) )
=> ( equal_set @ SY426 @ SY425 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(54,plain,
( ( ! [SY454: $i,SY455: $i,SY456: $i] :
( ( ( qmltpeq @ SY454 @ SY455 @ mactual )
& ( equal_set @ SY454 @ SY456 @ mactual ) )
=> ( equal_set @ SY455 @ SY456 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(55,plain,
( ( ! [SY481: $i,SY482: $i,SY483: $i] :
( ( qmltpeq @ SY481 @ SY482 @ mactual )
=> ( qmltpeq @ ( unordered_pair @ SY483 @ SY481 ) @ ( unordered_pair @ SY483 @ SY482 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(56,plain,
( ( ! [SY508: $i,SY509: $i,SY510: $i] :
( ( qmltpeq @ SY508 @ SY509 @ mactual )
=> ( qmltpeq @ ( unordered_pair @ SY508 @ SY510 ) @ ( unordered_pair @ SY509 @ SY510 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(57,plain,
( ( ! [SY535: $i,SY536: $i,SY537: $i] :
( ( qmltpeq @ SY535 @ SY536 @ mactual )
=> ( qmltpeq @ ( union @ SY537 @ SY535 ) @ ( union @ SY537 @ SY536 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(58,plain,
( ( ! [SY562: $i,SY563: $i,SY564: $i] :
( ( qmltpeq @ SY562 @ SY563 @ mactual )
=> ( qmltpeq @ ( union @ SY562 @ SY564 ) @ ( union @ SY563 @ SY564 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(59,plain,
( ( ! [SY581: $i,SY582: $i] :
( ( qmltpeq @ SY581 @ SY582 @ mactual )
=> ( qmltpeq @ ( sum @ SY581 ) @ ( sum @ SY582 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(60,plain,
( ( ! [SY598: $i,SY599: $i] :
( ( qmltpeq @ SY598 @ SY599 @ mactual )
=> ( qmltpeq @ ( singleton @ SY598 ) @ ( singleton @ SY599 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(61,plain,
( ( ! [SY615: $i,SY616: $i] :
( ( qmltpeq @ SY615 @ SY616 @ mactual )
=> ( qmltpeq @ ( product @ SY615 ) @ ( product @ SY616 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(62,plain,
( ( ! [SY632: $i,SY633: $i] :
( ( qmltpeq @ SY632 @ SY633 @ mactual )
=> ( qmltpeq @ ( power_set @ SY632 ) @ ( power_set @ SY633 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(63,plain,
( ( ! [SY657: $i,SY658: $i,SY659: $i] :
( ( qmltpeq @ SY657 @ SY658 @ mactual )
=> ( qmltpeq @ ( intersection @ SY659 @ SY657 ) @ ( intersection @ SY659 @ SY658 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(64,plain,
( ( ! [SY684: $i,SY685: $i,SY686: $i] :
( ( qmltpeq @ SY684 @ SY685 @ mactual )
=> ( qmltpeq @ ( intersection @ SY684 @ SY686 ) @ ( intersection @ SY685 @ SY686 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(65,plain,
( ( ! [SY711: $i,SY712: $i,SY713: $i] :
( ( qmltpeq @ SY711 @ SY712 @ mactual )
=> ( qmltpeq @ ( difference @ SY713 @ SY711 ) @ ( difference @ SY713 @ SY712 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(66,plain,
( ( ! [SY738: $i,SY739: $i,SY740: $i] :
( ( qmltpeq @ SY738 @ SY739 @ mactual )
=> ( qmltpeq @ ( difference @ SY738 @ SY740 ) @ ( difference @ SY739 @ SY740 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(67,plain,
( ( ! [SY768: $i,SY769: $i,SY770: $i] :
( ( ( qmltpeq @ SY768 @ SY769 @ mactual )
& ( qmltpeq @ SY769 @ SY770 @ mactual ) )
=> ( qmltpeq @ SY768 @ SY770 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(68,plain,
( ( ! [SY787: $i,SY788: $i] :
( ( qmltpeq @ SY787 @ SY788 @ mactual )
=> ( qmltpeq @ SY788 @ SY787 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(69,plain,
( ( ! [SY794: $i] : ( qmltpeq @ SY794 @ SY794 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[32,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(70,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(71,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[34,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(72,plain,
( ( equal_set @ ( intersection @ sK1_SY3 @ empty_set ) @ empty_set @ mactual )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(73,plain,
( ( ~ ( equal_set @ ( intersection @ sK1_SY3 @ empty_set ) @ empty_set @ mactual ) )
= $true ),
inference(polarity_switch,[status(thm)],[72]) ).
thf(74,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(75,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(76,plain,
( ( ! [SY794: $i] : ( qmltpeq @ SY794 @ SY794 @ mactual ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(77,plain,
( ( ! [SY787: $i,SY788: $i] :
( ( qmltpeq @ SY787 @ SY788 @ mactual )
=> ( qmltpeq @ SY788 @ SY787 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [SY768: $i,SY769: $i,SY770: $i] :
( ( ( qmltpeq @ SY768 @ SY769 @ mactual )
& ( qmltpeq @ SY769 @ SY770 @ mactual ) )
=> ( qmltpeq @ SY768 @ SY770 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(79,plain,
( ( ! [SY738: $i,SY739: $i,SY740: $i] :
( ( qmltpeq @ SY738 @ SY739 @ mactual )
=> ( qmltpeq @ ( difference @ SY738 @ SY740 ) @ ( difference @ SY739 @ SY740 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(80,plain,
( ( ! [SY711: $i,SY712: $i,SY713: $i] :
( ( qmltpeq @ SY711 @ SY712 @ mactual )
=> ( qmltpeq @ ( difference @ SY713 @ SY711 ) @ ( difference @ SY713 @ SY712 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(81,plain,
( ( ! [SY684: $i,SY685: $i,SY686: $i] :
( ( qmltpeq @ SY684 @ SY685 @ mactual )
=> ( qmltpeq @ ( intersection @ SY684 @ SY686 ) @ ( intersection @ SY685 @ SY686 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(82,plain,
( ( ! [SY657: $i,SY658: $i,SY659: $i] :
( ( qmltpeq @ SY657 @ SY658 @ mactual )
=> ( qmltpeq @ ( intersection @ SY659 @ SY657 ) @ ( intersection @ SY659 @ SY658 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(83,plain,
( ( ! [SY632: $i,SY633: $i] :
( ( qmltpeq @ SY632 @ SY633 @ mactual )
=> ( qmltpeq @ ( power_set @ SY632 ) @ ( power_set @ SY633 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(84,plain,
( ( ! [SY615: $i,SY616: $i] :
( ( qmltpeq @ SY615 @ SY616 @ mactual )
=> ( qmltpeq @ ( product @ SY615 ) @ ( product @ SY616 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(85,plain,
( ( ! [SY598: $i,SY599: $i] :
( ( qmltpeq @ SY598 @ SY599 @ mactual )
=> ( qmltpeq @ ( singleton @ SY598 ) @ ( singleton @ SY599 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(86,plain,
( ( ! [SY581: $i,SY582: $i] :
( ( qmltpeq @ SY581 @ SY582 @ mactual )
=> ( qmltpeq @ ( sum @ SY581 ) @ ( sum @ SY582 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(87,plain,
( ( ! [SY562: $i,SY563: $i,SY564: $i] :
( ( qmltpeq @ SY562 @ SY563 @ mactual )
=> ( qmltpeq @ ( union @ SY562 @ SY564 ) @ ( union @ SY563 @ SY564 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(88,plain,
( ( ! [SY535: $i,SY536: $i,SY537: $i] :
( ( qmltpeq @ SY535 @ SY536 @ mactual )
=> ( qmltpeq @ ( union @ SY537 @ SY535 ) @ ( union @ SY537 @ SY536 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(89,plain,
( ( ! [SY508: $i,SY509: $i,SY510: $i] :
( ( qmltpeq @ SY508 @ SY509 @ mactual )
=> ( qmltpeq @ ( unordered_pair @ SY508 @ SY510 ) @ ( unordered_pair @ SY509 @ SY510 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(90,plain,
( ( ! [SY481: $i,SY482: $i,SY483: $i] :
( ( qmltpeq @ SY481 @ SY482 @ mactual )
=> ( qmltpeq @ ( unordered_pair @ SY483 @ SY481 ) @ ( unordered_pair @ SY483 @ SY482 ) @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(91,plain,
( ( ! [SY454: $i,SY455: $i,SY456: $i] :
( ( ( qmltpeq @ SY454 @ SY455 @ mactual )
& ( equal_set @ SY454 @ SY456 @ mactual ) )
=> ( equal_set @ SY455 @ SY456 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(92,plain,
( ( ! [SY424: $i,SY425: $i,SY426: $i] :
( ( ( qmltpeq @ SY424 @ SY425 @ mactual )
& ( equal_set @ SY426 @ SY424 @ mactual ) )
=> ( equal_set @ SY426 @ SY425 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(93,plain,
( ( ! [SY394: $i,SY395: $i,SY396: $i] :
( ( ( qmltpeq @ SY394 @ SY395 @ mactual )
& ( member @ SY394 @ SY396 @ mactual ) )
=> ( member @ SY395 @ SY396 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(94,plain,
( ( ! [SY364: $i,SY365: $i,SY366: $i] :
( ( ( qmltpeq @ SY364 @ SY365 @ mactual )
& ( member @ SY366 @ SY364 @ mactual ) )
=> ( member @ SY366 @ SY365 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(95,plain,
( ( ! [SY334: $i,SY335: $i,SY336: $i] :
( ( ( qmltpeq @ SY334 @ SY335 @ mactual )
& ( subset @ SY334 @ SY336 @ mactual ) )
=> ( subset @ SY335 @ SY336 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(96,plain,
( ( ! [SY304: $i,SY305: $i,SY306: $i] :
( ( ( qmltpeq @ SY304 @ SY305 @ mactual )
& ( subset @ SY306 @ SY304 @ mactual ) )
=> ( subset @ SY306 @ SY305 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(97,plain,
( ( ! [SY274: $i,SY275: $i] :
( ( subset @ SY274 @ SY275 @ mactual )
<=> ! [SY276: $i] :
( ( member @ SY276 @ SY274 @ mactual )
=> ( member @ SY276 @ SY275 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(98,plain,
( ( ! [SY245: $i,SY246: $i] :
( ( equal_set @ SY245 @ SY246 @ mactual )
<=> ( ( subset @ SY245 @ SY246 @ mactual )
& ( subset @ SY246 @ SY245 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(99,plain,
( ( ! [SY225: $i,SY226: $i] :
( ( member @ SY225 @ ( power_set @ SY226 ) @ mactual )
<=> ( subset @ SY225 @ SY226 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(100,plain,
( ( ! [SY206: $i,SY207: $i,SY208: $i] :
( ( member @ SY206 @ ( intersection @ SY207 @ SY208 ) @ mactual )
<=> ( ( member @ SY206 @ SY207 @ mactual )
& ( member @ SY206 @ SY208 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(101,plain,
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ( member @ SY176 @ ( union @ SY177 @ SY178 ) @ mactual )
<=> ( ( member @ SY176 @ SY177 @ mactual )
| ( member @ SY176 @ SY178 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(102,plain,
( ( ! [SY150: $i] :
~ ( member @ SY150 @ empty_set @ mactual ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(103,plain,
( ( ! [SY139: $i,SY140: $i,SY141: $i] :
( ( member @ SY139 @ ( difference @ SY141 @ SY140 ) @ mactual )
<=> ( ( member @ SY139 @ SY141 @ mactual )
& ~ ( member @ SY139 @ SY140 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(104,plain,
( ( ! [SY110: $i,SY111: $i] :
( ( member @ SY110 @ ( singleton @ SY111 ) @ mactual )
<=> ( qmltpeq @ SY110 @ SY111 @ mactual ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(105,plain,
( ( ! [SY91: $i,SY92: $i,SY93: $i] :
( ( member @ SY91 @ ( unordered_pair @ SY92 @ SY93 ) @ mactual )
<=> ( ( qmltpeq @ SY91 @ SY92 @ mactual )
| ( qmltpeq @ SY91 @ SY93 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(106,plain,
( ( ! [SY61: $i,SY62: $i] :
( ( member @ SY61 @ ( sum @ SY62 ) @ mactual )
<=> ? [SY63: $i] :
( ( member @ SY63 @ SY62 @ mactual )
& ( member @ SY61 @ SY63 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(107,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( member @ SY30 @ ( product @ SY31 ) @ mactual )
<=> ! [SY32: $i] :
( ( member @ SY32 @ SY31 @ mactual )
=> ( member @ SY30 @ SY32 @ mactual ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(108,plain,
( ( ~ ( equal_set @ ( intersection @ sK1_SY3 @ empty_set ) @ empty_set @ mactual ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( sum @ SX0 ) @ ( sum @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( union @ SX2 @ SX0 ) @ ( union @ SX2 @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( power_set @ SX0 ) @ ( power_set @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( equal_set @ SX2 @ SX0 @ mactual ) )
| ( equal_set @ SX2 @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX0 @ SX2 @ mactual ) )
| ( subset @ SX1 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX0 @ SX2 @ mactual ) )
| ( member @ SX1 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( power_set @ SX1 ) @ mactual )
| ( subset @ SX0 @ SX1 @ mactual ) )
| ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ( member @ SX0 @ ( power_set @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 @ mactual )
| ( member @ SX2 @ SX1 @ mactual ) )
| ( subset @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( equal_set @ SX0 @ SX2 @ mactual ) )
| ( equal_set @ SX1 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(118,plain,
( ( ! [SX0: mworld,SX1: mworld,SX2: mworld] :
( ~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ( mrel @ SX1 @ SX2 ) )
| ( mrel @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( product @ SX0 ) @ ( product @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( union @ SX0 @ SX2 ) @ ( union @ SX1 @ SX2 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SX2 @ SX0 ) @ ( unordered_pair @ SX2 @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( product @ SX1 ) @ mactual )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 @ mactual )
| ( member @ SX0 @ SX2 @ mactual ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX1 @ mactual )
| ( member @ SX0 @ SX2 @ mactual ) )
| ( member @ SX0 @ ( product @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) @ mactual )
| ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ SX0 @ SX2 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ SX0 @ SX2 @ mactual ) )
| ( member @ SX0 @ ( unordered_pair @ SX1 @ SX2 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_set @ SX0 @ SX1 @ mactual )
| ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX1 @ SX0 @ mactual ) )
| ( equal_set @ SX0 @ SX1 @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) @ mactual )
| ~ ( ~ ( member @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX0 @ SX2 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX0 @ SX2 @ mactual ) )
| ( member @ SX0 @ ( intersection @ SX1 @ SX2 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( member @ SX2 @ SX0 @ mactual ) )
| ( member @ SX2 @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ SX1 @ SX0 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( intersection @ SX0 @ SX2 ) @ ( intersection @ SX1 @ SX2 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( qmltpeq @ SX1 @ SX2 @ mactual ) )
| ( qmltpeq @ SX0 @ SX2 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ~ ( subset @ SX2 @ SX0 @ mactual ) )
| ( subset @ SX2 @ SX1 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( union @ SX1 @ SX2 ) @ mactual )
| ( member @ SX0 @ SX1 @ mactual )
| ( member @ SX0 @ SX2 @ mactual ) )
| ~ ( ~ ( ( member @ SX0 @ SX1 @ mactual )
| ( member @ SX0 @ SX2 @ mactual ) )
| ( member @ SX0 @ ( union @ SX1 @ SX2 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( difference @ SX0 @ SX2 ) @ ( difference @ SX1 @ SX2 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(134,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SX0 @ SX2 ) @ ( unordered_pair @ SX1 @ SX2 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( intersection @ SX2 @ SX0 ) @ ( intersection @ SX2 @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(136,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( sum @ SX1 ) @ mactual )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX1 @ mactual )
| ~ ( member @ SX0 @ SX2 @ mactual ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( member @ SX2 @ SX1 @ mactual )
| ~ ( member @ SX0 @ SX2 @ mactual ) )
| ( member @ SX0 @ ( sum @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) @ mactual )
| ~ ( ~ ( member @ SX0 @ SX2 @ mactual )
| ~ ~ ( member @ SX0 @ SX1 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX2 @ mactual )
| ~ ~ ( member @ SX0 @ SX1 @ mactual ) )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( singleton @ SX1 ) @ mactual )
| ( qmltpeq @ SX0 @ SX1 @ mactual ) )
| ~ ( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( member @ SX0 @ ( singleton @ SX1 ) @ mactual ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( difference @ SX2 @ SX0 ) @ ( difference @ SX2 @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(140,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(141,plain,
! [SV2: $i] :
( ( qmltpeq @ SV2 @ SV2 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(142,plain,
! [SV3: $i] :
( ( ~ ( member @ SV3 @ empty_set @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(143,plain,
( ( equal_set @ ( intersection @ sK1_SY3 @ empty_set ) @ empty_set @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(144,plain,
! [SV4: $i] :
( ( ! [SY800: $i] :
( ~ ( qmltpeq @ SV4 @ SY800 @ mactual )
| ( qmltpeq @ ( sum @ SV4 ) @ ( sum @ SY800 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(145,plain,
! [SV5: $i] :
( ( ! [SY801: $i,SY802: $i] :
( ~ ( qmltpeq @ SV5 @ SY801 @ mactual )
| ( qmltpeq @ ( union @ SY802 @ SV5 ) @ ( union @ SY802 @ SY801 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(146,plain,
! [SV6: $i] :
( ( ! [SY803: $i] :
( ~ ( qmltpeq @ SV6 @ SY803 @ mactual )
| ( qmltpeq @ ( power_set @ SV6 ) @ ( power_set @ SY803 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(147,plain,
! [SV7: $i] :
( ( ! [SY804: $i,SY805: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV7 @ SY804 @ mactual )
| ~ ( equal_set @ SY805 @ SV7 @ mactual ) )
| ( equal_set @ SY805 @ SY804 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(148,plain,
! [SV8: $i] :
( ( ! [SY806: $i,SY807: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV8 @ SY806 @ mactual )
| ~ ( subset @ SV8 @ SY807 @ mactual ) )
| ( subset @ SY806 @ SY807 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(149,plain,
! [SV9: $i] :
( ( ! [SY808: $i,SY809: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV9 @ SY808 @ mactual )
| ~ ( member @ SV9 @ SY809 @ mactual ) )
| ( member @ SY808 @ SY809 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(150,plain,
! [SV10: $i] :
( ( ! [SY810: $i] :
~ ( ~ ( ~ ( member @ SV10 @ ( power_set @ SY810 ) @ mactual )
| ( subset @ SV10 @ SY810 @ mactual ) )
| ~ ( ~ ( subset @ SV10 @ SY810 @ mactual )
| ( member @ SV10 @ ( power_set @ SY810 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(151,plain,
! [SV11: $i] :
( ( ! [SY811: $i] :
~ ( ~ ( ~ ( subset @ SV11 @ SY811 @ mactual )
| ! [SY812: $i] :
( ~ ( member @ SY812 @ SV11 @ mactual )
| ( member @ SY812 @ SY811 @ mactual ) ) )
| ~ ( ~ ! [SY813: $i] :
( ~ ( member @ SY813 @ SV11 @ mactual )
| ( member @ SY813 @ SY811 @ mactual ) )
| ( subset @ SV11 @ SY811 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(152,plain,
! [SV12: $i] :
( ( ! [SY814: $i,SY815: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV12 @ SY814 @ mactual )
| ~ ( equal_set @ SV12 @ SY815 @ mactual ) )
| ( equal_set @ SY814 @ SY815 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(153,plain,
! [SV13: mworld] :
( ( ! [SY816: mworld,SY817: mworld] :
( ~ ~ ( ~ ( mrel @ SV13 @ SY816 )
| ~ ( mrel @ SY816 @ SY817 ) )
| ( mrel @ SV13 @ SY817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(154,plain,
! [SV14: $i] :
( ( ! [SY818: $i] :
( ~ ( qmltpeq @ SV14 @ SY818 @ mactual )
| ( qmltpeq @ ( product @ SV14 ) @ ( product @ SY818 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(155,plain,
! [SV15: $i] :
( ( ! [SY819: $i,SY820: $i] :
( ~ ( qmltpeq @ SV15 @ SY819 @ mactual )
| ( qmltpeq @ ( union @ SV15 @ SY820 ) @ ( union @ SY819 @ SY820 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(156,plain,
! [SV16: $i] :
( ( ! [SY821: $i,SY822: $i] :
( ~ ( qmltpeq @ SV16 @ SY821 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SY822 @ SV16 ) @ ( unordered_pair @ SY822 @ SY821 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(157,plain,
! [SV17: $i] :
( ( ! [SY823: $i] :
~ ( ~ ( ~ ( member @ SV17 @ ( product @ SY823 ) @ mactual )
| ! [SY824: $i] :
( ~ ( member @ SY824 @ SY823 @ mactual )
| ( member @ SV17 @ SY824 @ mactual ) ) )
| ~ ( ~ ! [SY825: $i] :
( ~ ( member @ SY825 @ SY823 @ mactual )
| ( member @ SV17 @ SY825 @ mactual ) )
| ( member @ SV17 @ ( product @ SY823 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(158,plain,
! [SV18: $i] :
( ( ! [SY826: $i,SY827: $i] :
~ ( ~ ( ~ ( member @ SV18 @ ( unordered_pair @ SY826 @ SY827 ) @ mactual )
| ( qmltpeq @ SV18 @ SY826 @ mactual )
| ( qmltpeq @ SV18 @ SY827 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV18 @ SY826 @ mactual )
| ( qmltpeq @ SV18 @ SY827 @ mactual ) )
| ( member @ SV18 @ ( unordered_pair @ SY826 @ SY827 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(159,plain,
! [SV19: $i] :
( ( ! [SY828: $i] :
~ ( ~ ( ~ ( equal_set @ SV19 @ SY828 @ mactual )
| ~ ( ~ ( subset @ SV19 @ SY828 @ mactual )
| ~ ( subset @ SY828 @ SV19 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV19 @ SY828 @ mactual )
| ~ ( subset @ SY828 @ SV19 @ mactual ) )
| ( equal_set @ SV19 @ SY828 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(160,plain,
! [SV20: $i] :
( ( ! [SY829: $i,SY830: $i] :
~ ( ~ ( ~ ( member @ SV20 @ ( intersection @ SY829 @ SY830 ) @ mactual )
| ~ ( ~ ( member @ SV20 @ SY829 @ mactual )
| ~ ( member @ SV20 @ SY830 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV20 @ SY829 @ mactual )
| ~ ( member @ SV20 @ SY830 @ mactual ) )
| ( member @ SV20 @ ( intersection @ SY829 @ SY830 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(161,plain,
! [SV21: $i] :
( ( ! [SY831: $i] :
( ~ ( qmltpeq @ SV21 @ SY831 @ mactual )
| ( qmltpeq @ ( singleton @ SV21 ) @ ( singleton @ SY831 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(162,plain,
! [SV22: $i] :
( ( ! [SY832: $i,SY833: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV22 @ SY832 @ mactual )
| ~ ( member @ SY833 @ SV22 @ mactual ) )
| ( member @ SY833 @ SY832 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(163,plain,
! [SV23: $i] :
( ( ! [SY834: $i] :
( ~ ( qmltpeq @ SV23 @ SY834 @ mactual )
| ( qmltpeq @ SY834 @ SV23 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(164,plain,
! [SV24: $i] :
( ( ! [SY835: $i,SY836: $i] :
( ~ ( qmltpeq @ SV24 @ SY835 @ mactual )
| ( qmltpeq @ ( intersection @ SV24 @ SY836 ) @ ( intersection @ SY835 @ SY836 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(165,plain,
! [SV25: $i] :
( ( ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV25 @ SY837 @ mactual )
| ~ ( qmltpeq @ SY837 @ SY838 @ mactual ) )
| ( qmltpeq @ SV25 @ SY838 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(166,plain,
! [SV26: $i] :
( ( ! [SY839: $i,SY840: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV26 @ SY839 @ mactual )
| ~ ( subset @ SY840 @ SV26 @ mactual ) )
| ( subset @ SY840 @ SY839 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(167,plain,
! [SV27: $i] :
( ( ! [SY841: $i,SY842: $i] :
~ ( ~ ( ~ ( member @ SV27 @ ( union @ SY841 @ SY842 ) @ mactual )
| ( member @ SV27 @ SY841 @ mactual )
| ( member @ SV27 @ SY842 @ mactual ) )
| ~ ( ~ ( ( member @ SV27 @ SY841 @ mactual )
| ( member @ SV27 @ SY842 @ mactual ) )
| ( member @ SV27 @ ( union @ SY841 @ SY842 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(168,plain,
! [SV28: $i] :
( ( ! [SY843: $i,SY844: $i] :
( ~ ( qmltpeq @ SV28 @ SY843 @ mactual )
| ( qmltpeq @ ( difference @ SV28 @ SY844 ) @ ( difference @ SY843 @ SY844 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(169,plain,
! [SV29: $i] :
( ( ! [SY845: $i,SY846: $i] :
( ~ ( qmltpeq @ SV29 @ SY845 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV29 @ SY846 ) @ ( unordered_pair @ SY845 @ SY846 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(170,plain,
! [SV30: $i] :
( ( ! [SY847: $i,SY848: $i] :
( ~ ( qmltpeq @ SV30 @ SY847 @ mactual )
| ( qmltpeq @ ( intersection @ SY848 @ SV30 ) @ ( intersection @ SY848 @ SY847 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(171,plain,
! [SV31: $i] :
( ( ! [SY849: $i] :
~ ( ~ ( ~ ( member @ SV31 @ ( sum @ SY849 ) @ mactual )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( member @ SY850 @ SY849 @ mactual )
| ~ ( member @ SV31 @ SY850 @ mactual ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( member @ SY851 @ SY849 @ mactual )
| ~ ( member @ SV31 @ SY851 @ mactual ) )
| ( member @ SV31 @ ( sum @ SY849 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(172,plain,
! [SV32: $i] :
( ( ! [SY852: $i,SY853: $i] :
~ ( ~ ( ~ ( member @ SV32 @ ( difference @ SY853 @ SY852 ) @ mactual )
| ~ ( ~ ( member @ SV32 @ SY853 @ mactual )
| ~ ~ ( member @ SV32 @ SY852 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV32 @ SY853 @ mactual )
| ~ ~ ( member @ SV32 @ SY852 @ mactual ) )
| ( member @ SV32 @ ( difference @ SY853 @ SY852 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(173,plain,
! [SV33: $i] :
( ( ! [SY854: $i] :
~ ( ~ ( ~ ( member @ SV33 @ ( singleton @ SY854 ) @ mactual )
| ( qmltpeq @ SV33 @ SY854 @ mactual ) )
| ~ ( ~ ( qmltpeq @ SV33 @ SY854 @ mactual )
| ( member @ SV33 @ ( singleton @ SY854 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(174,plain,
! [SV34: $i] :
( ( ! [SY855: $i,SY856: $i] :
( ~ ( qmltpeq @ SV34 @ SY855 @ mactual )
| ( qmltpeq @ ( difference @ SY856 @ SV34 ) @ ( difference @ SY856 @ SY855 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(175,plain,
! [SV3: $i] :
( ( member @ SV3 @ empty_set @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(176,plain,
! [SV35: $i,SV4: $i] :
( ( ~ ( qmltpeq @ SV4 @ SV35 @ mactual )
| ( qmltpeq @ ( sum @ SV4 ) @ ( sum @ SV35 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(177,plain,
! [SV36: $i,SV5: $i] :
( ( ! [SY857: $i] :
( ~ ( qmltpeq @ SV5 @ SV36 @ mactual )
| ( qmltpeq @ ( union @ SY857 @ SV5 ) @ ( union @ SY857 @ SV36 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(178,plain,
! [SV37: $i,SV6: $i] :
( ( ~ ( qmltpeq @ SV6 @ SV37 @ mactual )
| ( qmltpeq @ ( power_set @ SV6 ) @ ( power_set @ SV37 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(179,plain,
! [SV38: $i,SV7: $i] :
( ( ! [SY858: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV7 @ SV38 @ mactual )
| ~ ( equal_set @ SY858 @ SV7 @ mactual ) )
| ( equal_set @ SY858 @ SV38 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(180,plain,
! [SV39: $i,SV8: $i] :
( ( ! [SY859: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV8 @ SV39 @ mactual )
| ~ ( subset @ SV8 @ SY859 @ mactual ) )
| ( subset @ SV39 @ SY859 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(181,plain,
! [SV40: $i,SV9: $i] :
( ( ! [SY860: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV40 @ mactual )
| ~ ( member @ SV9 @ SY860 @ mactual ) )
| ( member @ SV40 @ SY860 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(182,plain,
! [SV41: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( member @ SV10 @ ( power_set @ SV41 ) @ mactual )
| ( subset @ SV10 @ SV41 @ mactual ) )
| ~ ( ~ ( subset @ SV10 @ SV41 @ mactual )
| ( member @ SV10 @ ( power_set @ SV41 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(183,plain,
! [SV42: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV11 @ SV42 @ mactual )
| ! [SY861: $i] :
( ~ ( member @ SY861 @ SV11 @ mactual )
| ( member @ SY861 @ SV42 @ mactual ) ) )
| ~ ( ~ ! [SY862: $i] :
( ~ ( member @ SY862 @ SV11 @ mactual )
| ( member @ SY862 @ SV42 @ mactual ) )
| ( subset @ SV11 @ SV42 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(184,plain,
! [SV43: $i,SV12: $i] :
( ( ! [SY863: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV12 @ SV43 @ mactual )
| ~ ( equal_set @ SV12 @ SY863 @ mactual ) )
| ( equal_set @ SV43 @ SY863 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(185,plain,
! [SV44: mworld,SV13: mworld] :
( ( ! [SY864: mworld] :
( ~ ~ ( ~ ( mrel @ SV13 @ SV44 )
| ~ ( mrel @ SV44 @ SY864 ) )
| ( mrel @ SV13 @ SY864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(186,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( qmltpeq @ SV14 @ SV45 @ mactual )
| ( qmltpeq @ ( product @ SV14 ) @ ( product @ SV45 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(187,plain,
! [SV46: $i,SV15: $i] :
( ( ! [SY865: $i] :
( ~ ( qmltpeq @ SV15 @ SV46 @ mactual )
| ( qmltpeq @ ( union @ SV15 @ SY865 ) @ ( union @ SV46 @ SY865 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(188,plain,
! [SV47: $i,SV16: $i] :
( ( ! [SY866: $i] :
( ~ ( qmltpeq @ SV16 @ SV47 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SY866 @ SV16 ) @ ( unordered_pair @ SY866 @ SV47 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(189,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( ~ ( ~ ( member @ SV17 @ ( product @ SV48 ) @ mactual )
| ! [SY867: $i] :
( ~ ( member @ SY867 @ SV48 @ mactual )
| ( member @ SV17 @ SY867 @ mactual ) ) )
| ~ ( ~ ! [SY868: $i] :
( ~ ( member @ SY868 @ SV48 @ mactual )
| ( member @ SV17 @ SY868 @ mactual ) )
| ( member @ SV17 @ ( product @ SV48 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(190,plain,
! [SV49: $i,SV18: $i] :
( ( ! [SY869: $i] :
~ ( ~ ( ~ ( member @ SV18 @ ( unordered_pair @ SV49 @ SY869 ) @ mactual )
| ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SY869 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SY869 @ mactual ) )
| ( member @ SV18 @ ( unordered_pair @ SV49 @ SY869 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(191,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV19 @ SV50 @ mactual )
| ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) )
| ( equal_set @ SV19 @ SV50 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(192,plain,
! [SV51: $i,SV20: $i] :
( ( ! [SY870: $i] :
~ ( ~ ( ~ ( member @ SV20 @ ( intersection @ SV51 @ SY870 ) @ mactual )
| ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SY870 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SY870 @ mactual ) )
| ( member @ SV20 @ ( intersection @ SV51 @ SY870 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(193,plain,
! [SV52: $i,SV21: $i] :
( ( ~ ( qmltpeq @ SV21 @ SV52 @ mactual )
| ( qmltpeq @ ( singleton @ SV21 ) @ ( singleton @ SV52 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(194,plain,
! [SV53: $i,SV22: $i] :
( ( ! [SY871: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual )
| ~ ( member @ SY871 @ SV22 @ mactual ) )
| ( member @ SY871 @ SV53 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(195,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( qmltpeq @ SV23 @ SV54 @ mactual )
| ( qmltpeq @ SV54 @ SV23 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(196,plain,
! [SV55: $i,SV24: $i] :
( ( ! [SY872: $i] :
( ~ ( qmltpeq @ SV24 @ SV55 @ mactual )
| ( qmltpeq @ ( intersection @ SV24 @ SY872 ) @ ( intersection @ SV55 @ SY872 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(197,plain,
! [SV56: $i,SV25: $i] :
( ( ! [SY873: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( qmltpeq @ SV56 @ SY873 @ mactual ) )
| ( qmltpeq @ SV25 @ SY873 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(198,plain,
! [SV57: $i,SV26: $i] :
( ( ! [SY874: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV57 @ mactual )
| ~ ( subset @ SY874 @ SV26 @ mactual ) )
| ( subset @ SY874 @ SV57 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(199,plain,
! [SV58: $i,SV27: $i] :
( ( ! [SY875: $i] :
~ ( ~ ( ~ ( member @ SV27 @ ( union @ SV58 @ SY875 ) @ mactual )
| ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SY875 @ mactual ) )
| ~ ( ~ ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SY875 @ mactual ) )
| ( member @ SV27 @ ( union @ SV58 @ SY875 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(200,plain,
! [SV59: $i,SV28: $i] :
( ( ! [SY876: $i] :
( ~ ( qmltpeq @ SV28 @ SV59 @ mactual )
| ( qmltpeq @ ( difference @ SV28 @ SY876 ) @ ( difference @ SV59 @ SY876 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(201,plain,
! [SV60: $i,SV29: $i] :
( ( ! [SY877: $i] :
( ~ ( qmltpeq @ SV29 @ SV60 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV29 @ SY877 ) @ ( unordered_pair @ SV60 @ SY877 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(202,plain,
! [SV61: $i,SV30: $i] :
( ( ! [SY878: $i] :
( ~ ( qmltpeq @ SV30 @ SV61 @ mactual )
| ( qmltpeq @ ( intersection @ SY878 @ SV30 ) @ ( intersection @ SY878 @ SV61 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(203,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
| ~ ! [SY879: $i] :
~ ~ ( ~ ( member @ SY879 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY879 @ mactual ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( member @ SY880 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY880 @ mactual ) )
| ( member @ SV31 @ ( sum @ SV62 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(204,plain,
! [SV63: $i,SV32: $i] :
( ( ! [SY881: $i] :
~ ( ~ ( ~ ( member @ SV32 @ ( difference @ SY881 @ SV63 ) @ mactual )
| ~ ( ~ ( member @ SV32 @ SY881 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV32 @ SY881 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
| ( member @ SV32 @ ( difference @ SY881 @ SV63 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(205,plain,
! [SV64: $i,SV33: $i] :
( ( ~ ( ~ ( ~ ( member @ SV33 @ ( singleton @ SV64 ) @ mactual )
| ( qmltpeq @ SV33 @ SV64 @ mactual ) )
| ~ ( ~ ( qmltpeq @ SV33 @ SV64 @ mactual )
| ( member @ SV33 @ ( singleton @ SV64 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(206,plain,
! [SV65: $i,SV34: $i] :
( ( ! [SY882: $i] :
( ~ ( qmltpeq @ SV34 @ SV65 @ mactual )
| ( qmltpeq @ ( difference @ SY882 @ SV34 ) @ ( difference @ SY882 @ SV65 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(207,plain,
! [SV35: $i,SV4: $i] :
( ( ( ~ ( qmltpeq @ SV4 @ SV35 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( sum @ SV4 ) @ ( sum @ SV35 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(208,plain,
! [SV66: $i,SV36: $i,SV5: $i] :
( ( ~ ( qmltpeq @ SV5 @ SV36 @ mactual )
| ( qmltpeq @ ( union @ SV66 @ SV5 ) @ ( union @ SV66 @ SV36 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(209,plain,
! [SV37: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV37 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( power_set @ SV6 ) @ ( power_set @ SV37 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(210,plain,
! [SV67: $i,SV38: $i,SV7: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV7 @ SV38 @ mactual )
| ~ ( equal_set @ SV67 @ SV7 @ mactual ) )
| ( equal_set @ SV67 @ SV38 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(211,plain,
! [SV68: $i,SV39: $i,SV8: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV8 @ SV39 @ mactual )
| ~ ( subset @ SV8 @ SV68 @ mactual ) )
| ( subset @ SV39 @ SV68 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(212,plain,
! [SV69: $i,SV40: $i,SV9: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV40 @ mactual )
| ~ ( member @ SV9 @ SV69 @ mactual ) )
| ( member @ SV40 @ SV69 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(213,plain,
! [SV41: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( power_set @ SV41 ) @ mactual )
| ( subset @ SV10 @ SV41 @ mactual ) )
| ~ ( ~ ( subset @ SV10 @ SV41 @ mactual )
| ( member @ SV10 @ ( power_set @ SV41 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(214,plain,
! [SV42: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ SV42 @ mactual )
| ! [SY861: $i] :
( ~ ( member @ SY861 @ SV11 @ mactual )
| ( member @ SY861 @ SV42 @ mactual ) ) )
| ~ ( ~ ! [SY862: $i] :
( ~ ( member @ SY862 @ SV11 @ mactual )
| ( member @ SY862 @ SV42 @ mactual ) )
| ( subset @ SV11 @ SV42 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(215,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV12 @ SV43 @ mactual )
| ~ ( equal_set @ SV12 @ SV70 @ mactual ) )
| ( equal_set @ SV43 @ SV70 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(216,plain,
! [SV71: mworld,SV44: mworld,SV13: mworld] :
( ( ~ ~ ( ~ ( mrel @ SV13 @ SV44 )
| ~ ( mrel @ SV44 @ SV71 ) )
| ( mrel @ SV13 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(217,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( qmltpeq @ SV14 @ SV45 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( product @ SV14 ) @ ( product @ SV45 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(218,plain,
! [SV72: $i,SV46: $i,SV15: $i] :
( ( ~ ( qmltpeq @ SV15 @ SV46 @ mactual )
| ( qmltpeq @ ( union @ SV15 @ SV72 ) @ ( union @ SV46 @ SV72 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(219,plain,
! [SV73: $i,SV47: $i,SV16: $i] :
( ( ~ ( qmltpeq @ SV16 @ SV47 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV73 @ SV16 ) @ ( unordered_pair @ SV73 @ SV47 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(220,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( ~ ( member @ SV17 @ ( product @ SV48 ) @ mactual )
| ! [SY867: $i] :
( ~ ( member @ SY867 @ SV48 @ mactual )
| ( member @ SV17 @ SY867 @ mactual ) ) )
| ~ ( ~ ! [SY868: $i] :
( ~ ( member @ SY868 @ SV48 @ mactual )
| ( member @ SV17 @ SY868 @ mactual ) )
| ( member @ SV17 @ ( product @ SV48 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(221,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
| ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
| ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(222,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ( ~ ( equal_set @ SV19 @ SV50 @ mactual )
| ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) )
| ( equal_set @ SV19 @ SV50 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(223,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
| ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) )
| ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(224,plain,
! [SV52: $i,SV21: $i] :
( ( ( ~ ( qmltpeq @ SV21 @ SV52 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV21 ) @ ( singleton @ SV52 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(225,plain,
! [SV76: $i,SV53: $i,SV22: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual )
| ~ ( member @ SV76 @ SV22 @ mactual ) )
| ( member @ SV76 @ SV53 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(226,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( qmltpeq @ SV23 @ SV54 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV54 @ SV23 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(227,plain,
! [SV77: $i,SV55: $i,SV24: $i] :
( ( ~ ( qmltpeq @ SV24 @ SV55 @ mactual )
| ( qmltpeq @ ( intersection @ SV24 @ SV77 ) @ ( intersection @ SV55 @ SV77 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(228,plain,
! [SV78: $i,SV56: $i,SV25: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( qmltpeq @ SV56 @ SV78 @ mactual ) )
| ( qmltpeq @ SV25 @ SV78 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(229,plain,
! [SV79: $i,SV57: $i,SV26: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV57 @ mactual )
| ~ ( subset @ SV79 @ SV26 @ mactual ) )
| ( subset @ SV79 @ SV57 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(230,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ~ ( ~ ( ~ ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
| ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
| ~ ( ~ ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
| ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(231,plain,
! [SV81: $i,SV59: $i,SV28: $i] :
( ( ~ ( qmltpeq @ SV28 @ SV59 @ mactual )
| ( qmltpeq @ ( difference @ SV28 @ SV81 ) @ ( difference @ SV59 @ SV81 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(232,plain,
! [SV82: $i,SV60: $i,SV29: $i] :
( ( ~ ( qmltpeq @ SV29 @ SV60 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV29 @ SV82 ) @ ( unordered_pair @ SV60 @ SV82 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(233,plain,
! [SV83: $i,SV61: $i,SV30: $i] :
( ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual )
| ( qmltpeq @ ( intersection @ SV83 @ SV30 ) @ ( intersection @ SV83 @ SV61 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(234,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( ~ ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
| ~ ! [SY879: $i] :
~ ~ ( ~ ( member @ SY879 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY879 @ mactual ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( member @ SY880 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY880 @ mactual ) )
| ( member @ SV31 @ ( sum @ SV62 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(235,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ~ ( ~ ( ~ ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
| ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
| ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(236,plain,
! [SV64: $i,SV33: $i] :
( ( ~ ( ~ ( member @ SV33 @ ( singleton @ SV64 ) @ mactual )
| ( qmltpeq @ SV33 @ SV64 @ mactual ) )
| ~ ( ~ ( qmltpeq @ SV33 @ SV64 @ mactual )
| ( member @ SV33 @ ( singleton @ SV64 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(237,plain,
! [SV85: $i,SV65: $i,SV34: $i] :
( ( ~ ( qmltpeq @ SV34 @ SV65 @ mactual )
| ( qmltpeq @ ( difference @ SV85 @ SV34 ) @ ( difference @ SV85 @ SV65 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(238,plain,
! [SV35: $i,SV4: $i] :
( ( ( qmltpeq @ SV4 @ SV35 @ mactual )
= $false )
| ( ( qmltpeq @ ( sum @ SV4 ) @ ( sum @ SV35 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(239,plain,
! [SV66: $i,SV36: $i,SV5: $i] :
( ( ( ~ ( qmltpeq @ SV5 @ SV36 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( union @ SV66 @ SV5 ) @ ( union @ SV66 @ SV36 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(240,plain,
! [SV37: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV37 @ mactual )
= $false )
| ( ( qmltpeq @ ( power_set @ SV6 ) @ ( power_set @ SV37 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(241,plain,
! [SV67: $i,SV38: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV7 @ SV38 @ mactual )
| ~ ( equal_set @ SV67 @ SV7 @ mactual ) ) )
= $true )
| ( ( equal_set @ SV67 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(242,plain,
! [SV68: $i,SV39: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV8 @ SV39 @ mactual )
| ~ ( subset @ SV8 @ SV68 @ mactual ) ) )
= $true )
| ( ( subset @ SV39 @ SV68 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(243,plain,
! [SV69: $i,SV40: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV9 @ SV40 @ mactual )
| ~ ( member @ SV9 @ SV69 @ mactual ) ) )
= $true )
| ( ( member @ SV40 @ SV69 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(244,plain,
! [SV41: $i,SV10: $i] :
( ( ~ ( ~ ( member @ SV10 @ ( power_set @ SV41 ) @ mactual )
| ( subset @ SV10 @ SV41 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(245,plain,
! [SV41: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV41 @ mactual )
| ( member @ SV10 @ ( power_set @ SV41 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(246,plain,
! [SV42: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ SV42 @ mactual )
| ! [SY861: $i] :
( ~ ( member @ SY861 @ SV11 @ mactual )
| ( member @ SY861 @ SV42 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(247,plain,
! [SV42: $i,SV11: $i] :
( ( ~ ( ~ ! [SY862: $i] :
( ~ ( member @ SY862 @ SV11 @ mactual )
| ( member @ SY862 @ SV42 @ mactual ) )
| ( subset @ SV11 @ SV42 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(248,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV12 @ SV43 @ mactual )
| ~ ( equal_set @ SV12 @ SV70 @ mactual ) ) )
= $true )
| ( ( equal_set @ SV43 @ SV70 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(249,plain,
! [SV71: mworld,SV44: mworld,SV13: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV13 @ SV44 )
| ~ ( mrel @ SV44 @ SV71 ) ) )
= $true )
| ( ( mrel @ SV13 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(250,plain,
! [SV45: $i,SV14: $i] :
( ( ( qmltpeq @ SV14 @ SV45 @ mactual )
= $false )
| ( ( qmltpeq @ ( product @ SV14 ) @ ( product @ SV45 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(251,plain,
! [SV72: $i,SV46: $i,SV15: $i] :
( ( ( ~ ( qmltpeq @ SV15 @ SV46 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( union @ SV15 @ SV72 ) @ ( union @ SV46 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(252,plain,
! [SV73: $i,SV47: $i,SV16: $i] :
( ( ( ~ ( qmltpeq @ SV16 @ SV47 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV73 @ SV16 ) @ ( unordered_pair @ SV73 @ SV47 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(253,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( ~ ( member @ SV17 @ ( product @ SV48 ) @ mactual )
| ! [SY867: $i] :
( ~ ( member @ SY867 @ SV48 @ mactual )
| ( member @ SV17 @ SY867 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(254,plain,
! [SV17: $i,SV48: $i] :
( ( ~ ( ~ ! [SY868: $i] :
( ~ ( member @ SY868 @ SV48 @ mactual )
| ( member @ SV17 @ SY868 @ mactual ) )
| ( member @ SV17 @ ( product @ SV48 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(255,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
| ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
| ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(256,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ( ~ ( equal_set @ SV19 @ SV50 @ mactual )
| ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(257,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) )
| ( equal_set @ SV19 @ SV50 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(258,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ~ ( ~ ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
| ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) )
| ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(259,plain,
! [SV52: $i,SV21: $i] :
( ( ( qmltpeq @ SV21 @ SV52 @ mactual )
= $false )
| ( ( qmltpeq @ ( singleton @ SV21 ) @ ( singleton @ SV52 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(260,plain,
! [SV76: $i,SV53: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual )
| ~ ( member @ SV76 @ SV22 @ mactual ) ) )
= $true )
| ( ( member @ SV76 @ SV53 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(261,plain,
! [SV54: $i,SV23: $i] :
( ( ( qmltpeq @ SV23 @ SV54 @ mactual )
= $false )
| ( ( qmltpeq @ SV54 @ SV23 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(262,plain,
! [SV77: $i,SV55: $i,SV24: $i] :
( ( ( ~ ( qmltpeq @ SV24 @ SV55 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV24 @ SV77 ) @ ( intersection @ SV55 @ SV77 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(263,plain,
! [SV78: $i,SV56: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( qmltpeq @ SV56 @ SV78 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV78 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(264,plain,
! [SV79: $i,SV57: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV57 @ mactual )
| ~ ( subset @ SV79 @ SV26 @ mactual ) ) )
= $true )
| ( ( subset @ SV79 @ SV57 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(265,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ~ ( ~ ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
| ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
| ~ ( ~ ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
| ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(266,plain,
! [SV81: $i,SV59: $i,SV28: $i] :
( ( ( ~ ( qmltpeq @ SV28 @ SV59 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV28 @ SV81 ) @ ( difference @ SV59 @ SV81 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(267,plain,
! [SV82: $i,SV60: $i,SV29: $i] :
( ( ( ~ ( qmltpeq @ SV29 @ SV60 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV29 @ SV82 ) @ ( unordered_pair @ SV60 @ SV82 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(268,plain,
! [SV83: $i,SV61: $i,SV30: $i] :
( ( ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV83 @ SV30 ) @ ( intersection @ SV83 @ SV61 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(269,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( ~ ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
| ~ ! [SY879: $i] :
~ ~ ( ~ ( member @ SY879 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY879 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(270,plain,
! [SV31: $i,SV62: $i] :
( ( ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( member @ SY880 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY880 @ mactual ) )
| ( member @ SV31 @ ( sum @ SV62 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(271,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ~ ( ~ ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
| ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
| ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(272,plain,
! [SV64: $i,SV33: $i] :
( ( ~ ( ~ ( member @ SV33 @ ( singleton @ SV64 ) @ mactual )
| ( qmltpeq @ SV33 @ SV64 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(273,plain,
! [SV64: $i,SV33: $i] :
( ( ~ ( ~ ( qmltpeq @ SV33 @ SV64 @ mactual )
| ( member @ SV33 @ ( singleton @ SV64 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(274,plain,
! [SV85: $i,SV65: $i,SV34: $i] :
( ( ( ~ ( qmltpeq @ SV34 @ SV65 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV85 @ SV34 ) @ ( difference @ SV85 @ SV65 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(275,plain,
! [SV66: $i,SV36: $i,SV5: $i] :
( ( ( qmltpeq @ SV5 @ SV36 @ mactual )
= $false )
| ( ( qmltpeq @ ( union @ SV66 @ SV5 ) @ ( union @ SV66 @ SV36 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(276,plain,
! [SV67: $i,SV38: $i,SV7: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV7 @ SV38 @ mactual )
| ~ ( equal_set @ SV67 @ SV7 @ mactual ) ) )
= $false )
| ( ( equal_set @ SV67 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(277,plain,
! [SV68: $i,SV39: $i,SV8: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV8 @ SV39 @ mactual )
| ~ ( subset @ SV8 @ SV68 @ mactual ) ) )
= $false )
| ( ( subset @ SV39 @ SV68 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(278,plain,
! [SV69: $i,SV40: $i,SV9: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV9 @ SV40 @ mactual )
| ~ ( member @ SV9 @ SV69 @ mactual ) ) )
= $false )
| ( ( member @ SV40 @ SV69 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(279,plain,
! [SV41: $i,SV10: $i] :
( ( ~ ( member @ SV10 @ ( power_set @ SV41 ) @ mactual )
| ( subset @ SV10 @ SV41 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(280,plain,
! [SV41: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV41 @ mactual )
| ( member @ SV10 @ ( power_set @ SV41 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(281,plain,
! [SV42: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV42 @ mactual )
| ! [SY861: $i] :
( ~ ( member @ SY861 @ SV11 @ mactual )
| ( member @ SY861 @ SV42 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(282,plain,
! [SV42: $i,SV11: $i] :
( ( ~ ! [SY862: $i] :
( ~ ( member @ SY862 @ SV11 @ mactual )
| ( member @ SY862 @ SV42 @ mactual ) )
| ( subset @ SV11 @ SV42 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(283,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV12 @ SV43 @ mactual )
| ~ ( equal_set @ SV12 @ SV70 @ mactual ) ) )
= $false )
| ( ( equal_set @ SV43 @ SV70 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(284,plain,
! [SV71: mworld,SV44: mworld,SV13: mworld] :
( ( ( ~ ( ~ ( mrel @ SV13 @ SV44 )
| ~ ( mrel @ SV44 @ SV71 ) ) )
= $false )
| ( ( mrel @ SV13 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(285,plain,
! [SV72: $i,SV46: $i,SV15: $i] :
( ( ( qmltpeq @ SV15 @ SV46 @ mactual )
= $false )
| ( ( qmltpeq @ ( union @ SV15 @ SV72 ) @ ( union @ SV46 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(286,plain,
! [SV73: $i,SV47: $i,SV16: $i] :
( ( ( qmltpeq @ SV16 @ SV47 @ mactual )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV73 @ SV16 ) @ ( unordered_pair @ SV73 @ SV47 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(287,plain,
! [SV48: $i,SV17: $i] :
( ( ~ ( member @ SV17 @ ( product @ SV48 ) @ mactual )
| ! [SY867: $i] :
( ~ ( member @ SY867 @ SV48 @ mactual )
| ( member @ SV17 @ SY867 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(288,plain,
! [SV17: $i,SV48: $i] :
( ( ~ ! [SY868: $i] :
( ~ ( member @ SY868 @ SV48 @ mactual )
| ( member @ SV17 @ SY868 @ mactual ) )
| ( member @ SV17 @ ( product @ SV48 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(289,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
| ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(290,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ~ ( ~ ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
| ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(291,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ( equal_set @ SV19 @ SV50 @ mactual )
| ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(292,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) )
| ( equal_set @ SV19 @ SV50 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(293,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ~ ( ~ ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
| ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(294,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) )
| ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(295,plain,
! [SV76: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual )
| ~ ( member @ SV76 @ SV22 @ mactual ) ) )
= $false )
| ( ( member @ SV76 @ SV53 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(296,plain,
! [SV77: $i,SV55: $i,SV24: $i] :
( ( ( qmltpeq @ SV24 @ SV55 @ mactual )
= $false )
| ( ( qmltpeq @ ( intersection @ SV24 @ SV77 ) @ ( intersection @ SV55 @ SV77 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(297,plain,
! [SV78: $i,SV56: $i,SV25: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( qmltpeq @ SV56 @ SV78 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV25 @ SV78 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(298,plain,
! [SV79: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV26 @ SV57 @ mactual )
| ~ ( subset @ SV79 @ SV26 @ mactual ) ) )
= $false )
| ( ( subset @ SV79 @ SV57 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(299,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ~ ( ~ ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
| ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(300,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ~ ( ~ ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
| ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(301,plain,
! [SV81: $i,SV59: $i,SV28: $i] :
( ( ( qmltpeq @ SV28 @ SV59 @ mactual )
= $false )
| ( ( qmltpeq @ ( difference @ SV28 @ SV81 ) @ ( difference @ SV59 @ SV81 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(302,plain,
! [SV82: $i,SV60: $i,SV29: $i] :
( ( ( qmltpeq @ SV29 @ SV60 @ mactual )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV29 @ SV82 ) @ ( unordered_pair @ SV60 @ SV82 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(303,plain,
! [SV83: $i,SV61: $i,SV30: $i] :
( ( ( qmltpeq @ SV30 @ SV61 @ mactual )
= $false )
| ( ( qmltpeq @ ( intersection @ SV83 @ SV30 ) @ ( intersection @ SV83 @ SV61 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(304,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
| ~ ! [SY879: $i] :
~ ~ ( ~ ( member @ SY879 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY879 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(305,plain,
! [SV31: $i,SV62: $i] :
( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( member @ SY880 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY880 @ mactual ) )
| ( member @ SV31 @ ( sum @ SV62 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(306,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ~ ( ~ ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
| ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(307,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
| ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(308,plain,
! [SV64: $i,SV33: $i] :
( ( ~ ( member @ SV33 @ ( singleton @ SV64 ) @ mactual )
| ( qmltpeq @ SV33 @ SV64 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(309,plain,
! [SV64: $i,SV33: $i] :
( ( ~ ( qmltpeq @ SV33 @ SV64 @ mactual )
| ( member @ SV33 @ ( singleton @ SV64 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(310,plain,
! [SV85: $i,SV65: $i,SV34: $i] :
( ( ( qmltpeq @ SV34 @ SV65 @ mactual )
= $false )
| ( ( qmltpeq @ ( difference @ SV85 @ SV34 ) @ ( difference @ SV85 @ SV65 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(311,plain,
! [SV67: $i,SV38: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV38 @ mactual )
| ~ ( equal_set @ SV67 @ SV7 @ mactual ) )
= $true )
| ( ( equal_set @ SV67 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(312,plain,
! [SV68: $i,SV39: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV39 @ mactual )
| ~ ( subset @ SV8 @ SV68 @ mactual ) )
= $true )
| ( ( subset @ SV39 @ SV68 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(313,plain,
! [SV69: $i,SV40: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV40 @ mactual )
| ~ ( member @ SV9 @ SV69 @ mactual ) )
= $true )
| ( ( member @ SV40 @ SV69 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(314,plain,
! [SV41: $i,SV10: $i] :
( ( ( ~ ( member @ SV10 @ ( power_set @ SV41 ) @ mactual ) )
= $true )
| ( ( subset @ SV10 @ SV41 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(315,plain,
! [SV41: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV41 @ mactual ) )
= $true )
| ( ( member @ SV10 @ ( power_set @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(316,plain,
! [SV42: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV42 @ mactual ) )
= $true )
| ( ( ! [SY861: $i] :
( ~ ( member @ SY861 @ SV11 @ mactual )
| ( member @ SY861 @ SV42 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(317,plain,
! [SV42: $i,SV11: $i] :
( ( ( ~ ! [SY862: $i] :
( ~ ( member @ SY862 @ SV11 @ mactual )
| ( member @ SY862 @ SV42 @ mactual ) ) )
= $true )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(318,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ( ~ ( qmltpeq @ SV12 @ SV43 @ mactual )
| ~ ( equal_set @ SV12 @ SV70 @ mactual ) )
= $true )
| ( ( equal_set @ SV43 @ SV70 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(319,plain,
! [SV71: mworld,SV44: mworld,SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ SV44 )
| ~ ( mrel @ SV44 @ SV71 ) )
= $true )
| ( ( mrel @ SV13 @ SV71 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(320,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( member @ SV17 @ ( product @ SV48 ) @ mactual ) )
= $true )
| ( ( ! [SY867: $i] :
( ~ ( member @ SY867 @ SV48 @ mactual )
| ( member @ SV17 @ SY867 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(321,plain,
! [SV17: $i,SV48: $i] :
( ( ( ~ ! [SY868: $i] :
( ~ ( member @ SY868 @ SV48 @ mactual )
| ( member @ SV17 @ SY868 @ mactual ) ) )
= $true )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(322,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ~ ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
| ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(323,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ~ ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
| ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(324,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( equal_set @ SV19 @ SV50 @ mactual ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(325,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) )
= $true )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(326,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ~ ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
| ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(327,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ~ ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) )
| ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(328,plain,
! [SV76: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual )
| ~ ( member @ SV76 @ SV22 @ mactual ) )
= $true )
| ( ( member @ SV76 @ SV53 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(329,plain,
! [SV78: $i,SV56: $i,SV25: $i] :
( ( ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( qmltpeq @ SV56 @ SV78 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV78 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(330,plain,
! [SV79: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( qmltpeq @ SV26 @ SV57 @ mactual )
| ~ ( subset @ SV79 @ SV26 @ mactual ) )
= $true )
| ( ( subset @ SV79 @ SV57 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(331,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ~ ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
| ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(332,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ~ ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
| ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(333,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ ( sum @ SV62 ) @ mactual ) )
= $true )
| ( ( ~ ! [SY879: $i] :
~ ~ ( ~ ( member @ SY879 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY879 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(334,plain,
! [SV31: $i,SV62: $i] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( member @ SY880 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY880 @ mactual ) ) )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(335,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ~ ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
| ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(336,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ~ ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
| ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(337,plain,
! [SV64: $i,SV33: $i] :
( ( ( ~ ( member @ SV33 @ ( singleton @ SV64 ) @ mactual ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV64 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(338,plain,
! [SV64: $i,SV33: $i] :
( ( ( ~ ( qmltpeq @ SV33 @ SV64 @ mactual ) )
= $true )
| ( ( member @ SV33 @ ( singleton @ SV64 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(339,plain,
! [SV67: $i,SV38: $i,SV7: $i] :
( ( ( ~ ( qmltpeq @ SV7 @ SV38 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV67 @ SV7 @ mactual ) )
= $true )
| ( ( equal_set @ SV67 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(340,plain,
! [SV68: $i,SV39: $i,SV8: $i] :
( ( ( ~ ( qmltpeq @ SV8 @ SV39 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV8 @ SV68 @ mactual ) )
= $true )
| ( ( subset @ SV39 @ SV68 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(341,plain,
! [SV69: $i,SV40: $i,SV9: $i] :
( ( ( ~ ( qmltpeq @ SV9 @ SV40 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV9 @ SV69 @ mactual ) )
= $true )
| ( ( member @ SV40 @ SV69 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(342,plain,
! [SV41: $i,SV10: $i] :
( ( ( member @ SV10 @ ( power_set @ SV41 ) @ mactual )
= $false )
| ( ( subset @ SV10 @ SV41 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(343,plain,
! [SV41: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV41 @ mactual )
= $false )
| ( ( member @ SV10 @ ( power_set @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(344,plain,
! [SV42: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV42 @ mactual )
= $false )
| ( ( ! [SY861: $i] :
( ~ ( member @ SY861 @ SV11 @ mactual )
| ( member @ SY861 @ SV42 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(345,plain,
! [SV42: $i,SV11: $i] :
( ( ( ! [SY862: $i] :
( ~ ( member @ SY862 @ SV11 @ mactual )
| ( member @ SY862 @ SV42 @ mactual ) ) )
= $false )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(346,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ( ~ ( qmltpeq @ SV12 @ SV43 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV12 @ SV70 @ mactual ) )
= $true )
| ( ( equal_set @ SV43 @ SV70 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(347,plain,
! [SV71: mworld,SV44: mworld,SV13: mworld] :
( ( ( ~ ( mrel @ SV13 @ SV44 ) )
= $true )
| ( ( ~ ( mrel @ SV44 @ SV71 ) )
= $true )
| ( ( mrel @ SV13 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(348,plain,
! [SV48: $i,SV17: $i] :
( ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $false )
| ( ( ! [SY867: $i] :
( ~ ( member @ SY867 @ SV48 @ mactual )
| ( member @ SV17 @ SY867 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(349,plain,
! [SV17: $i,SV48: $i] :
( ( ( ! [SY868: $i] :
( ~ ( member @ SY868 @ SV48 @ mactual )
| ( member @ SV17 @ SY868 @ mactual ) ) )
= $false )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(350,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual ) )
= $true )
| ( ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(351,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) ) )
= $true )
| ( ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(352,plain,
! [SV50: $i,SV19: $i] :
( ( ( equal_set @ SV19 @ SV50 @ mactual )
= $false )
| ( ( ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(353,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) ) )
= $false )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(354,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual ) )
= $true )
| ( ( ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(355,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) )
= $true )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(356,plain,
! [SV76: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV76 @ SV22 @ mactual ) )
= $true )
| ( ( member @ SV76 @ SV53 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(357,plain,
! [SV78: $i,SV56: $i,SV25: $i] :
( ( ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV56 @ SV78 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV78 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(358,plain,
! [SV79: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( qmltpeq @ SV26 @ SV57 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV79 @ SV26 @ mactual ) )
= $true )
| ( ( subset @ SV79 @ SV57 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(359,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ( ~ ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual ) )
= $true )
| ( ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(360,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ( ~ ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) ) )
= $true )
| ( ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(361,plain,
! [SV62: $i,SV31: $i] :
( ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false )
| ( ( ~ ! [SY879: $i] :
~ ~ ( ~ ( member @ SY879 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY879 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(362,plain,
! [SV31: $i,SV62: $i] :
( ( ( ~ ! [SY880: $i] :
~ ~ ( ~ ( member @ SY880 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY880 @ mactual ) ) )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(363,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual ) )
= $true )
| ( ( ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(364,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
= $true )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(365,plain,
! [SV64: $i,SV33: $i] :
( ( ( member @ SV33 @ ( singleton @ SV64 ) @ mactual )
= $false )
| ( ( qmltpeq @ SV33 @ SV64 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(366,plain,
! [SV64: $i,SV33: $i] :
( ( ( qmltpeq @ SV33 @ SV64 @ mactual )
= $false )
| ( ( member @ SV33 @ ( singleton @ SV64 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(367,plain,
! [SV67: $i,SV38: $i,SV7: $i] :
( ( ( qmltpeq @ SV7 @ SV38 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV67 @ SV7 @ mactual ) )
= $true )
| ( ( equal_set @ SV67 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(368,plain,
! [SV68: $i,SV39: $i,SV8: $i] :
( ( ( qmltpeq @ SV8 @ SV39 @ mactual )
= $false )
| ( ( ~ ( subset @ SV8 @ SV68 @ mactual ) )
= $true )
| ( ( subset @ SV39 @ SV68 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(369,plain,
! [SV69: $i,SV40: $i,SV9: $i] :
( ( ( qmltpeq @ SV9 @ SV40 @ mactual )
= $false )
| ( ( ~ ( member @ SV9 @ SV69 @ mactual ) )
= $true )
| ( ( member @ SV40 @ SV69 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(370,plain,
! [SV42: $i,SV11: $i,SV86: $i] :
( ( ( ~ ( member @ SV86 @ SV11 @ mactual )
| ( member @ SV86 @ SV42 @ mactual ) )
= $true )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(371,plain,
! [SV11: $i,SV42: $i] :
( ( ( ~ ( member @ ( sK2_SY862 @ SV42 @ SV11 ) @ SV11 @ mactual )
| ( member @ ( sK2_SY862 @ SV42 @ SV11 ) @ SV42 @ mactual ) )
= $false )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[345]) ).
thf(372,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ( qmltpeq @ SV12 @ SV43 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV12 @ SV70 @ mactual ) )
= $true )
| ( ( equal_set @ SV43 @ SV70 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(373,plain,
! [SV71: mworld,SV44: mworld,SV13: mworld] :
( ( ( mrel @ SV13 @ SV44 )
= $false )
| ( ( ~ ( mrel @ SV44 @ SV71 ) )
= $true )
| ( ( mrel @ SV13 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(374,plain,
! [SV17: $i,SV48: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ SV48 @ mactual )
| ( member @ SV17 @ SV87 @ mactual ) )
= $true )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(375,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK3_SY868 @ SV17 @ SV48 ) @ SV48 @ mactual )
| ( member @ SV17 @ ( sK3_SY868 @ SV17 @ SV48 ) @ mactual ) )
= $false )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[349]) ).
thf(376,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
= $false )
| ( ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(377,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ( ( qmltpeq @ SV18 @ SV49 @ mactual )
| ( qmltpeq @ SV18 @ SV74 @ mactual ) )
= $false )
| ( ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(378,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) )
= $false )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(379,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV50 @ mactual )
| ~ ( subset @ SV50 @ SV19 @ mactual ) )
= $true )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(380,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $false )
| ( ( ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(381,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( ~ ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) ) )
= $false )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(382,plain,
! [SV76: $i,SV53: $i,SV22: $i] :
( ( ( qmltpeq @ SV22 @ SV53 @ mactual )
= $false )
| ( ( ~ ( member @ SV76 @ SV22 @ mactual ) )
= $true )
| ( ( member @ SV76 @ SV53 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(383,plain,
! [SV78: $i,SV56: $i,SV25: $i] :
( ( ( qmltpeq @ SV25 @ SV56 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV56 @ SV78 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV25 @ SV78 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(384,plain,
! [SV79: $i,SV57: $i,SV26: $i] :
( ( ( qmltpeq @ SV26 @ SV57 @ mactual )
= $false )
| ( ( ~ ( subset @ SV79 @ SV26 @ mactual ) )
= $true )
| ( ( subset @ SV79 @ SV57 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(385,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
= $false )
| ( ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(386,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ( ( member @ SV27 @ SV58 @ mactual )
| ( member @ SV27 @ SV80 @ mactual ) )
= $false )
| ( ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(387,plain,
! [SV31: $i,SV62: $i] :
( ( ( ! [SY879: $i] :
~ ~ ( ~ ( member @ SY879 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY879 @ mactual ) ) )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(388,plain,
! [SV31: $i,SV62: $i] :
( ( ( ! [SY880: $i] :
~ ~ ( ~ ( member @ SY880 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SY880 @ mactual ) ) )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(389,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $false )
| ( ( ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(390,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( ~ ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) ) )
= $false )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(391,plain,
! [SV38: $i,SV7: $i,SV67: $i] :
( ( ( equal_set @ SV67 @ SV7 @ mactual )
= $false )
| ( ( qmltpeq @ SV7 @ SV38 @ mactual )
= $false )
| ( ( equal_set @ SV67 @ SV38 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(392,plain,
! [SV39: $i,SV68: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV68 @ mactual )
= $false )
| ( ( qmltpeq @ SV8 @ SV39 @ mactual )
= $false )
| ( ( subset @ SV39 @ SV68 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(393,plain,
! [SV40: $i,SV69: $i,SV9: $i] :
( ( ( member @ SV9 @ SV69 @ mactual )
= $false )
| ( ( qmltpeq @ SV9 @ SV40 @ mactual )
= $false )
| ( ( member @ SV40 @ SV69 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(394,plain,
! [SV42: $i,SV11: $i,SV86: $i] :
( ( ( ~ ( member @ SV86 @ SV11 @ mactual ) )
= $true )
| ( ( member @ SV86 @ SV42 @ mactual )
= $true )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(395,plain,
! [SV11: $i,SV42: $i] :
( ( ( ~ ( member @ ( sK2_SY862 @ SV42 @ SV11 ) @ SV11 @ mactual ) )
= $false )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(396,plain,
! [SV11: $i,SV42: $i] :
( ( ( member @ ( sK2_SY862 @ SV42 @ SV11 ) @ SV42 @ mactual )
= $false )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(397,plain,
! [SV43: $i,SV70: $i,SV12: $i] :
( ( ( equal_set @ SV12 @ SV70 @ mactual )
= $false )
| ( ( qmltpeq @ SV12 @ SV43 @ mactual )
= $false )
| ( ( equal_set @ SV43 @ SV70 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(398,plain,
! [SV13: mworld,SV71: mworld,SV44: mworld] :
( ( ( mrel @ SV44 @ SV71 )
= $false )
| ( ( mrel @ SV13 @ SV44 )
= $false )
| ( ( mrel @ SV13 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(399,plain,
! [SV17: $i,SV48: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ SV48 @ mactual ) )
= $true )
| ( ( member @ SV17 @ SV87 @ mactual )
= $true )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(400,plain,
! [SV48: $i,SV17: $i] :
( ( ( ~ ( member @ ( sK3_SY868 @ SV17 @ SV48 ) @ SV48 @ mactual ) )
= $false )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(401,plain,
! [SV48: $i,SV17: $i] :
( ( ( member @ SV17 @ ( sK3_SY868 @ SV17 @ SV48 ) @ mactual )
= $false )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(402,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ( qmltpeq @ SV18 @ SV49 @ mactual )
= $true )
| ( ( qmltpeq @ SV18 @ SV74 @ mactual )
= $true )
| ( ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(403,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ( qmltpeq @ SV18 @ SV49 @ mactual )
= $false )
| ( ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(404,plain,
! [SV49: $i,SV74: $i,SV18: $i] :
( ( ( qmltpeq @ SV18 @ SV74 @ mactual )
= $false )
| ( ( member @ SV18 @ ( unordered_pair @ SV49 @ SV74 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(405,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV50 @ mactual ) )
= $false )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(406,plain,
! [SV19: $i,SV50: $i] :
( ( ( ~ ( subset @ SV50 @ SV19 @ mactual ) )
= $false )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(407,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV50 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV50 @ SV19 @ mactual ) )
= $true )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(408,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) )
= $false )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(409,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV51 @ mactual )
| ~ ( member @ SV20 @ SV75 @ mactual ) )
= $true )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(410,plain,
! [SV53: $i,SV22: $i,SV76: $i] :
( ( ( member @ SV76 @ SV22 @ mactual )
= $false )
| ( ( qmltpeq @ SV22 @ SV53 @ mactual )
= $false )
| ( ( member @ SV76 @ SV53 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(411,plain,
! [SV25: $i,SV78: $i,SV56: $i] :
( ( ( qmltpeq @ SV56 @ SV78 @ mactual )
= $false )
| ( ( qmltpeq @ SV25 @ SV56 @ mactual )
= $false )
| ( ( qmltpeq @ SV25 @ SV78 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(412,plain,
! [SV57: $i,SV26: $i,SV79: $i] :
( ( ( subset @ SV79 @ SV26 @ mactual )
= $false )
| ( ( qmltpeq @ SV26 @ SV57 @ mactual )
= $false )
| ( ( subset @ SV79 @ SV57 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(413,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ( member @ SV27 @ SV58 @ mactual )
= $true )
| ( ( member @ SV27 @ SV80 @ mactual )
= $true )
| ( ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(414,plain,
! [SV80: $i,SV58: $i,SV27: $i] :
( ( ( member @ SV27 @ SV58 @ mactual )
= $false )
| ( ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(415,plain,
! [SV58: $i,SV80: $i,SV27: $i] :
( ( ( member @ SV27 @ SV80 @ mactual )
= $false )
| ( ( member @ SV27 @ ( union @ SV58 @ SV80 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(416,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY879 @ SV31 @ SV62 ) @ SV62 @ mactual )
| ~ ( member @ SV31 @ ( sK4_SY879 @ SV31 @ SV62 ) @ mactual ) ) )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[387]) ).
thf(417,plain,
! [SV31: $i,SV62: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( member @ SV88 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SV88 @ mactual ) ) )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(418,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
= $false )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(419,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV84 @ mactual )
| ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
= $true )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(420,plain,
! [SV42: $i,SV11: $i,SV86: $i] :
( ( ( member @ SV86 @ SV11 @ mactual )
= $false )
| ( ( member @ SV86 @ SV42 @ mactual )
= $true )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(421,plain,
! [SV11: $i,SV42: $i] :
( ( ( member @ ( sK2_SY862 @ SV42 @ SV11 ) @ SV11 @ mactual )
= $true )
| ( ( subset @ SV11 @ SV42 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(422,plain,
! [SV17: $i,SV48: $i,SV87: $i] :
( ( ( member @ SV87 @ SV48 @ mactual )
= $false )
| ( ( member @ SV17 @ SV87 @ mactual )
= $true )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(423,plain,
! [SV48: $i,SV17: $i] :
( ( ( member @ ( sK3_SY868 @ SV17 @ SV48 ) @ SV48 @ mactual )
= $true )
| ( ( member @ SV17 @ ( product @ SV48 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(424,plain,
! [SV50: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV50 @ mactual )
= $true )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(425,plain,
! [SV19: $i,SV50: $i] :
( ( ( subset @ SV50 @ SV19 @ mactual )
= $true )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(426,plain,
! [SV50: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV50 @ mactual )
= $false )
| ( ( ~ ( subset @ SV50 @ SV19 @ mactual ) )
= $true )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(427,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV51 @ mactual ) )
= $false )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(428,plain,
! [SV51: $i,SV75: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV75 @ mactual ) )
= $false )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(429,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( ~ ( member @ SV20 @ SV51 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV20 @ SV75 @ mactual ) )
= $true )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(430,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY879 @ SV31 @ SV62 ) @ SV62 @ mactual )
| ~ ( member @ SV31 @ ( sK4_SY879 @ SV31 @ SV62 ) @ mactual ) ) )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(431,plain,
! [SV31: $i,SV62: $i,SV88: $i] :
( ( ( ~ ( ~ ( member @ SV88 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SV88 @ mactual ) ) )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV84 @ mactual ) )
= $false )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(433,plain,
! [SV84: $i,SV63: $i,SV32: $i] :
( ( ( ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
= $false )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(434,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV84 @ mactual ) )
= $true )
| ( ( ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
= $true )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(435,plain,
! [SV19: $i,SV50: $i] :
( ( ( subset @ SV50 @ SV19 @ mactual )
= $false )
| ( ( subset @ SV19 @ SV50 @ mactual )
= $false )
| ( ( equal_set @ SV19 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(436,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( member @ SV20 @ SV51 @ mactual )
= $true )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(437,plain,
! [SV51: $i,SV75: $i,SV20: $i] :
( ( ( member @ SV20 @ SV75 @ mactual )
= $true )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(438,plain,
! [SV75: $i,SV51: $i,SV20: $i] :
( ( ( member @ SV20 @ SV51 @ mactual )
= $false )
| ( ( ~ ( member @ SV20 @ SV75 @ mactual ) )
= $true )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(439,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ( member @ ( sK4_SY879 @ SV31 @ SV62 ) @ SV62 @ mactual )
| ~ ( member @ SV31 @ ( sK4_SY879 @ SV31 @ SV62 ) @ mactual ) )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(440,plain,
! [SV31: $i,SV62: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ SV62 @ mactual )
| ~ ( member @ SV31 @ SV88 @ mactual ) )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(441,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( member @ SV32 @ SV84 @ mactual )
= $true )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(442,plain,
! [SV84: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV63 @ mactual ) )
= $true )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(443,plain,
! [SV63: $i,SV84: $i,SV32: $i] :
( ( ( member @ SV32 @ SV84 @ mactual )
= $false )
| ( ( ~ ~ ( member @ SV32 @ SV63 @ mactual ) )
= $true )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(444,plain,
! [SV51: $i,SV75: $i,SV20: $i] :
( ( ( member @ SV20 @ SV75 @ mactual )
= $false )
| ( ( member @ SV20 @ SV51 @ mactual )
= $false )
| ( ( member @ SV20 @ ( intersection @ SV51 @ SV75 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(445,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ( member @ ( sK4_SY879 @ SV31 @ SV62 ) @ SV62 @ mactual ) )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(446,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ( member @ SV31 @ ( sK4_SY879 @ SV31 @ SV62 ) @ mactual ) )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(447,plain,
! [SV31: $i,SV62: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ SV62 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV31 @ SV88 @ mactual ) )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(448,plain,
! [SV84: $i,SV63: $i,SV32: $i] :
( ( ( member @ SV32 @ SV63 @ mactual )
= $false )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(449,plain,
! [SV84: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( member @ SV32 @ SV63 @ mactual ) )
= $false )
| ( ( member @ SV32 @ SV84 @ mactual )
= $false )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(450,plain,
! [SV62: $i,SV31: $i] :
( ( ( member @ ( sK4_SY879 @ SV31 @ SV62 ) @ SV62 @ mactual )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(451,plain,
! [SV62: $i,SV31: $i] :
( ( ( member @ SV31 @ ( sK4_SY879 @ SV31 @ SV62 ) @ mactual )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(452,plain,
! [SV31: $i,SV62: $i,SV88: $i] :
( ( ( member @ SV88 @ SV62 @ mactual )
= $false )
| ( ( ~ ( member @ SV31 @ SV88 @ mactual ) )
= $true )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(453,plain,
! [SV84: $i,SV63: $i,SV32: $i] :
( ( ( member @ SV32 @ SV63 @ mactual )
= $true )
| ( ( member @ SV32 @ SV84 @ mactual )
= $false )
| ( ( member @ SV32 @ ( difference @ SV84 @ SV63 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(454,plain,
! [SV62: $i,SV88: $i,SV31: $i] :
( ( ( member @ SV31 @ SV88 @ mactual )
= $false )
| ( ( member @ SV88 @ SV62 @ mactual )
= $false )
| ( ( member @ SV31 @ ( sum @ SV62 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(455,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[140,454,453,451,450,448,444,441,437,436,435,425,424,423,422,421,420,415,414,413,412,411,410,404,403,402,401,398,397,396,393,392,391,366,365,343,342,310,303,302,301,296,286,285,275,261,259,250,240,238,175,143,141]) ).
thf(456,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET063^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n001.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 14:35:39 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/0.44
% 1.23/0.44 No.of.Axioms: 34
% 1.23/0.44
% 1.23/0.44 Length.of.Defs: 1624
% 1.23/0.44
% 1.23/0.44 Contains.Choice.Funs: false
% 1.23/0.44 .........................
% 1.23/0.44
% 1.23/0.44 ********************************
% 1.23/0.44 * All subproblems solved! *
% 1.23/0.44 ********************************
% 1.23/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:34,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:455,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.23/0.44
% 1.23/0.44 %**** Beginning of derivation protocol ****
% 1.23/0.44 % SZS output start CNFRefutation
% See solution above
% 1.23/0.45
% 1.23/0.45 %**** End of derivation protocol ****
% 1.23/0.45 %**** no. of clauses in derivation: 456 ****
% 1.23/0.45 %**** clause counter: 455 ****
% 1.23/0.45
% 1.23/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:34,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:455,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------