TSTP Solution File: SET063^4 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET063^4 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 02:58:59 EDT 2022
% Result : Theorem 0.40s 0.75s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 75
% Syntax : Number of formulae : 462 ( 222 unt; 30 typ; 10 def)
% Number of atoms : 2760 ( 615 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 6115 ( 926 ~; 681 |; 3 &;4501 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 5 con; 0-3 aty)
% Number of variables : 1159 ( 195 ^ 962 !; 2 ?;1159 :)
% 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_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY62,type,
sK2_SY62: $i > $i > $i ).
thf(tp_sK3_SY81,type,
sK3_SY81: $i > $i > $i ).
thf(tp_sK4_SY67,type,
sK4_SY67: $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/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_di,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di) ).
thf(mforall_di,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',difference_0) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(32,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).
thf(34,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(35,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( equal_set @ ( intersection @ A @ empty_set ) @ empty_set ) ) ),
file('/export/starexec/sandbox/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,
( ( ~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( equal_set @ ( intersection @ A @ empty_set ) @ empty_set ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ V )
| ~ ( mrel @ V @ U )
| ( mrel @ W @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(39,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ V )
| ~ ( mrel @ V @ U )
| ( mrel @ W @ U ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(41,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mforall_di
@ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(46,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(47,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(48,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(50,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(51,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(55,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(56,plain,
( ( 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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(57,plain,
( ( 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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(58,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(59,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(60,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(61,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(62,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_di
@ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(63,plain,
( ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(64,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(65,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(66,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(67,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(68,plain,
( ( 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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(69,plain,
( ( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(70,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(71,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(72,plain,
( ( 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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(73,plain,
( ( ~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( equal_set @ ( intersection @ A @ empty_set ) @ empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(74,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)],[43,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(75,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)],[66,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(76,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)],[46,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ SX1 @ SX0 @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(78,plain,
( ( ! [SX0: $i] : ( qmltpeq @ SX0 @ SX0 @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[41,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(79,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)],[64,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(80,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)],[72,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(81,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)],[44,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(82,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)],[47,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] : ( equal_set @ ( intersection @ SX0 @ empty_set ) @ empty_set @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[73,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(84,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)],[65,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(85,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)],[53,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(86,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)],[71,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( power_set @ SX0 ) @ ( power_set @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(88,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)],[58,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(89,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)],[61,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(90,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)],[59,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(91,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)],[60,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(92,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)],[55,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(93,plain,
( ( ! [SX0: $i] :
~ ( member @ SX0 @ empty_set @ mactual ) )
= $true ),
inference(unfold_def,[status(thm)],[67,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( sum @ SX0 ) @ ( sum @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(95,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)],[63,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(96,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)],[68,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(97,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)],[57,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(98,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)],[70,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(99,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)],[54,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(100,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)],[45,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(101,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)],[69,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(102,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)],[56,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(103,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)],[62,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(104,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)],[52,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( product @ SX0 ) @ ( product @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( qmltpeq @ SX0 @ SX1 @ mactual )
| ( qmltpeq @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) @ mactual ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).
thf(107,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(108,plain,
! [SV2: mworld] :
( ( ! [SY0: mworld,SY1: mworld] :
( ~ ( mrel @ SV2 @ SY0 )
| ~ ( mrel @ SY0 @ SY1 )
| ( mrel @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(109,plain,
! [SV3: $i] :
( ( ! [SY2: $i,SY3: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV3 @ SY2 @ mactual )
| ~ ( qmltpeq @ SY2 @ SY3 @ mactual ) )
| ( qmltpeq @ SV3 @ SY3 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(110,plain,
! [SV4: $i] :
( ( ! [SY4: $i,SY5: $i] :
~ ( ~ ( ~ ( member @ SV4 @ ( union @ SY4 @ SY5 ) @ mactual )
| ( member @ SV4 @ SY4 @ mactual )
| ( member @ SV4 @ SY5 @ mactual ) )
| ~ ( ~ ( ( member @ SV4 @ SY4 @ mactual )
| ( member @ SV4 @ SY5 @ mactual ) )
| ( member @ SV4 @ ( union @ SY4 @ SY5 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(111,plain,
! [SV5: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ~ ( qmltpeq @ SV5 @ SY6 @ mactual )
| ( qmltpeq @ ( intersection @ SV5 @ SY7 ) @ ( intersection @ SY6 @ SY7 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(112,plain,
! [SV6: $i] :
( ( ! [SY8: $i] :
( ~ ( qmltpeq @ SV6 @ SY8 @ mactual )
| ( qmltpeq @ SY8 @ SV6 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(113,plain,
! [SV7: $i] :
( ( qmltpeq @ SV7 @ SV7 @ mactual )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(114,plain,
! [SV8: $i] :
( ( ! [SY9: $i] :
~ ( ~ ( ~ ( member @ SV8 @ ( power_set @ SY9 ) @ mactual )
| ( subset @ SV8 @ SY9 @ mactual ) )
| ~ ( ~ ( subset @ SV8 @ SY9 @ mactual )
| ( member @ SV8 @ ( power_set @ SY9 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(115,plain,
! [SV9: $i] :
( ( ! [SY10: $i] :
~ ( ~ ( ~ ( member @ SV9 @ ( product @ SY10 ) @ mactual )
| ! [SY11: $i] :
( ~ ( member @ SY11 @ SY10 @ mactual )
| ( member @ SV9 @ SY11 @ mactual ) ) )
| ~ ( ~ ! [SY12: $i] :
( ~ ( member @ SY12 @ SY10 @ mactual )
| ( member @ SV9 @ SY12 @ mactual ) )
| ( member @ SV9 @ ( product @ SY10 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(116,plain,
! [SV10: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ~ ( qmltpeq @ SV10 @ SY13 @ mactual )
| ( qmltpeq @ ( difference @ SV10 @ SY14 ) @ ( difference @ SY13 @ SY14 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(117,plain,
! [SV11: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ~ ( qmltpeq @ SV11 @ SY15 @ mactual )
| ( qmltpeq @ ( intersection @ SY16 @ SV11 ) @ ( intersection @ SY16 @ SY15 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(118,plain,
( ( ! [SX0: $i] : ( equal_set @ ( intersection @ SX0 @ empty_set ) @ empty_set @ mactual ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(119,plain,
! [SV12: $i] :
( ( ! [SY17: $i,SY18: $i] :
~ ( ~ ( ~ ( member @ SV12 @ ( intersection @ SY17 @ SY18 ) @ mactual )
| ~ ( ~ ( member @ SV12 @ SY17 @ mactual )
| ~ ( member @ SV12 @ SY18 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ SY17 @ mactual )
| ~ ( member @ SV12 @ SY18 @ mactual ) )
| ( member @ SV12 @ ( intersection @ SY17 @ SY18 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(120,plain,
! [SV13: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ( qmltpeq @ SV13 @ SY19 @ mactual )
| ( qmltpeq @ ( union @ SY20 @ SV13 ) @ ( union @ SY20 @ SY19 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(121,plain,
! [SV14: $i] :
( ( ! [SY21: $i] :
~ ( ~ ( ~ ( member @ SV14 @ ( sum @ SY21 ) @ mactual )
| ~ ! [SY22: $i] :
~ ~ ( ~ ( member @ SY22 @ SY21 @ mactual )
| ~ ( member @ SV14 @ SY22 @ mactual ) ) )
| ~ ( ~ ~ ! [SY23: $i] :
~ ~ ( ~ ( member @ SY23 @ SY21 @ mactual )
| ~ ( member @ SV14 @ SY23 @ mactual ) )
| ( member @ SV14 @ ( sum @ SY21 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(122,plain,
! [SV15: $i] :
( ( ! [SY24: $i] :
( ~ ( qmltpeq @ SV15 @ SY24 @ mactual )
| ( qmltpeq @ ( power_set @ SV15 ) @ ( power_set @ SY24 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(123,plain,
! [SV16: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV16 @ SY25 @ mactual )
| ~ ( member @ SV16 @ SY26 @ mactual ) )
| ( member @ SY25 @ SY26 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(124,plain,
! [SV17: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV17 @ SY27 @ mactual )
| ~ ( subset @ SY28 @ SV17 @ mactual ) )
| ( subset @ SY28 @ SY27 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(125,plain,
! [SV18: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV18 @ SY29 @ mactual )
| ~ ( member @ SY30 @ SV18 @ mactual ) )
| ( member @ SY30 @ SY29 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(126,plain,
! [SV19: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV19 @ SY31 @ mactual )
| ~ ( subset @ SV19 @ SY32 @ mactual ) )
| ( subset @ SY31 @ SY32 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(127,plain,
! [SV20: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( qmltpeq @ SV20 @ SY33 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SY34 @ SV20 ) @ ( unordered_pair @ SY34 @ SY33 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(128,plain,
! [SV21: $i] :
( ( ~ ( member @ SV21 @ empty_set @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(129,plain,
! [SV22: $i] :
( ( ! [SY35: $i] :
( ~ ( qmltpeq @ SV22 @ SY35 @ mactual )
| ( qmltpeq @ ( sum @ SV22 ) @ ( sum @ SY35 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(130,plain,
! [SV23: $i] :
( ( ! [SY36: $i] :
~ ( ~ ( ~ ( equal_set @ SV23 @ SY36 @ mactual )
| ~ ( ~ ( subset @ SV23 @ SY36 @ mactual )
| ~ ( subset @ SY36 @ SV23 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV23 @ SY36 @ mactual )
| ~ ( subset @ SY36 @ SV23 @ mactual ) )
| ( equal_set @ SV23 @ SY36 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(131,plain,
! [SV24: $i] :
( ( ! [SY37: $i,SY38: $i] :
~ ( ~ ( ~ ( member @ SV24 @ ( difference @ SY38 @ SY37 ) @ mactual )
| ~ ( ~ ( member @ SV24 @ SY38 @ mactual )
| ~ ~ ( member @ SV24 @ SY37 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SY38 @ mactual )
| ~ ~ ( member @ SV24 @ SY37 @ mactual ) )
| ( member @ SV24 @ ( difference @ SY38 @ SY37 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(132,plain,
! [SV25: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV25 @ SY39 @ mactual )
| ~ ( equal_set @ SY40 @ SV25 @ mactual ) )
| ( equal_set @ SY40 @ SY39 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(133,plain,
! [SV26: $i] :
( ( ! [SY41: $i,SY42: $i] :
~ ( ~ ( ~ ( member @ SV26 @ ( unordered_pair @ SY41 @ SY42 ) @ mactual )
| ( qmltpeq @ SV26 @ SY41 @ mactual )
| ( qmltpeq @ SV26 @ SY42 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV26 @ SY41 @ mactual )
| ( qmltpeq @ SV26 @ SY42 @ mactual ) )
| ( member @ SV26 @ ( unordered_pair @ SY41 @ SY42 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(134,plain,
! [SV27: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( qmltpeq @ SV27 @ SY43 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV27 @ SY44 ) @ ( unordered_pair @ SY43 @ SY44 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(135,plain,
! [SV28: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ( qmltpeq @ SV28 @ SY45 @ mactual )
| ( qmltpeq @ ( difference @ SY46 @ SV28 ) @ ( difference @ SY46 @ SY45 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(136,plain,
! [SV29: $i] :
( ( ! [SY47: $i] :
~ ( ~ ( ~ ( member @ SV29 @ ( singleton @ SY47 ) @ mactual )
| ( qmltpeq @ SV29 @ SY47 @ mactual ) )
| ~ ( ~ ( qmltpeq @ SV29 @ SY47 @ mactual )
| ( member @ SV29 @ ( singleton @ SY47 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(137,plain,
! [SV30: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV30 @ SY48 @ mactual )
| ~ ( equal_set @ SV30 @ SY49 @ mactual ) )
| ( equal_set @ SY48 @ SY49 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(138,plain,
! [SV31: $i] :
( ( ! [SY50: $i] :
~ ( ~ ( ~ ( subset @ SV31 @ SY50 @ mactual )
| ! [SY51: $i] :
( ~ ( member @ SY51 @ SV31 @ mactual )
| ( member @ SY51 @ SY50 @ mactual ) ) )
| ~ ( ~ ! [SY52: $i] :
( ~ ( member @ SY52 @ SV31 @ mactual )
| ( member @ SY52 @ SY50 @ mactual ) )
| ( subset @ SV31 @ SY50 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(139,plain,
! [SV32: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ( qmltpeq @ SV32 @ SY53 @ mactual )
| ( qmltpeq @ ( union @ SV32 @ SY54 ) @ ( union @ SY53 @ SY54 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(140,plain,
! [SV33: $i] :
( ( ! [SY55: $i] :
( ~ ( qmltpeq @ SV33 @ SY55 @ mactual )
| ( qmltpeq @ ( product @ SV33 ) @ ( product @ SY55 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(141,plain,
! [SV34: $i] :
( ( ! [SY56: $i] :
( ~ ( qmltpeq @ SV34 @ SY56 @ mactual )
| ( qmltpeq @ ( singleton @ SV34 ) @ ( singleton @ SY56 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(142,plain,
! [SV35: mworld,SV2: mworld] :
( ( ! [SY57: mworld] :
( ~ ( mrel @ SV2 @ SV35 )
| ~ ( mrel @ SV35 @ SY57 )
| ( mrel @ SV2 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(143,plain,
! [SV36: $i,SV3: $i] :
( ( ! [SY58: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV3 @ SV36 @ mactual )
| ~ ( qmltpeq @ SV36 @ SY58 @ mactual ) )
| ( qmltpeq @ SV3 @ SY58 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(144,plain,
! [SV37: $i,SV4: $i] :
( ( ! [SY59: $i] :
~ ( ~ ( ~ ( member @ SV4 @ ( union @ SV37 @ SY59 ) @ mactual )
| ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SY59 @ mactual ) )
| ~ ( ~ ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SY59 @ mactual ) )
| ( member @ SV4 @ ( union @ SV37 @ SY59 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(145,plain,
! [SV38: $i,SV5: $i] :
( ( ! [SY60: $i] :
( ~ ( qmltpeq @ SV5 @ SV38 @ mactual )
| ( qmltpeq @ ( intersection @ SV5 @ SY60 ) @ ( intersection @ SV38 @ SY60 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(146,plain,
! [SV39: $i,SV6: $i] :
( ( ~ ( qmltpeq @ SV6 @ SV39 @ mactual )
| ( qmltpeq @ SV39 @ SV6 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(147,plain,
! [SV40: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( member @ SV8 @ ( power_set @ SV40 ) @ mactual )
| ( subset @ SV8 @ SV40 @ mactual ) )
| ~ ( ~ ( subset @ SV8 @ SV40 @ mactual )
| ( member @ SV8 @ ( power_set @ SV40 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(148,plain,
! [SV41: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( member @ SV9 @ ( product @ SV41 ) @ mactual )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV41 @ mactual )
| ( member @ SV9 @ SY61 @ mactual ) ) )
| ~ ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV41 @ mactual )
| ( member @ SV9 @ SY62 @ mactual ) )
| ( member @ SV9 @ ( product @ SV41 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(149,plain,
! [SV42: $i,SV10: $i] :
( ( ! [SY63: $i] :
( ~ ( qmltpeq @ SV10 @ SV42 @ mactual )
| ( qmltpeq @ ( difference @ SV10 @ SY63 ) @ ( difference @ SV42 @ SY63 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(150,plain,
! [SV43: $i,SV11: $i] :
( ( ! [SY64: $i] :
( ~ ( qmltpeq @ SV11 @ SV43 @ mactual )
| ( qmltpeq @ ( intersection @ SY64 @ SV11 ) @ ( intersection @ SY64 @ SV43 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(151,plain,
( ( equal_set @ ( intersection @ sK1_SX0 @ empty_set ) @ empty_set @ mactual )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(152,plain,
! [SV44: $i,SV12: $i] :
( ( ! [SY65: $i] :
~ ( ~ ( ~ ( member @ SV12 @ ( intersection @ SV44 @ SY65 ) @ mactual )
| ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SY65 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SY65 @ mactual ) )
| ( member @ SV12 @ ( intersection @ SV44 @ SY65 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(153,plain,
! [SV45: $i,SV13: $i] :
( ( ! [SY66: $i] :
( ~ ( qmltpeq @ SV13 @ SV45 @ mactual )
| ( qmltpeq @ ( union @ SY66 @ SV13 ) @ ( union @ SY66 @ SV45 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(154,plain,
! [SV46: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( member @ SY67 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY67 @ mactual ) ) )
| ~ ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( member @ SY68 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY68 @ mactual ) )
| ( member @ SV14 @ ( sum @ SV46 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(155,plain,
! [SV47: $i,SV15: $i] :
( ( ~ ( qmltpeq @ SV15 @ SV47 @ mactual )
| ( qmltpeq @ ( power_set @ SV15 ) @ ( power_set @ SV47 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(156,plain,
! [SV48: $i,SV16: $i] :
( ( ! [SY69: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV16 @ SV48 @ mactual )
| ~ ( member @ SV16 @ SY69 @ mactual ) )
| ( member @ SV48 @ SY69 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(157,plain,
! [SV49: $i,SV17: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV17 @ SV49 @ mactual )
| ~ ( subset @ SY70 @ SV17 @ mactual ) )
| ( subset @ SY70 @ SV49 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(158,plain,
! [SV50: $i,SV18: $i] :
( ( ! [SY71: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV18 @ SV50 @ mactual )
| ~ ( member @ SY71 @ SV18 @ mactual ) )
| ( member @ SY71 @ SV50 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(159,plain,
! [SV51: $i,SV19: $i] :
( ( ! [SY72: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV19 @ SV51 @ mactual )
| ~ ( subset @ SV19 @ SY72 @ mactual ) )
| ( subset @ SV51 @ SY72 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(160,plain,
! [SV52: $i,SV20: $i] :
( ( ! [SY73: $i] :
( ~ ( qmltpeq @ SV20 @ SV52 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SY73 @ SV20 ) @ ( unordered_pair @ SY73 @ SV52 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(161,plain,
! [SV21: $i] :
( ( member @ SV21 @ empty_set @ mactual )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(162,plain,
! [SV53: $i,SV22: $i] :
( ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual )
| ( qmltpeq @ ( sum @ SV22 ) @ ( sum @ SV53 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(163,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV23 @ SV54 @ mactual )
| ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) )
| ( equal_set @ SV23 @ SV54 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(164,plain,
! [SV55: $i,SV24: $i] :
( ( ! [SY74: $i] :
~ ( ~ ( ~ ( member @ SV24 @ ( difference @ SY74 @ SV55 ) @ mactual )
| ~ ( ~ ( member @ SV24 @ SY74 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SY74 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
| ( member @ SV24 @ ( difference @ SY74 @ SV55 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(165,plain,
! [SV56: $i,SV25: $i] :
( ( ! [SY75: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( equal_set @ SY75 @ SV25 @ mactual ) )
| ( equal_set @ SY75 @ SV56 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(166,plain,
! [SV57: $i,SV26: $i] :
( ( ! [SY76: $i] :
~ ( ~ ( ~ ( member @ SV26 @ ( unordered_pair @ SV57 @ SY76 ) @ mactual )
| ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SY76 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SY76 @ mactual ) )
| ( member @ SV26 @ ( unordered_pair @ SV57 @ SY76 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(167,plain,
! [SV58: $i,SV27: $i] :
( ( ! [SY77: $i] :
( ~ ( qmltpeq @ SV27 @ SV58 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV27 @ SY77 ) @ ( unordered_pair @ SV58 @ SY77 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(168,plain,
! [SV59: $i,SV28: $i] :
( ( ! [SY78: $i] :
( ~ ( qmltpeq @ SV28 @ SV59 @ mactual )
| ( qmltpeq @ ( difference @ SY78 @ SV28 ) @ ( difference @ SY78 @ SV59 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(169,plain,
! [SV60: $i,SV29: $i] :
( ( ~ ( ~ ( ~ ( member @ SV29 @ ( singleton @ SV60 ) @ mactual )
| ( qmltpeq @ SV29 @ SV60 @ mactual ) )
| ~ ( ~ ( qmltpeq @ SV29 @ SV60 @ mactual )
| ( member @ SV29 @ ( singleton @ SV60 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(170,plain,
! [SV61: $i,SV30: $i] :
( ( ! [SY79: $i] :
( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual )
| ~ ( equal_set @ SV30 @ SY79 @ mactual ) )
| ( equal_set @ SV61 @ SY79 @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(171,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV31 @ SV62 @ mactual )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SV31 @ mactual )
| ( member @ SY80 @ SV62 @ mactual ) ) )
| ~ ( ~ ! [SY81: $i] :
( ~ ( member @ SY81 @ SV31 @ mactual )
| ( member @ SY81 @ SV62 @ mactual ) )
| ( subset @ SV31 @ SV62 @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(172,plain,
! [SV63: $i,SV32: $i] :
( ( ! [SY82: $i] :
( ~ ( qmltpeq @ SV32 @ SV63 @ mactual )
| ( qmltpeq @ ( union @ SV32 @ SY82 ) @ ( union @ SV63 @ SY82 ) @ mactual ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(173,plain,
! [SV64: $i,SV33: $i] :
( ( ~ ( qmltpeq @ SV33 @ SV64 @ mactual )
| ( qmltpeq @ ( product @ SV33 ) @ ( product @ SV64 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(174,plain,
! [SV65: $i,SV34: $i] :
( ( ~ ( qmltpeq @ SV34 @ SV65 @ mactual )
| ( qmltpeq @ ( singleton @ SV34 ) @ ( singleton @ SV65 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(175,plain,
! [SV66: mworld,SV35: mworld,SV2: mworld] :
( ( ~ ( mrel @ SV2 @ SV35 )
| ~ ( mrel @ SV35 @ SV66 )
| ( mrel @ SV2 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(176,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV3 @ SV36 @ mactual )
| ~ ( qmltpeq @ SV36 @ SV67 @ mactual ) )
| ( qmltpeq @ SV3 @ SV67 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(177,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
| ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
| ~ ( ~ ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
| ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(178,plain,
! [SV69: $i,SV38: $i,SV5: $i] :
( ( ~ ( qmltpeq @ SV5 @ SV38 @ mactual )
| ( qmltpeq @ ( intersection @ SV5 @ SV69 ) @ ( intersection @ SV38 @ SV69 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(179,plain,
! [SV39: $i,SV6: $i] :
( ( ( ~ ( qmltpeq @ SV6 @ SV39 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV39 @ SV6 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(180,plain,
! [SV40: $i,SV8: $i] :
( ( ~ ( ~ ( member @ SV8 @ ( power_set @ SV40 ) @ mactual )
| ( subset @ SV8 @ SV40 @ mactual ) )
| ~ ( ~ ( subset @ SV8 @ SV40 @ mactual )
| ( member @ SV8 @ ( power_set @ SV40 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(181,plain,
! [SV41: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( product @ SV41 ) @ mactual )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV41 @ mactual )
| ( member @ SV9 @ SY61 @ mactual ) ) )
| ~ ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV41 @ mactual )
| ( member @ SV9 @ SY62 @ mactual ) )
| ( member @ SV9 @ ( product @ SV41 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(182,plain,
! [SV70: $i,SV42: $i,SV10: $i] :
( ( ~ ( qmltpeq @ SV10 @ SV42 @ mactual )
| ( qmltpeq @ ( difference @ SV10 @ SV70 ) @ ( difference @ SV42 @ SV70 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(183,plain,
! [SV71: $i,SV43: $i,SV11: $i] :
( ( ~ ( qmltpeq @ SV11 @ SV43 @ mactual )
| ( qmltpeq @ ( intersection @ SV71 @ SV11 ) @ ( intersection @ SV71 @ SV43 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(184,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
| ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) )
| ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(185,plain,
! [SV73: $i,SV45: $i,SV13: $i] :
( ( ~ ( qmltpeq @ SV13 @ SV45 @ mactual )
| ( qmltpeq @ ( union @ SV73 @ SV13 ) @ ( union @ SV73 @ SV45 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(186,plain,
! [SV46: $i,SV14: $i] :
( ( ~ ( ~ ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( member @ SY67 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY67 @ mactual ) ) )
| ~ ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( member @ SY68 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY68 @ mactual ) )
| ( member @ SV14 @ ( sum @ SV46 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(187,plain,
! [SV47: $i,SV15: $i] :
( ( ( ~ ( qmltpeq @ SV15 @ SV47 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( power_set @ SV15 ) @ ( power_set @ SV47 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(188,plain,
! [SV74: $i,SV48: $i,SV16: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV16 @ SV48 @ mactual )
| ~ ( member @ SV16 @ SV74 @ mactual ) )
| ( member @ SV48 @ SV74 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(189,plain,
! [SV75: $i,SV49: $i,SV17: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV17 @ SV49 @ mactual )
| ~ ( subset @ SV75 @ SV17 @ mactual ) )
| ( subset @ SV75 @ SV49 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(190,plain,
! [SV76: $i,SV50: $i,SV18: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV18 @ SV50 @ mactual )
| ~ ( member @ SV76 @ SV18 @ mactual ) )
| ( member @ SV76 @ SV50 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(191,plain,
! [SV77: $i,SV51: $i,SV19: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV19 @ SV51 @ mactual )
| ~ ( subset @ SV19 @ SV77 @ mactual ) )
| ( subset @ SV51 @ SV77 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(192,plain,
! [SV78: $i,SV52: $i,SV20: $i] :
( ( ~ ( qmltpeq @ SV20 @ SV52 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV78 @ SV20 ) @ ( unordered_pair @ SV78 @ SV52 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(193,plain,
! [SV53: $i,SV22: $i] :
( ( ( ~ ( qmltpeq @ SV22 @ SV53 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( sum @ SV22 ) @ ( sum @ SV53 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(194,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ( equal_set @ SV23 @ SV54 @ mactual )
| ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) )
| ( equal_set @ SV23 @ SV54 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(195,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
| ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
| ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(196,plain,
! [SV80: $i,SV56: $i,SV25: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( equal_set @ SV80 @ SV25 @ mactual ) )
| ( equal_set @ SV80 @ SV56 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(197,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ~ ( ~ ( ~ ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
| ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
| ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(198,plain,
! [SV82: $i,SV58: $i,SV27: $i] :
( ( ~ ( qmltpeq @ SV27 @ SV58 @ mactual )
| ( qmltpeq @ ( unordered_pair @ SV27 @ SV82 ) @ ( unordered_pair @ SV58 @ SV82 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(199,plain,
! [SV83: $i,SV59: $i,SV28: $i] :
( ( ~ ( qmltpeq @ SV28 @ SV59 @ mactual )
| ( qmltpeq @ ( difference @ SV83 @ SV28 ) @ ( difference @ SV83 @ SV59 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(200,plain,
! [SV60: $i,SV29: $i] :
( ( ~ ( ~ ( member @ SV29 @ ( singleton @ SV60 ) @ mactual )
| ( qmltpeq @ SV29 @ SV60 @ mactual ) )
| ~ ( ~ ( qmltpeq @ SV29 @ SV60 @ mactual )
| ( member @ SV29 @ ( singleton @ SV60 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(201,plain,
! [SV84: $i,SV61: $i,SV30: $i] :
( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual )
| ~ ( equal_set @ SV30 @ SV84 @ mactual ) )
| ( equal_set @ SV61 @ SV84 @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(202,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( ~ ( subset @ SV31 @ SV62 @ mactual )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SV31 @ mactual )
| ( member @ SY80 @ SV62 @ mactual ) ) )
| ~ ( ~ ! [SY81: $i] :
( ~ ( member @ SY81 @ SV31 @ mactual )
| ( member @ SY81 @ SV62 @ mactual ) )
| ( subset @ SV31 @ SV62 @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(203,plain,
! [SV85: $i,SV63: $i,SV32: $i] :
( ( ~ ( qmltpeq @ SV32 @ SV63 @ mactual )
| ( qmltpeq @ ( union @ SV32 @ SV85 ) @ ( union @ SV63 @ SV85 ) @ mactual ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(204,plain,
! [SV64: $i,SV33: $i] :
( ( ( ~ ( qmltpeq @ SV33 @ SV64 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( product @ SV33 ) @ ( product @ SV64 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(205,plain,
! [SV65: $i,SV34: $i] :
( ( ( ~ ( qmltpeq @ SV34 @ SV65 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV34 ) @ ( singleton @ SV65 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(206,plain,
! [SV66: mworld,SV35: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV35 )
| ~ ( mrel @ SV35 @ SV66 ) )
= $true )
| ( ( mrel @ SV2 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(207,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV3 @ SV36 @ mactual )
| ~ ( qmltpeq @ SV36 @ SV67 @ mactual ) ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV67 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(208,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ~ ( ~ ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
| ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
| ~ ( ~ ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
| ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(209,plain,
! [SV69: $i,SV38: $i,SV5: $i] :
( ( ( ~ ( qmltpeq @ SV5 @ SV38 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV5 @ SV69 ) @ ( intersection @ SV38 @ SV69 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(210,plain,
! [SV39: $i,SV6: $i] :
( ( ( qmltpeq @ SV6 @ SV39 @ mactual )
= $false )
| ( ( qmltpeq @ SV39 @ SV6 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(211,plain,
! [SV40: $i,SV8: $i] :
( ( ~ ( ~ ( member @ SV8 @ ( power_set @ SV40 ) @ mactual )
| ( subset @ SV8 @ SV40 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(212,plain,
! [SV40: $i,SV8: $i] :
( ( ~ ( ~ ( subset @ SV8 @ SV40 @ mactual )
| ( member @ SV8 @ ( power_set @ SV40 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(213,plain,
! [SV41: $i,SV9: $i] :
( ( ~ ( ~ ( member @ SV9 @ ( product @ SV41 ) @ mactual )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV41 @ mactual )
| ( member @ SV9 @ SY61 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(214,plain,
! [SV9: $i,SV41: $i] :
( ( ~ ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV41 @ mactual )
| ( member @ SV9 @ SY62 @ mactual ) )
| ( member @ SV9 @ ( product @ SV41 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(215,plain,
! [SV70: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( qmltpeq @ SV10 @ SV42 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV10 @ SV70 ) @ ( difference @ SV42 @ SV70 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(216,plain,
! [SV71: $i,SV43: $i,SV11: $i] :
( ( ( ~ ( qmltpeq @ SV11 @ SV43 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV71 @ SV11 ) @ ( intersection @ SV71 @ SV43 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(217,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
| ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) )
| ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(218,plain,
! [SV73: $i,SV45: $i,SV13: $i] :
( ( ( ~ ( qmltpeq @ SV13 @ SV45 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( union @ SV73 @ SV13 ) @ ( union @ SV73 @ SV45 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(219,plain,
! [SV46: $i,SV14: $i] :
( ( ~ ( ~ ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( member @ SY67 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY67 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(220,plain,
! [SV14: $i,SV46: $i] :
( ( ~ ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( member @ SY68 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY68 @ mactual ) )
| ( member @ SV14 @ ( sum @ SV46 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(221,plain,
! [SV47: $i,SV15: $i] :
( ( ( qmltpeq @ SV15 @ SV47 @ mactual )
= $false )
| ( ( qmltpeq @ ( power_set @ SV15 ) @ ( power_set @ SV47 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(222,plain,
! [SV74: $i,SV48: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV16 @ SV48 @ mactual )
| ~ ( member @ SV16 @ SV74 @ mactual ) ) )
= $true )
| ( ( member @ SV48 @ SV74 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(223,plain,
! [SV75: $i,SV49: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV17 @ SV49 @ mactual )
| ~ ( subset @ SV75 @ SV17 @ mactual ) ) )
= $true )
| ( ( subset @ SV75 @ SV49 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(224,plain,
! [SV76: $i,SV50: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV18 @ SV50 @ mactual )
| ~ ( member @ SV76 @ SV18 @ mactual ) ) )
= $true )
| ( ( member @ SV76 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(225,plain,
! [SV77: $i,SV51: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV19 @ SV51 @ mactual )
| ~ ( subset @ SV19 @ SV77 @ mactual ) ) )
= $true )
| ( ( subset @ SV51 @ SV77 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(226,plain,
! [SV78: $i,SV52: $i,SV20: $i] :
( ( ( ~ ( qmltpeq @ SV20 @ SV52 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV78 @ SV20 ) @ ( unordered_pair @ SV78 @ SV52 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(227,plain,
! [SV53: $i,SV22: $i] :
( ( ( qmltpeq @ SV22 @ SV53 @ mactual )
= $false )
| ( ( qmltpeq @ ( sum @ SV22 ) @ ( sum @ SV53 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(228,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ( equal_set @ SV23 @ SV54 @ mactual )
| ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(229,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) )
| ( equal_set @ SV23 @ SV54 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(230,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ~ ( ~ ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
| ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
| ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(231,plain,
! [SV80: $i,SV56: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( equal_set @ SV80 @ SV25 @ mactual ) ) )
= $true )
| ( ( equal_set @ SV80 @ SV56 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(232,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ~ ( ~ ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
| ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
| ~ ( ~ ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
| ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(233,plain,
! [SV82: $i,SV58: $i,SV27: $i] :
( ( ( ~ ( qmltpeq @ SV27 @ SV58 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV27 @ SV82 ) @ ( unordered_pair @ SV58 @ SV82 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(234,plain,
! [SV83: $i,SV59: $i,SV28: $i] :
( ( ( ~ ( qmltpeq @ SV28 @ SV59 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV83 @ SV28 ) @ ( difference @ SV83 @ SV59 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(235,plain,
! [SV60: $i,SV29: $i] :
( ( ~ ( ~ ( member @ SV29 @ ( singleton @ SV60 ) @ mactual )
| ( qmltpeq @ SV29 @ SV60 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(236,plain,
! [SV60: $i,SV29: $i] :
( ( ~ ( ~ ( qmltpeq @ SV29 @ SV60 @ mactual )
| ( member @ SV29 @ ( singleton @ SV60 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(237,plain,
! [SV84: $i,SV61: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual )
| ~ ( equal_set @ SV30 @ SV84 @ mactual ) ) )
= $true )
| ( ( equal_set @ SV61 @ SV84 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(238,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( ~ ( subset @ SV31 @ SV62 @ mactual )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SV31 @ mactual )
| ( member @ SY80 @ SV62 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(239,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( ~ ! [SY81: $i] :
( ~ ( member @ SY81 @ SV31 @ mactual )
| ( member @ SY81 @ SV62 @ mactual ) )
| ( subset @ SV31 @ SV62 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(240,plain,
! [SV85: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( qmltpeq @ SV32 @ SV63 @ mactual ) )
= $true )
| ( ( qmltpeq @ ( union @ SV32 @ SV85 ) @ ( union @ SV63 @ SV85 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV64: $i,SV33: $i] :
( ( ( qmltpeq @ SV33 @ SV64 @ mactual )
= $false )
| ( ( qmltpeq @ ( product @ SV33 ) @ ( product @ SV64 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV65: $i,SV34: $i] :
( ( ( qmltpeq @ SV34 @ SV65 @ mactual )
= $false )
| ( ( qmltpeq @ ( singleton @ SV34 ) @ ( singleton @ SV65 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV66: mworld,SV35: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV35 ) )
= $true )
| ( ( ~ ( mrel @ SV35 @ SV66 ) )
= $true )
| ( ( mrel @ SV2 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV3 @ SV36 @ mactual )
| ~ ( qmltpeq @ SV36 @ SV67 @ mactual ) ) )
= $false )
| ( ( qmltpeq @ SV3 @ SV67 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ~ ( ~ ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
| ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(246,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ~ ( ~ ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
| ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(247,plain,
! [SV69: $i,SV38: $i,SV5: $i] :
( ( ( qmltpeq @ SV5 @ SV38 @ mactual )
= $false )
| ( ( qmltpeq @ ( intersection @ SV5 @ SV69 ) @ ( intersection @ SV38 @ SV69 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(248,plain,
! [SV40: $i,SV8: $i] :
( ( ~ ( member @ SV8 @ ( power_set @ SV40 ) @ mactual )
| ( subset @ SV8 @ SV40 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(249,plain,
! [SV40: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV40 @ mactual )
| ( member @ SV8 @ ( power_set @ SV40 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(250,plain,
! [SV41: $i,SV9: $i] :
( ( ~ ( member @ SV9 @ ( product @ SV41 ) @ mactual )
| ! [SY61: $i] :
( ~ ( member @ SY61 @ SV41 @ mactual )
| ( member @ SV9 @ SY61 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(251,plain,
! [SV9: $i,SV41: $i] :
( ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV41 @ mactual )
| ( member @ SV9 @ SY62 @ mactual ) )
| ( member @ SV9 @ ( product @ SV41 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(252,plain,
! [SV70: $i,SV42: $i,SV10: $i] :
( ( ( qmltpeq @ SV10 @ SV42 @ mactual )
= $false )
| ( ( qmltpeq @ ( difference @ SV10 @ SV70 ) @ ( difference @ SV42 @ SV70 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(253,plain,
! [SV71: $i,SV43: $i,SV11: $i] :
( ( ( qmltpeq @ SV11 @ SV43 @ mactual )
= $false )
| ( ( qmltpeq @ ( intersection @ SV71 @ SV11 ) @ ( intersection @ SV71 @ SV43 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(254,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ~ ( ~ ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
| ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(255,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) )
| ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(256,plain,
! [SV73: $i,SV45: $i,SV13: $i] :
( ( ( qmltpeq @ SV13 @ SV45 @ mactual )
= $false )
| ( ( qmltpeq @ ( union @ SV73 @ SV13 ) @ ( union @ SV73 @ SV45 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(257,plain,
! [SV46: $i,SV14: $i] :
( ( ~ ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
| ~ ! [SY67: $i] :
~ ~ ( ~ ( member @ SY67 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY67 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(258,plain,
! [SV14: $i,SV46: $i] :
( ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( member @ SY68 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY68 @ mactual ) )
| ( member @ SV14 @ ( sum @ SV46 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(259,plain,
! [SV74: $i,SV48: $i,SV16: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV16 @ SV48 @ mactual )
| ~ ( member @ SV16 @ SV74 @ mactual ) ) )
= $false )
| ( ( member @ SV48 @ SV74 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(260,plain,
! [SV75: $i,SV49: $i,SV17: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV17 @ SV49 @ mactual )
| ~ ( subset @ SV75 @ SV17 @ mactual ) ) )
= $false )
| ( ( subset @ SV75 @ SV49 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(261,plain,
! [SV76: $i,SV50: $i,SV18: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV18 @ SV50 @ mactual )
| ~ ( member @ SV76 @ SV18 @ mactual ) ) )
= $false )
| ( ( member @ SV76 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(262,plain,
! [SV77: $i,SV51: $i,SV19: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV19 @ SV51 @ mactual )
| ~ ( subset @ SV19 @ SV77 @ mactual ) ) )
= $false )
| ( ( subset @ SV51 @ SV77 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(263,plain,
! [SV78: $i,SV52: $i,SV20: $i] :
( ( ( qmltpeq @ SV20 @ SV52 @ mactual )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV78 @ SV20 ) @ ( unordered_pair @ SV78 @ SV52 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(264,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ( equal_set @ SV23 @ SV54 @ mactual )
| ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(265,plain,
! [SV54: $i,SV23: $i] :
( ( ~ ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) )
| ( equal_set @ SV23 @ SV54 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(266,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ~ ( ~ ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
| ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(267,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
| ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(268,plain,
! [SV80: $i,SV56: $i,SV25: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( equal_set @ SV80 @ SV25 @ mactual ) ) )
= $false )
| ( ( equal_set @ SV80 @ SV56 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(269,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ~ ( ~ ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
| ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(270,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ~ ( ~ ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
| ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(271,plain,
! [SV82: $i,SV58: $i,SV27: $i] :
( ( ( qmltpeq @ SV27 @ SV58 @ mactual )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV27 @ SV82 ) @ ( unordered_pair @ SV58 @ SV82 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(272,plain,
! [SV83: $i,SV59: $i,SV28: $i] :
( ( ( qmltpeq @ SV28 @ SV59 @ mactual )
= $false )
| ( ( qmltpeq @ ( difference @ SV83 @ SV28 ) @ ( difference @ SV83 @ SV59 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(273,plain,
! [SV60: $i,SV29: $i] :
( ( ~ ( member @ SV29 @ ( singleton @ SV60 ) @ mactual )
| ( qmltpeq @ SV29 @ SV60 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(274,plain,
! [SV60: $i,SV29: $i] :
( ( ~ ( qmltpeq @ SV29 @ SV60 @ mactual )
| ( member @ SV29 @ ( singleton @ SV60 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(275,plain,
! [SV84: $i,SV61: $i,SV30: $i] :
( ( ( ~ ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual )
| ~ ( equal_set @ SV30 @ SV84 @ mactual ) ) )
= $false )
| ( ( equal_set @ SV61 @ SV84 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(276,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV62 @ mactual )
| ! [SY80: $i] :
( ~ ( member @ SY80 @ SV31 @ mactual )
| ( member @ SY80 @ SV62 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(277,plain,
! [SV62: $i,SV31: $i] :
( ( ~ ! [SY81: $i] :
( ~ ( member @ SY81 @ SV31 @ mactual )
| ( member @ SY81 @ SV62 @ mactual ) )
| ( subset @ SV31 @ SV62 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(278,plain,
! [SV85: $i,SV63: $i,SV32: $i] :
( ( ( qmltpeq @ SV32 @ SV63 @ mactual )
= $false )
| ( ( qmltpeq @ ( union @ SV32 @ SV85 ) @ ( union @ SV63 @ SV85 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(279,plain,
! [SV66: mworld,SV35: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV35 )
= $false )
| ( ( ~ ( mrel @ SV35 @ SV66 ) )
= $true )
| ( ( mrel @ SV2 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(280,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV36 @ mactual )
| ~ ( qmltpeq @ SV36 @ SV67 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV67 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(281,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ~ ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
| ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(282,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ~ ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
| ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(283,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ ( power_set @ SV40 ) @ mactual ) )
= $true )
| ( ( subset @ SV8 @ SV40 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(284,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV40 @ mactual ) )
= $true )
| ( ( member @ SV8 @ ( power_set @ SV40 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(285,plain,
! [SV41: $i,SV9: $i] :
( ( ( ~ ( member @ SV9 @ ( product @ SV41 ) @ mactual ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( member @ SY61 @ SV41 @ mactual )
| ( member @ SV9 @ SY61 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(286,plain,
! [SV9: $i,SV41: $i] :
( ( ( ~ ! [SY62: $i] :
( ~ ( member @ SY62 @ SV41 @ mactual )
| ( member @ SV9 @ SY62 @ mactual ) ) )
= $true )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(287,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ~ ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
| ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(288,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ~ ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) )
| ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(289,plain,
! [SV46: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ ( sum @ SV46 ) @ mactual ) )
= $true )
| ( ( ~ ! [SY67: $i] :
~ ~ ( ~ ( member @ SY67 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY67 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(290,plain,
! [SV14: $i,SV46: $i] :
( ( ( ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( member @ SY68 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY68 @ mactual ) ) )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(291,plain,
! [SV74: $i,SV48: $i,SV16: $i] :
( ( ( ~ ( qmltpeq @ SV16 @ SV48 @ mactual )
| ~ ( member @ SV16 @ SV74 @ mactual ) )
= $true )
| ( ( member @ SV48 @ SV74 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(292,plain,
! [SV75: $i,SV49: $i,SV17: $i] :
( ( ( ~ ( qmltpeq @ SV17 @ SV49 @ mactual )
| ~ ( subset @ SV75 @ SV17 @ mactual ) )
= $true )
| ( ( subset @ SV75 @ SV49 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(293,plain,
! [SV76: $i,SV50: $i,SV18: $i] :
( ( ( ~ ( qmltpeq @ SV18 @ SV50 @ mactual )
| ~ ( member @ SV76 @ SV18 @ mactual ) )
= $true )
| ( ( member @ SV76 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(294,plain,
! [SV77: $i,SV51: $i,SV19: $i] :
( ( ( ~ ( qmltpeq @ SV19 @ SV51 @ mactual )
| ~ ( subset @ SV19 @ SV77 @ mactual ) )
= $true )
| ( ( subset @ SV51 @ SV77 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(295,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( equal_set @ SV23 @ SV54 @ mactual ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(296,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) )
= $true )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(297,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ~ ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
| ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(298,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ~ ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
| ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(299,plain,
! [SV80: $i,SV56: $i,SV25: $i] :
( ( ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual )
| ~ ( equal_set @ SV80 @ SV25 @ mactual ) )
= $true )
| ( ( equal_set @ SV80 @ SV56 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(300,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ~ ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
| ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(301,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ~ ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
| ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(302,plain,
! [SV60: $i,SV29: $i] :
( ( ( ~ ( member @ SV29 @ ( singleton @ SV60 ) @ mactual ) )
= $true )
| ( ( qmltpeq @ SV29 @ SV60 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(303,plain,
! [SV60: $i,SV29: $i] :
( ( ( ~ ( qmltpeq @ SV29 @ SV60 @ mactual ) )
= $true )
| ( ( member @ SV29 @ ( singleton @ SV60 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(304,plain,
! [SV84: $i,SV61: $i,SV30: $i] :
( ( ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual )
| ~ ( equal_set @ SV30 @ SV84 @ mactual ) )
= $true )
| ( ( equal_set @ SV61 @ SV84 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(305,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV62 @ mactual ) )
= $true )
| ( ( ! [SY80: $i] :
( ~ ( member @ SY80 @ SV31 @ mactual )
| ( member @ SY80 @ SV62 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(306,plain,
! [SV62: $i,SV31: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( member @ SY81 @ SV31 @ mactual )
| ( member @ SY81 @ SV62 @ mactual ) ) )
= $true )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(307,plain,
! [SV2: mworld,SV66: mworld,SV35: mworld] :
( ( ( mrel @ SV35 @ SV66 )
= $false )
| ( ( mrel @ SV2 @ SV35 )
= $false )
| ( ( mrel @ SV2 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(308,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ( ~ ( qmltpeq @ SV3 @ SV36 @ mactual ) )
= $true )
| ( ( ~ ( qmltpeq @ SV36 @ SV67 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV67 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(309,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ( ~ ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual ) )
= $true )
| ( ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(310,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ( ~ ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) ) )
= $true )
| ( ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(311,plain,
! [SV40: $i,SV8: $i] :
( ( ( member @ SV8 @ ( power_set @ SV40 ) @ mactual )
= $false )
| ( ( subset @ SV8 @ SV40 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(312,plain,
! [SV40: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV40 @ mactual )
= $false )
| ( ( member @ SV8 @ ( power_set @ SV40 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(313,plain,
! [SV41: $i,SV9: $i] :
( ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( member @ SY61 @ SV41 @ mactual )
| ( member @ SV9 @ SY61 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(314,plain,
! [SV9: $i,SV41: $i] :
( ( ( ! [SY62: $i] :
( ~ ( member @ SY62 @ SV41 @ mactual )
| ( member @ SV9 @ SY62 @ mactual ) ) )
= $false )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(315,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual ) )
= $true )
| ( ( ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(316,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) )
= $true )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(317,plain,
! [SV46: $i,SV14: $i] :
( ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false )
| ( ( ~ ! [SY67: $i] :
~ ~ ( ~ ( member @ SY67 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY67 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(318,plain,
! [SV14: $i,SV46: $i] :
( ( ( ~ ! [SY68: $i] :
~ ~ ( ~ ( member @ SY68 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY68 @ mactual ) ) )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(319,plain,
! [SV74: $i,SV48: $i,SV16: $i] :
( ( ( ~ ( qmltpeq @ SV16 @ SV48 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV16 @ SV74 @ mactual ) )
= $true )
| ( ( member @ SV48 @ SV74 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(320,plain,
! [SV75: $i,SV49: $i,SV17: $i] :
( ( ( ~ ( qmltpeq @ SV17 @ SV49 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV75 @ SV17 @ mactual ) )
= $true )
| ( ( subset @ SV75 @ SV49 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(321,plain,
! [SV76: $i,SV50: $i,SV18: $i] :
( ( ( ~ ( qmltpeq @ SV18 @ SV50 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV76 @ SV18 @ mactual ) )
= $true )
| ( ( member @ SV76 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(322,plain,
! [SV77: $i,SV51: $i,SV19: $i] :
( ( ( ~ ( qmltpeq @ SV19 @ SV51 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV19 @ SV77 @ mactual ) )
= $true )
| ( ( subset @ SV51 @ SV77 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(323,plain,
! [SV54: $i,SV23: $i] :
( ( ( equal_set @ SV23 @ SV54 @ mactual )
= $false )
| ( ( ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(324,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) ) )
= $false )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(325,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual ) )
= $true )
| ( ( ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(326,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
= $true )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(327,plain,
! [SV80: $i,SV56: $i,SV25: $i] :
( ( ( ~ ( qmltpeq @ SV25 @ SV56 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV80 @ SV25 @ mactual ) )
= $true )
| ( ( equal_set @ SV80 @ SV56 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(328,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual ) )
= $true )
| ( ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(329,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ( ~ ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) ) )
= $true )
| ( ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(330,plain,
! [SV60: $i,SV29: $i] :
( ( ( member @ SV29 @ ( singleton @ SV60 ) @ mactual )
= $false )
| ( ( qmltpeq @ SV29 @ SV60 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(331,plain,
! [SV60: $i,SV29: $i] :
( ( ( qmltpeq @ SV29 @ SV60 @ mactual )
= $false )
| ( ( member @ SV29 @ ( singleton @ SV60 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(332,plain,
! [SV84: $i,SV61: $i,SV30: $i] :
( ( ( ~ ( qmltpeq @ SV30 @ SV61 @ mactual ) )
= $true )
| ( ( ~ ( equal_set @ SV30 @ SV84 @ mactual ) )
= $true )
| ( ( equal_set @ SV61 @ SV84 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(333,plain,
! [SV62: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV62 @ mactual )
= $false )
| ( ( ! [SY80: $i] :
( ~ ( member @ SY80 @ SV31 @ mactual )
| ( member @ SY80 @ SV62 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(334,plain,
! [SV62: $i,SV31: $i] :
( ( ( ! [SY81: $i] :
( ~ ( member @ SY81 @ SV31 @ mactual )
| ( member @ SY81 @ SV62 @ mactual ) ) )
= $false )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(335,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ( qmltpeq @ SV3 @ SV36 @ mactual )
= $false )
| ( ( ~ ( qmltpeq @ SV36 @ SV67 @ mactual ) )
= $true )
| ( ( qmltpeq @ SV3 @ SV67 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(336,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
= $false )
| ( ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(337,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ( ( member @ SV4 @ SV37 @ mactual )
| ( member @ SV4 @ SV68 @ mactual ) )
= $false )
| ( ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(338,plain,
! [SV9: $i,SV41: $i,SV86: $i] :
( ( ( ~ ( member @ SV86 @ SV41 @ mactual )
| ( member @ SV9 @ SV86 @ mactual ) )
= $true )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(339,plain,
! [SV41: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK2_SY62 @ SV9 @ SV41 ) @ SV41 @ mactual )
| ( member @ SV9 @ ( sK2_SY62 @ SV9 @ SV41 ) @ mactual ) )
= $false )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[314]) ).
thf(340,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $false )
| ( ( ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(341,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( ~ ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) ) )
= $false )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(342,plain,
! [SV14: $i,SV46: $i] :
( ( ( ! [SY67: $i] :
~ ~ ( ~ ( member @ SY67 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY67 @ mactual ) ) )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(343,plain,
! [SV14: $i,SV46: $i] :
( ( ( ! [SY68: $i] :
~ ~ ( ~ ( member @ SY68 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SY68 @ mactual ) ) )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(344,plain,
! [SV74: $i,SV48: $i,SV16: $i] :
( ( ( qmltpeq @ SV16 @ SV48 @ mactual )
= $false )
| ( ( ~ ( member @ SV16 @ SV74 @ mactual ) )
= $true )
| ( ( member @ SV48 @ SV74 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(345,plain,
! [SV75: $i,SV49: $i,SV17: $i] :
( ( ( qmltpeq @ SV17 @ SV49 @ mactual )
= $false )
| ( ( ~ ( subset @ SV75 @ SV17 @ mactual ) )
= $true )
| ( ( subset @ SV75 @ SV49 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(346,plain,
! [SV76: $i,SV50: $i,SV18: $i] :
( ( ( qmltpeq @ SV18 @ SV50 @ mactual )
= $false )
| ( ( ~ ( member @ SV76 @ SV18 @ mactual ) )
= $true )
| ( ( member @ SV76 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(347,plain,
! [SV77: $i,SV51: $i,SV19: $i] :
( ( ( qmltpeq @ SV19 @ SV51 @ mactual )
= $false )
| ( ( ~ ( subset @ SV19 @ SV77 @ mactual ) )
= $true )
| ( ( subset @ SV51 @ SV77 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(348,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) )
= $false )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(349,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV54 @ mactual )
| ~ ( subset @ SV54 @ SV23 @ mactual ) )
= $true )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(350,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $false )
| ( ( ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(351,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( ~ ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) ) )
= $false )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(352,plain,
! [SV80: $i,SV56: $i,SV25: $i] :
( ( ( qmltpeq @ SV25 @ SV56 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV80 @ SV25 @ mactual ) )
= $true )
| ( ( equal_set @ SV80 @ SV56 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(353,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
= $false )
| ( ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(354,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ( ( qmltpeq @ SV26 @ SV57 @ mactual )
| ( qmltpeq @ SV26 @ SV81 @ mactual ) )
= $false )
| ( ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(355,plain,
! [SV84: $i,SV61: $i,SV30: $i] :
( ( ( qmltpeq @ SV30 @ SV61 @ mactual )
= $false )
| ( ( ~ ( equal_set @ SV30 @ SV84 @ mactual ) )
= $true )
| ( ( equal_set @ SV61 @ SV84 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(356,plain,
! [SV62: $i,SV31: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ SV31 @ mactual )
| ( member @ SV87 @ SV62 @ mactual ) )
= $true )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(357,plain,
! [SV31: $i,SV62: $i] :
( ( ( ~ ( member @ ( sK3_SY81 @ SV62 @ SV31 ) @ SV31 @ mactual )
| ( member @ ( sK3_SY81 @ SV62 @ SV31 ) @ SV62 @ mactual ) )
= $false )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[334]) ).
thf(358,plain,
! [SV3: $i,SV67: $i,SV36: $i] :
( ( ( qmltpeq @ SV36 @ SV67 @ mactual )
= $false )
| ( ( qmltpeq @ SV3 @ SV36 @ mactual )
= $false )
| ( ( qmltpeq @ SV3 @ SV67 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(359,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ( member @ SV4 @ SV37 @ mactual )
= $true )
| ( ( member @ SV4 @ SV68 @ mactual )
= $true )
| ( ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(360,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ( member @ SV4 @ SV37 @ mactual )
= $false )
| ( ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(361,plain,
! [SV37: $i,SV68: $i,SV4: $i] :
( ( ( member @ SV4 @ SV68 @ mactual )
= $false )
| ( ( member @ SV4 @ ( union @ SV37 @ SV68 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(362,plain,
! [SV9: $i,SV41: $i,SV86: $i] :
( ( ( ~ ( member @ SV86 @ SV41 @ mactual ) )
= $true )
| ( ( member @ SV9 @ SV86 @ mactual )
= $true )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(363,plain,
! [SV41: $i,SV9: $i] :
( ( ( ~ ( member @ ( sK2_SY62 @ SV9 @ SV41 ) @ SV41 @ mactual ) )
= $false )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(364,plain,
! [SV41: $i,SV9: $i] :
( ( ( member @ SV9 @ ( sK2_SY62 @ SV9 @ SV41 ) @ mactual )
= $false )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(365,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) )
= $false )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(366,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ SV44 @ mactual )
| ~ ( member @ SV12 @ SV72 @ mactual ) )
= $true )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(367,plain,
! [SV46: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( member @ ( sK4_SY67 @ SV14 @ SV46 ) @ SV46 @ mactual )
| ~ ( member @ SV14 @ ( sK4_SY67 @ SV14 @ SV46 ) @ mactual ) ) )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[342]) ).
thf(368,plain,
! [SV14: $i,SV46: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( member @ SV88 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SV88 @ mactual ) ) )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(369,plain,
! [SV48: $i,SV74: $i,SV16: $i] :
( ( ( member @ SV16 @ SV74 @ mactual )
= $false )
| ( ( qmltpeq @ SV16 @ SV48 @ mactual )
= $false )
| ( ( member @ SV48 @ SV74 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(370,plain,
! [SV49: $i,SV17: $i,SV75: $i] :
( ( ( subset @ SV75 @ SV17 @ mactual )
= $false )
| ( ( qmltpeq @ SV17 @ SV49 @ mactual )
= $false )
| ( ( subset @ SV75 @ SV49 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(371,plain,
! [SV50: $i,SV18: $i,SV76: $i] :
( ( ( member @ SV76 @ SV18 @ mactual )
= $false )
| ( ( qmltpeq @ SV18 @ SV50 @ mactual )
= $false )
| ( ( member @ SV76 @ SV50 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(372,plain,
! [SV51: $i,SV77: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV77 @ mactual )
= $false )
| ( ( qmltpeq @ SV19 @ SV51 @ mactual )
= $false )
| ( ( subset @ SV51 @ SV77 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(373,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV54 @ mactual ) )
= $false )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(374,plain,
! [SV23: $i,SV54: $i] :
( ( ( ~ ( subset @ SV54 @ SV23 @ mactual ) )
= $false )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(375,plain,
! [SV54: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV54 @ mactual ) )
= $true )
| ( ( ~ ( subset @ SV54 @ SV23 @ mactual ) )
= $true )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(376,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
= $false )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(377,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV79 @ mactual )
| ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
= $true )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(378,plain,
! [SV56: $i,SV25: $i,SV80: $i] :
( ( ( equal_set @ SV80 @ SV25 @ mactual )
= $false )
| ( ( qmltpeq @ SV25 @ SV56 @ mactual )
= $false )
| ( ( equal_set @ SV80 @ SV56 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(379,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ( qmltpeq @ SV26 @ SV57 @ mactual )
= $true )
| ( ( qmltpeq @ SV26 @ SV81 @ mactual )
= $true )
| ( ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(380,plain,
! [SV81: $i,SV57: $i,SV26: $i] :
( ( ( qmltpeq @ SV26 @ SV57 @ mactual )
= $false )
| ( ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(381,plain,
! [SV57: $i,SV81: $i,SV26: $i] :
( ( ( qmltpeq @ SV26 @ SV81 @ mactual )
= $false )
| ( ( member @ SV26 @ ( unordered_pair @ SV57 @ SV81 ) @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(382,plain,
! [SV61: $i,SV84: $i,SV30: $i] :
( ( ( equal_set @ SV30 @ SV84 @ mactual )
= $false )
| ( ( qmltpeq @ SV30 @ SV61 @ mactual )
= $false )
| ( ( equal_set @ SV61 @ SV84 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(383,plain,
! [SV62: $i,SV31: $i,SV87: $i] :
( ( ( ~ ( member @ SV87 @ SV31 @ mactual ) )
= $true )
| ( ( member @ SV87 @ SV62 @ mactual )
= $true )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(384,plain,
! [SV31: $i,SV62: $i] :
( ( ( ~ ( member @ ( sK3_SY81 @ SV62 @ SV31 ) @ SV31 @ mactual ) )
= $false )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(385,plain,
! [SV31: $i,SV62: $i] :
( ( ( member @ ( sK3_SY81 @ SV62 @ SV31 ) @ SV62 @ mactual )
= $false )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(386,plain,
! [SV9: $i,SV41: $i,SV86: $i] :
( ( ( member @ SV86 @ SV41 @ mactual )
= $false )
| ( ( member @ SV9 @ SV86 @ mactual )
= $true )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(387,plain,
! [SV41: $i,SV9: $i] :
( ( ( member @ ( sK2_SY62 @ SV9 @ SV41 ) @ SV41 @ mactual )
= $true )
| ( ( member @ SV9 @ ( product @ SV41 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(388,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ SV44 @ mactual ) )
= $false )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(389,plain,
! [SV44: $i,SV72: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ SV72 @ mactual ) )
= $false )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(390,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( ~ ( member @ SV12 @ SV44 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV12 @ SV72 @ mactual ) )
= $true )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(391,plain,
! [SV46: $i,SV14: $i] :
( ( ( ~ ( ~ ( member @ ( sK4_SY67 @ SV14 @ SV46 ) @ SV46 @ mactual )
| ~ ( member @ SV14 @ ( sK4_SY67 @ SV14 @ SV46 ) @ mactual ) ) )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(392,plain,
! [SV14: $i,SV46: $i,SV88: $i] :
( ( ( ~ ( ~ ( member @ SV88 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SV88 @ mactual ) ) )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(393,plain,
! [SV54: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV54 @ mactual )
= $true )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(394,plain,
! [SV23: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV23 @ mactual )
= $true )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(395,plain,
! [SV54: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV54 @ mactual )
= $false )
| ( ( ~ ( subset @ SV54 @ SV23 @ mactual ) )
= $true )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(396,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV79 @ mactual ) )
= $false )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(397,plain,
! [SV79: $i,SV55: $i,SV24: $i] :
( ( ( ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
= $false )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(398,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV79 @ mactual ) )
= $true )
| ( ( ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
= $true )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(399,plain,
! [SV62: $i,SV31: $i,SV87: $i] :
( ( ( member @ SV87 @ SV31 @ mactual )
= $false )
| ( ( member @ SV87 @ SV62 @ mactual )
= $true )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(400,plain,
! [SV31: $i,SV62: $i] :
( ( ( member @ ( sK3_SY81 @ SV62 @ SV31 ) @ SV31 @ mactual )
= $true )
| ( ( subset @ SV31 @ SV62 @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(401,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( member @ SV12 @ SV44 @ mactual )
= $true )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(402,plain,
! [SV44: $i,SV72: $i,SV12: $i] :
( ( ( member @ SV12 @ SV72 @ mactual )
= $true )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(403,plain,
! [SV72: $i,SV44: $i,SV12: $i] :
( ( ( member @ SV12 @ SV44 @ mactual )
= $false )
| ( ( ~ ( member @ SV12 @ SV72 @ mactual ) )
= $true )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(404,plain,
! [SV46: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK4_SY67 @ SV14 @ SV46 ) @ SV46 @ mactual )
| ~ ( member @ SV14 @ ( sK4_SY67 @ SV14 @ SV46 ) @ mactual ) )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(405,plain,
! [SV14: $i,SV46: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ SV46 @ mactual )
| ~ ( member @ SV14 @ SV88 @ mactual ) )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(406,plain,
! [SV23: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV23 @ mactual )
= $false )
| ( ( subset @ SV23 @ SV54 @ mactual )
= $false )
| ( ( equal_set @ SV23 @ SV54 @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(407,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( member @ SV24 @ SV79 @ mactual )
= $true )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(408,plain,
! [SV79: $i,SV55: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV55 @ mactual ) )
= $true )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(409,plain,
! [SV55: $i,SV79: $i,SV24: $i] :
( ( ( member @ SV24 @ SV79 @ mactual )
= $false )
| ( ( ~ ~ ( member @ SV24 @ SV55 @ mactual ) )
= $true )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(410,plain,
! [SV44: $i,SV72: $i,SV12: $i] :
( ( ( member @ SV12 @ SV72 @ mactual )
= $false )
| ( ( member @ SV12 @ SV44 @ mactual )
= $false )
| ( ( member @ SV12 @ ( intersection @ SV44 @ SV72 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(411,plain,
! [SV46: $i,SV14: $i] :
( ( ( ~ ( member @ ( sK4_SY67 @ SV14 @ SV46 ) @ SV46 @ mactual ) )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(412,plain,
! [SV46: $i,SV14: $i] :
( ( ( ~ ( member @ SV14 @ ( sK4_SY67 @ SV14 @ SV46 ) @ mactual ) )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(413,plain,
! [SV14: $i,SV46: $i,SV88: $i] :
( ( ( ~ ( member @ SV88 @ SV46 @ mactual ) )
= $true )
| ( ( ~ ( member @ SV14 @ SV88 @ mactual ) )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(414,plain,
! [SV79: $i,SV55: $i,SV24: $i] :
( ( ( member @ SV24 @ SV55 @ mactual )
= $false )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(415,plain,
! [SV79: $i,SV55: $i,SV24: $i] :
( ( ( ~ ( member @ SV24 @ SV55 @ mactual ) )
= $false )
| ( ( member @ SV24 @ SV79 @ mactual )
= $false )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(416,plain,
! [SV46: $i,SV14: $i] :
( ( ( member @ ( sK4_SY67 @ SV14 @ SV46 ) @ SV46 @ mactual )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(417,plain,
! [SV46: $i,SV14: $i] :
( ( ( member @ SV14 @ ( sK4_SY67 @ SV14 @ SV46 ) @ mactual )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(418,plain,
! [SV14: $i,SV46: $i,SV88: $i] :
( ( ( member @ SV88 @ SV46 @ mactual )
= $false )
| ( ( ~ ( member @ SV14 @ SV88 @ mactual ) )
= $true )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(419,plain,
! [SV79: $i,SV55: $i,SV24: $i] :
( ( ( member @ SV24 @ SV55 @ mactual )
= $true )
| ( ( member @ SV24 @ SV79 @ mactual )
= $false )
| ( ( member @ SV24 @ ( difference @ SV79 @ SV55 ) @ mactual )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(420,plain,
! [SV46: $i,SV88: $i,SV14: $i] :
( ( ( member @ SV14 @ SV88 @ mactual )
= $false )
| ( ( member @ SV88 @ SV46 @ mactual )
= $false )
| ( ( member @ SV14 @ ( sum @ SV46 ) @ mactual )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(421,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[107,420,419,417,416,414,410,407,406,402,401,400,399,394,393,387,386,385,382,381,380,379,378,372,371,370,369,364,361,360,359,358,331,330,312,311,307,278,272,271,263,256,253,252,247,242,241,227,221,210,161,151,113]) ).
thf(422,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET063^4 : TPTP v8.1.0. Released v8.1.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 04:55:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.38
% 0.19/0.38 No.of.Axioms: 34
% 0.19/0.38
% 0.19/0.38 Length.of.Defs: 1574
% 0.19/0.38
% 0.19/0.38 Contains.Choice.Funs: false
% 0.19/0.42 (rf:0,axioms:34,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:36,loop_count:0,foatp_calls:0,translation:fof_full)....................
% 0.40/0.75
% 0.40/0.75 ********************************
% 0.40/0.75 * All subproblems solved! *
% 0.40/0.75 ********************************
% 0.40/0.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:34,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:421,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.59/0.82
% 0.59/0.82 %**** Beginning of derivation protocol ****
% 0.59/0.82 % SZS output start CNFRefutation
% See solution above
% 0.59/0.82
% 0.59/0.82 %**** End of derivation protocol ****
% 0.59/0.82 %**** no. of clauses in derivation: 422 ****
% 0.59/0.82 %**** clause counter: 421 ****
% 0.59/0.82
% 0.59/0.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:34,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:421,loop_count:0,foatp_calls:1,translation:fof_full)
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