TSTP Solution File: SET062^7 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET062^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n014.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 02:58:57 EDT 2022
% Result : Theorem 0.59s 0.83s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 132
% Syntax : Number of formulae : 777 ( 228 unt; 54 typ; 32 def)
% Number of atoms : 7631 (1899 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 15427 (2369 ~;2691 |; 9 &;10348 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 211 ( 211 >; 0 *; 0 +; 0 <<)
% Number of symbols : 56 ( 53 usr; 5 con; 0-3 aty)
% Number of variables : 2475 ( 221 ^2247 !; 7 ?;2475 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_difference,type,
difference: mu > mu > mu ).
thf(tp_empty_set,type,
empty_set: mu ).
thf(tp_equal_set,type,
equal_set: mu > mu > $i > $o ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_intersection,type,
intersection: mu > mu > mu ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia_s4,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(tp_member,type,
member: mu > mu > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_power_set,type,
power_set: mu > mu ).
thf(tp_product,type,
product: mu > mu ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i > mu ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY154,type,
sK3_SY154: mu ).
thf(tp_sK4_SY169,type,
sK4_SY169: mu > mu > $i > mu ).
thf(tp_sK5_SY176,type,
sK5_SY176: mu > mu > $i > mu ).
thf(tp_sK6_SY179,type,
sK6_SY179: mu > mu > $i > mu ).
thf(tp_singleton,type,
singleton: mu > mu ).
thf(tp_subset,type,
subset: mu > mu > $i > $o ).
thf(tp_sum,type,
sum: mu > mu ).
thf(tp_union,type,
union: mu > mu > mu ).
thf(tp_unordered_pair,type,
unordered_pair: mu > mu > mu ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mequiv @ ( member @ X @ ( product @ A ) )
@ ( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
thf(2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mequiv @ ( member @ X @ ( sum @ A ) )
@ ( mexists_ind
@ ^ [Y: mu] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
thf(4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(5,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [E: mu] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
thf(6,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( member @ X @ empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(8,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
thf(10,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
thf(11,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(13,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(14,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(15,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(16,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_2) ).
thf(17,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_1) ).
thf(18,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(19,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(20,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(21,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(22,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution_1) ).
thf(23,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(24,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution_1) ).
thf(25,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set_substitution_1) ).
thf(26,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_2) ).
thf(27,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_1) ).
thf(28,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_2) ).
thf(29,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_1) ).
thf(30,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(31,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(32,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(33,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(34,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( product @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_product_ax) ).
thf(35,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( sum @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_sum_ax) ).
thf(36,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_unordered_pair_ax) ).
thf(37,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_singleton_ax) ).
thf(38,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( difference @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_difference_ax) ).
thf(39,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_union_ax) ).
thf(40,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( intersection @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_intersection_ax) ).
thf(41,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( power_set @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_power_set_ax) ).
thf(42,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax) ).
thf(43,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(44,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(45,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(46,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( subset @ empty_set @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI15) ).
thf(47,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( subset @ empty_set @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[46]) ).
thf(48,plain,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( subset @ empty_set @ A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(50,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(51,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(52,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(55,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( power_set @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( intersection @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( union @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( difference @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(60,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( unordered_pair @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(61,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( sum @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(62,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( product @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(63,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(64,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(65,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(66,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(67,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(68,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(69,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(70,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(71,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(72,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(73,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(74,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(75,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(76,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(77,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(78,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(79,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(80,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(81,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(82,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(83,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(84,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(85,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(86,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(87,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(88,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(89,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(90,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( member @ X @ empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(91,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [E: mu] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(92,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(93,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(94,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mequiv @ ( member @ X @ ( sum @ A ) )
@ ( mexists_ind
@ ^ [Y: mu] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(95,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] :
( mequiv @ ( member @ X @ ( product @ A ) )
@ ( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(96,plain,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( subset @ empty_set @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( equal_set @ SX1 @ SX2 @ SX0 )
| ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 @ SX0 ) )
| ( equal_set @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( intersection @ SX2 @ SX3 ) @ SX0 )
| ~ ( ~ ( member @ SX1 @ SX2 @ SX0 )
| ~ ( member @ SX1 @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX1 @ SX2 @ SX0 )
| ~ ( member @ SX1 @ SX3 @ SX0 ) )
| ( member @ SX1 @ ( intersection @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX1 @ SX3 @ SX0 ) )
| ( subset @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX2 @ SX3 @ SX0 ) )
| ( qmltpeq @ SX1 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( singleton @ SX2 ) @ SX0 )
| ( qmltpeq @ SX1 @ SX2 @ SX0 ) )
| ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( member @ SX1 @ ( singleton @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( product @ SX2 ) @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX2 @ SX0 )
| ( member @ SX1 @ SX3 @ SX0 ) ) )
| ~ ( ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX2 @ SX0 )
| ( member @ SX1 @ SX3 @ SX0 ) )
| ( member @ SX1 @ ( product @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( unordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ SX1 @ SX3 @ SX0 ) )
| ~ ( ~ ( ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ SX1 @ SX3 @ SX0 ) )
| ( member @ SX1 @ ( unordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( product @ SX1 ) @ ( product @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( difference @ SX3 @ SX2 ) @ SX0 )
| ~ ( ~ ( member @ SX1 @ SX3 @ SX0 )
| ~ ~ ( member @ SX1 @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX1 @ SX3 @ SX0 )
| ~ ~ ( member @ SX1 @ SX2 @ SX0 ) )
| ( member @ SX1 @ ( difference @ SX3 @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( singleton @ SX1 ) @ ( singleton @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( rel_s4 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( power_set @ SX1 ) @ ( power_set @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( union @ SX1 @ SX3 ) @ ( union @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( sum @ SX1 ) @ ( sum @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX3 @ SX1 @ SX0 ) )
| ( subset @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( power_set @ SX2 ) @ SX0 )
| ( subset @ SX1 @ SX2 @ SX0 ) )
| ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ( member @ SX1 @ ( power_set @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( difference @ SX1 @ SX3 ) @ ( difference @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ( member @ SX1 @ empty_set @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( subset @ SX1 @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 )
| ( member @ SX3 @ SX2 @ SX0 ) )
| ( subset @ SX1 @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( difference @ SX3 @ SX1 ) @ ( difference @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( union @ SX3 @ SX1 ) @ ( union @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( sum @ SX2 ) @ SX0 )
| ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( member @ SX3 @ SX2 @ SX0 )
| ~ ( member @ SX1 @ SX3 @ SX0 ) ) ) )
| ~ ( ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( member @ SX3 @ SX2 @ SX0 )
| ~ ( member @ SX1 @ SX3 @ SX0 ) ) )
| ( member @ SX1 @ ( sum @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( intersection @ SX3 @ SX1 ) @ ( intersection @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( unordered_pair @ SX1 @ SX3 ) @ ( unordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(123,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( member @ SX1 @ SX3 @ SX0 ) )
| ( member @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( unordered_pair @ SX3 @ SX1 ) @ ( unordered_pair @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(125,plain,
( ( ~ ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( subset @ empty_set @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( intersection @ SX1 @ SX3 ) @ ( intersection @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( equal_set @ SX1 @ SX3 @ SX0 ) )
| ( equal_set @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( ~ ( ~ ( member @ SX1 @ ( union @ SX2 @ SX3 ) @ SX0 )
| ( member @ SX1 @ SX2 @ SX0 )
| ( member @ SX1 @ SX3 @ SX0 ) )
| ~ ( ~ ( ( member @ SX1 @ SX2 @ SX0 )
| ( member @ SX1 @ SX3 @ SX0 ) )
| ( member @ SX1 @ ( union @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( member @ SX3 @ SX1 @ SX0 ) )
| ( member @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(130,plain,
( ( ! [SX0: $i] : ( rel_s4 @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[52,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( equal_set @ SX3 @ SX1 @ SX0 ) )
| ( equal_set @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(132,plain,
! [SV1: $i] :
( ( exists_in_world @ ( sK1_X @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(133,plain,
! [SV2: mu] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ( exists_in_world @ SV2 @ SY0 )
| ~ ( rel_s4 @ SY0 @ SY1 )
| ( exists_in_world @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(134,plain,
! [SV3: $i] :
( ( ! [SY2: mu] : ( exists_in_world @ ( power_set @ SY2 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(135,plain,
! [SV4: $i] :
( ( ! [SY3: mu,SY4: mu] : ( exists_in_world @ ( intersection @ SY3 @ SY4 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(136,plain,
! [SV5: $i] :
( ( ! [SY5: mu,SY6: mu] : ( exists_in_world @ ( union @ SY5 @ SY6 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(137,plain,
! [SV6: $i] :
( ( ! [SY7: mu,SY8: mu] : ( exists_in_world @ ( difference @ SY7 @ SY8 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(138,plain,
! [SV7: $i] :
( ( ! [SY9: mu] : ( exists_in_world @ ( singleton @ SY9 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(139,plain,
! [SV8: $i] :
( ( ! [SY10: mu,SY11: mu] : ( exists_in_world @ ( unordered_pair @ SY10 @ SY11 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(140,plain,
! [SV9: $i] :
( ( ! [SY12: mu] : ( exists_in_world @ ( sum @ SY12 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(141,plain,
! [SV10: $i] :
( ( ! [SY13: mu] : ( exists_in_world @ ( product @ SY13 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(142,plain,
! [SV11: $i] :
( ( exists_in_world @ empty_set @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(143,plain,
! [SV12: $i] :
( ( ! [SY14: mu] :
( ~ ( exists_in_world @ SY14 @ SV12 )
| ! [SY15: mu] :
( ~ ( exists_in_world @ SY15 @ SV12 )
| ~ ( ~ ( ~ ( equal_set @ SY14 @ SY15 @ SV12 )
| ~ ( ~ ( subset @ SY14 @ SY15 @ SV12 )
| ~ ( subset @ SY15 @ SY14 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY14 @ SY15 @ SV12 )
| ~ ( subset @ SY15 @ SY14 @ SV12 ) )
| ( equal_set @ SY14 @ SY15 @ SV12 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(144,plain,
! [SV13: $i] :
( ( ! [SY16: mu] :
( ~ ( exists_in_world @ SY16 @ SV13 )
| ! [SY17: mu] :
( ~ ( exists_in_world @ SY17 @ SV13 )
| ! [SY18: mu] :
( ~ ( exists_in_world @ SY18 @ SV13 )
| ~ ( ~ ( ~ ( member @ SY16 @ ( intersection @ SY17 @ SY18 ) @ SV13 )
| ~ ( ~ ( member @ SY16 @ SY17 @ SV13 )
| ~ ( member @ SY16 @ SY18 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY16 @ SY17 @ SV13 )
| ~ ( member @ SY16 @ SY18 @ SV13 ) )
| ( member @ SY16 @ ( intersection @ SY17 @ SY18 ) @ SV13 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(145,plain,
! [SV14: $i] :
( ( ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV14 )
| ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV14 )
| ! [SY21: mu] :
( ~ ( exists_in_world @ SY21 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SY19 @ SY20 @ SV14 )
| ~ ( subset @ SY19 @ SY21 @ SV14 ) )
| ( subset @ SY20 @ SY21 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(146,plain,
! [SV15: $i] :
( ( ! [SY22: mu] :
( ~ ( exists_in_world @ SY22 @ SV15 )
| ! [SY23: mu] :
( ~ ( exists_in_world @ SY23 @ SV15 )
| ! [SY24: mu] :
( ~ ( exists_in_world @ SY24 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SY22 @ SY23 @ SV15 )
| ~ ( qmltpeq @ SY23 @ SY24 @ SV15 ) )
| ( qmltpeq @ SY22 @ SY24 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(147,plain,
! [SV16: $i] :
( ( ! [SY25: mu] :
( ~ ( exists_in_world @ SY25 @ SV16 )
| ! [SY26: mu] :
( ~ ( exists_in_world @ SY26 @ SV16 )
| ~ ( ~ ( ~ ( member @ SY25 @ ( singleton @ SY26 ) @ SV16 )
| ( qmltpeq @ SY25 @ SY26 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SY25 @ SY26 @ SV16 )
| ( member @ SY25 @ ( singleton @ SY26 ) @ SV16 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(148,plain,
! [SV17: $i] :
( ( ! [SY27: mu] :
( ~ ( exists_in_world @ SY27 @ SV17 )
| ! [SY28: mu] :
( ~ ( exists_in_world @ SY28 @ SV17 )
| ~ ( ~ ( ~ ( member @ SY27 @ ( product @ SY28 ) @ SV17 )
| ! [SY29: mu] :
( ~ ( exists_in_world @ SY29 @ SV17 )
| ~ ( member @ SY29 @ SY28 @ SV17 )
| ( member @ SY27 @ SY29 @ SV17 ) ) )
| ~ ( ~ ! [SY30: mu] :
( ~ ( exists_in_world @ SY30 @ SV17 )
| ~ ( member @ SY30 @ SY28 @ SV17 )
| ( member @ SY27 @ SY30 @ SV17 ) )
| ( member @ SY27 @ ( product @ SY28 ) @ SV17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(149,plain,
! [SV18: $i] :
( ( ! [SY31: mu] :
( ~ ( exists_in_world @ SY31 @ SV18 )
| ! [SY32: mu] :
( ~ ( exists_in_world @ SY32 @ SV18 )
| ! [SY33: mu] :
( ~ ( exists_in_world @ SY33 @ SV18 )
| ~ ( ~ ( ~ ( member @ SY31 @ ( unordered_pair @ SY32 @ SY33 ) @ SV18 )
| ( qmltpeq @ SY31 @ SY32 @ SV18 )
| ( qmltpeq @ SY31 @ SY33 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SY31 @ SY32 @ SV18 )
| ( qmltpeq @ SY31 @ SY33 @ SV18 ) )
| ( member @ SY31 @ ( unordered_pair @ SY32 @ SY33 ) @ SV18 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(150,plain,
! [SV19: $i] :
( ( ! [SY34: mu] :
( ~ ( exists_in_world @ SY34 @ SV19 )
| ( qmltpeq @ SY34 @ SY34 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(151,plain,
! [SV20: $i] :
( ( ! [SY35: mu] :
( ~ ( exists_in_world @ SY35 @ SV20 )
| ! [SY36: mu] :
( ~ ( exists_in_world @ SY36 @ SV20 )
| ~ ( qmltpeq @ SY35 @ SY36 @ SV20 )
| ( qmltpeq @ ( product @ SY35 ) @ ( product @ SY36 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(152,plain,
! [SV21: $i] :
( ( ! [SY37: mu] :
( ~ ( exists_in_world @ SY37 @ SV21 )
| ! [SY38: mu] :
( ~ ( exists_in_world @ SY38 @ SV21 )
| ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV21 )
| ~ ( ~ ( ~ ( member @ SY37 @ ( difference @ SY39 @ SY38 ) @ SV21 )
| ~ ( ~ ( member @ SY37 @ SY39 @ SV21 )
| ~ ~ ( member @ SY37 @ SY38 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SY37 @ SY39 @ SV21 )
| ~ ~ ( member @ SY37 @ SY38 @ SV21 ) )
| ( member @ SY37 @ ( difference @ SY39 @ SY38 ) @ SV21 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(153,plain,
! [SV22: $i] :
( ( ! [SY40: mu] :
( ~ ( exists_in_world @ SY40 @ SV22 )
| ! [SY41: mu] :
( ~ ( exists_in_world @ SY41 @ SV22 )
| ~ ( qmltpeq @ SY40 @ SY41 @ SV22 )
| ( qmltpeq @ ( singleton @ SY40 ) @ ( singleton @ SY41 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(154,plain,
! [SV23: $i] :
( ( ! [SY42: mu] :
( ~ ( exists_in_world @ SY42 @ SV23 )
| ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV23 )
| ~ ( qmltpeq @ SY42 @ SY43 @ SV23 )
| ( qmltpeq @ SY43 @ SY42 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(155,plain,
! [SV24: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV24 @ SY44 )
| ~ ( rel_s4 @ SY44 @ SY45 ) )
| ( rel_s4 @ SV24 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(156,plain,
! [SV25: $i] :
( ( ! [SY46: mu] :
( ~ ( exists_in_world @ SY46 @ SV25 )
| ! [SY47: mu] :
( ~ ( exists_in_world @ SY47 @ SV25 )
| ~ ( qmltpeq @ SY46 @ SY47 @ SV25 )
| ( qmltpeq @ ( power_set @ SY46 ) @ ( power_set @ SY47 ) @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(157,plain,
! [SV26: $i] :
( ( ! [SY48: mu] :
( ~ ( exists_in_world @ SY48 @ SV26 )
| ! [SY49: mu] :
( ~ ( exists_in_world @ SY49 @ SV26 )
| ! [SY50: mu] :
( ~ ( exists_in_world @ SY50 @ SV26 )
| ~ ( qmltpeq @ SY48 @ SY49 @ SV26 )
| ( qmltpeq @ ( union @ SY48 @ SY50 ) @ ( union @ SY49 @ SY50 ) @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(158,plain,
! [SV27: $i] :
( ( ! [SY51: mu] :
( ~ ( exists_in_world @ SY51 @ SV27 )
| ! [SY52: mu] :
( ~ ( exists_in_world @ SY52 @ SV27 )
| ~ ( qmltpeq @ SY51 @ SY52 @ SV27 )
| ( qmltpeq @ ( sum @ SY51 ) @ ( sum @ SY52 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(159,plain,
! [SV28: $i] :
( ( ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV28 )
| ! [SY54: mu] :
( ~ ( exists_in_world @ SY54 @ SV28 )
| ! [SY55: mu] :
( ~ ( exists_in_world @ SY55 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SY53 @ SY54 @ SV28 )
| ~ ( subset @ SY55 @ SY53 @ SV28 ) )
| ( subset @ SY55 @ SY54 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(160,plain,
! [SV29: $i] :
( ( ! [SY56: mu] :
( ~ ( exists_in_world @ SY56 @ SV29 )
| ! [SY57: mu] :
( ~ ( exists_in_world @ SY57 @ SV29 )
| ~ ( ~ ( ~ ( member @ SY56 @ ( power_set @ SY57 ) @ SV29 )
| ( subset @ SY56 @ SY57 @ SV29 ) )
| ~ ( ~ ( subset @ SY56 @ SY57 @ SV29 )
| ( member @ SY56 @ ( power_set @ SY57 ) @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(161,plain,
! [SV30: $i] :
( ( ! [SY58: mu] :
( ~ ( exists_in_world @ SY58 @ SV30 )
| ! [SY59: mu] :
( ~ ( exists_in_world @ SY59 @ SV30 )
| ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ SV30 )
| ~ ( qmltpeq @ SY58 @ SY59 @ SV30 )
| ( qmltpeq @ ( difference @ SY58 @ SY60 ) @ ( difference @ SY59 @ SY60 ) @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(162,plain,
! [SV31: $i] :
( ( ! [SY61: mu] :
( ~ ( exists_in_world @ SY61 @ SV31 )
| ~ ( member @ SY61 @ empty_set @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(163,plain,
! [SV32: $i] :
( ( ! [SY62: mu] :
( ~ ( exists_in_world @ SY62 @ SV32 )
| ! [SY63: mu] :
( ~ ( exists_in_world @ SY63 @ SV32 )
| ~ ( ~ ( ~ ( subset @ SY62 @ SY63 @ SV32 )
| ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ SV32 )
| ~ ( member @ SY64 @ SY62 @ SV32 )
| ( member @ SY64 @ SY63 @ SV32 ) ) )
| ~ ( ~ ! [SY65: mu] :
( ~ ( exists_in_world @ SY65 @ SV32 )
| ~ ( member @ SY65 @ SY62 @ SV32 )
| ( member @ SY65 @ SY63 @ SV32 ) )
| ( subset @ SY62 @ SY63 @ SV32 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(164,plain,
! [SV33: $i] :
( ( ! [SY66: mu] :
( ~ ( exists_in_world @ SY66 @ SV33 )
| ! [SY67: mu] :
( ~ ( exists_in_world @ SY67 @ SV33 )
| ! [SY68: mu] :
( ~ ( exists_in_world @ SY68 @ SV33 )
| ~ ( qmltpeq @ SY66 @ SY67 @ SV33 )
| ( qmltpeq @ ( difference @ SY68 @ SY66 ) @ ( difference @ SY68 @ SY67 ) @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(165,plain,
! [SV34: $i] :
( ( ! [SY69: mu] :
( ~ ( exists_in_world @ SY69 @ SV34 )
| ! [SY70: mu] :
( ~ ( exists_in_world @ SY70 @ SV34 )
| ! [SY71: mu] :
( ~ ( exists_in_world @ SY71 @ SV34 )
| ~ ( qmltpeq @ SY69 @ SY70 @ SV34 )
| ( qmltpeq @ ( union @ SY71 @ SY69 ) @ ( union @ SY71 @ SY70 ) @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(166,plain,
! [SV35: $i] :
( ( ! [SY72: mu] :
( ~ ( exists_in_world @ SY72 @ SV35 )
| ! [SY73: mu] :
( ~ ( exists_in_world @ SY73 @ SV35 )
| ~ ( ~ ( ~ ( member @ SY72 @ ( sum @ SY73 ) @ SV35 )
| ~ ! [SY74: mu] :
( ~ ( exists_in_world @ SY74 @ SV35 )
| ~ ~ ( ~ ( member @ SY74 @ SY73 @ SV35 )
| ~ ( member @ SY72 @ SY74 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY75: mu] :
( ~ ( exists_in_world @ SY75 @ SV35 )
| ~ ~ ( ~ ( member @ SY75 @ SY73 @ SV35 )
| ~ ( member @ SY72 @ SY75 @ SV35 ) ) )
| ( member @ SY72 @ ( sum @ SY73 ) @ SV35 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(167,plain,
! [SV36: $i] :
( ( ! [SY76: mu] :
( ~ ( exists_in_world @ SY76 @ SV36 )
| ! [SY77: mu] :
( ~ ( exists_in_world @ SY77 @ SV36 )
| ! [SY78: mu] :
( ~ ( exists_in_world @ SY78 @ SV36 )
| ~ ( qmltpeq @ SY76 @ SY77 @ SV36 )
| ( qmltpeq @ ( intersection @ SY78 @ SY76 ) @ ( intersection @ SY78 @ SY77 ) @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(168,plain,
! [SV37: $i] :
( ( ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ SV37 )
| ! [SY80: mu] :
( ~ ( exists_in_world @ SY80 @ SV37 )
| ! [SY81: mu] :
( ~ ( exists_in_world @ SY81 @ SV37 )
| ~ ( qmltpeq @ SY79 @ SY80 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SY79 @ SY81 ) @ ( unordered_pair @ SY80 @ SY81 ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(169,plain,
! [SV38: $i] :
( ( ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SV38 )
| ! [SY83: mu] :
( ~ ( exists_in_world @ SY83 @ SV38 )
| ! [SY84: mu] :
( ~ ( exists_in_world @ SY84 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SY82 @ SY83 @ SV38 )
| ~ ( member @ SY82 @ SY84 @ SV38 ) )
| ( member @ SY83 @ SY84 @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(170,plain,
! [SV39: $i] :
( ( ! [SY85: mu] :
( ~ ( exists_in_world @ SY85 @ SV39 )
| ! [SY86: mu] :
( ~ ( exists_in_world @ SY86 @ SV39 )
| ! [SY87: mu] :
( ~ ( exists_in_world @ SY87 @ SV39 )
| ~ ( qmltpeq @ SY85 @ SY86 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SY87 @ SY85 ) @ ( unordered_pair @ SY87 @ SY86 ) @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( subset @ empty_set @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(172,plain,
! [SV40: $i] :
( ( ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ SV40 )
| ! [SY89: mu] :
( ~ ( exists_in_world @ SY89 @ SV40 )
| ! [SY90: mu] :
( ~ ( exists_in_world @ SY90 @ SV40 )
| ~ ( qmltpeq @ SY88 @ SY89 @ SV40 )
| ( qmltpeq @ ( intersection @ SY88 @ SY90 ) @ ( intersection @ SY89 @ SY90 ) @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(173,plain,
! [SV41: $i] :
( ( ! [SY91: mu] :
( ~ ( exists_in_world @ SY91 @ SV41 )
| ! [SY92: mu] :
( ~ ( exists_in_world @ SY92 @ SV41 )
| ! [SY93: mu] :
( ~ ( exists_in_world @ SY93 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SY91 @ SY92 @ SV41 )
| ~ ( equal_set @ SY91 @ SY93 @ SV41 ) )
| ( equal_set @ SY92 @ SY93 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(174,plain,
! [SV42: $i] :
( ( ! [SY94: mu] :
( ~ ( exists_in_world @ SY94 @ SV42 )
| ! [SY95: mu] :
( ~ ( exists_in_world @ SY95 @ SV42 )
| ! [SY96: mu] :
( ~ ( exists_in_world @ SY96 @ SV42 )
| ~ ( ~ ( ~ ( member @ SY94 @ ( union @ SY95 @ SY96 ) @ SV42 )
| ( member @ SY94 @ SY95 @ SV42 )
| ( member @ SY94 @ SY96 @ SV42 ) )
| ~ ( ~ ( ( member @ SY94 @ SY95 @ SV42 )
| ( member @ SY94 @ SY96 @ SV42 ) )
| ( member @ SY94 @ ( union @ SY95 @ SY96 ) @ SV42 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(175,plain,
! [SV43: $i] :
( ( ! [SY97: mu] :
( ~ ( exists_in_world @ SY97 @ SV43 )
| ! [SY98: mu] :
( ~ ( exists_in_world @ SY98 @ SV43 )
| ! [SY99: mu] :
( ~ ( exists_in_world @ SY99 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SY97 @ SY98 @ SV43 )
| ~ ( member @ SY99 @ SY97 @ SV43 ) )
| ( member @ SY99 @ SY98 @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(176,plain,
! [SV44: $i] :
( ( rel_s4 @ SV44 @ SV44 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(177,plain,
! [SV45: $i] :
( ( ! [SY100: mu] :
( ~ ( exists_in_world @ SY100 @ SV45 )
| ! [SY101: mu] :
( ~ ( exists_in_world @ SY101 @ SV45 )
| ! [SY102: mu] :
( ~ ( exists_in_world @ SY102 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SY100 @ SY101 @ SV45 )
| ~ ( equal_set @ SY102 @ SY100 @ SV45 ) )
| ( equal_set @ SY102 @ SY101 @ SV45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(178,plain,
! [SV46: $i,SV2: mu] :
( ( ! [SY103: $i] :
( ~ ( exists_in_world @ SV2 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SY103 )
| ( exists_in_world @ SV2 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(179,plain,
! [SV3: $i,SV47: mu] :
( ( exists_in_world @ ( power_set @ SV47 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(180,plain,
! [SV4: $i,SV48: mu] :
( ( ! [SY104: mu] : ( exists_in_world @ ( intersection @ SV48 @ SY104 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(181,plain,
! [SV5: $i,SV49: mu] :
( ( ! [SY105: mu] : ( exists_in_world @ ( union @ SV49 @ SY105 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(182,plain,
! [SV6: $i,SV50: mu] :
( ( ! [SY106: mu] : ( exists_in_world @ ( difference @ SV50 @ SY106 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(183,plain,
! [SV7: $i,SV51: mu] :
( ( exists_in_world @ ( singleton @ SV51 ) @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(184,plain,
! [SV8: $i,SV52: mu] :
( ( ! [SY107: mu] : ( exists_in_world @ ( unordered_pair @ SV52 @ SY107 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(185,plain,
! [SV9: $i,SV53: mu] :
( ( exists_in_world @ ( sum @ SV53 ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(186,plain,
! [SV10: $i,SV54: mu] :
( ( exists_in_world @ ( product @ SV54 ) @ SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(187,plain,
! [SV12: $i,SV55: mu] :
( ( ~ ( exists_in_world @ SV55 @ SV12 )
| ! [SY108: mu] :
( ~ ( exists_in_world @ SY108 @ SV12 )
| ~ ( ~ ( ~ ( equal_set @ SV55 @ SY108 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SY108 @ SV12 )
| ~ ( subset @ SY108 @ SV55 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV55 @ SY108 @ SV12 )
| ~ ( subset @ SY108 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SY108 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(188,plain,
! [SV13: $i,SV56: mu] :
( ( ~ ( exists_in_world @ SV56 @ SV13 )
| ! [SY109: mu] :
( ~ ( exists_in_world @ SY109 @ SV13 )
| ! [SY110: mu] :
( ~ ( exists_in_world @ SY110 @ SV13 )
| ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SY109 @ SY110 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SY109 @ SV13 )
| ~ ( member @ SV56 @ SY110 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SY109 @ SV13 )
| ~ ( member @ SV56 @ SY110 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SY109 @ SY110 ) @ SV13 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(189,plain,
! [SV14: $i,SV57: mu] :
( ( ~ ( exists_in_world @ SV57 @ SV14 )
| ! [SY111: mu] :
( ~ ( exists_in_world @ SY111 @ SV14 )
| ! [SY112: mu] :
( ~ ( exists_in_world @ SY112 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV57 @ SY111 @ SV14 )
| ~ ( subset @ SV57 @ SY112 @ SV14 ) )
| ( subset @ SY111 @ SY112 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(190,plain,
! [SV15: $i,SV58: mu] :
( ( ~ ( exists_in_world @ SV58 @ SV15 )
| ! [SY113: mu] :
( ~ ( exists_in_world @ SY113 @ SV15 )
| ! [SY114: mu] :
( ~ ( exists_in_world @ SY114 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV58 @ SY113 @ SV15 )
| ~ ( qmltpeq @ SY113 @ SY114 @ SV15 ) )
| ( qmltpeq @ SV58 @ SY114 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(191,plain,
! [SV16: $i,SV59: mu] :
( ( ~ ( exists_in_world @ SV59 @ SV16 )
| ! [SY115: mu] :
( ~ ( exists_in_world @ SY115 @ SV16 )
| ~ ( ~ ( ~ ( member @ SV59 @ ( singleton @ SY115 ) @ SV16 )
| ( qmltpeq @ SV59 @ SY115 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SV59 @ SY115 @ SV16 )
| ( member @ SV59 @ ( singleton @ SY115 ) @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(192,plain,
! [SV17: $i,SV60: mu] :
( ( ~ ( exists_in_world @ SV60 @ SV17 )
| ! [SY116: mu] :
( ~ ( exists_in_world @ SY116 @ SV17 )
| ~ ( ~ ( ~ ( member @ SV60 @ ( product @ SY116 ) @ SV17 )
| ! [SY117: mu] :
( ~ ( exists_in_world @ SY117 @ SV17 )
| ~ ( member @ SY117 @ SY116 @ SV17 )
| ( member @ SV60 @ SY117 @ SV17 ) ) )
| ~ ( ~ ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ SV17 )
| ~ ( member @ SY118 @ SY116 @ SV17 )
| ( member @ SV60 @ SY118 @ SV17 ) )
| ( member @ SV60 @ ( product @ SY116 ) @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(193,plain,
! [SV18: $i,SV61: mu] :
( ( ~ ( exists_in_world @ SV61 @ SV18 )
| ! [SY119: mu] :
( ~ ( exists_in_world @ SY119 @ SV18 )
| ! [SY120: mu] :
( ~ ( exists_in_world @ SY120 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SY119 @ SY120 ) @ SV18 )
| ( qmltpeq @ SV61 @ SY119 @ SV18 )
| ( qmltpeq @ SV61 @ SY120 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SY119 @ SV18 )
| ( qmltpeq @ SV61 @ SY120 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SY119 @ SY120 ) @ SV18 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(194,plain,
! [SV19: $i,SV62: mu] :
( ( ~ ( exists_in_world @ SV62 @ SV19 )
| ( qmltpeq @ SV62 @ SV62 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(195,plain,
! [SV20: $i,SV63: mu] :
( ( ~ ( exists_in_world @ SV63 @ SV20 )
| ! [SY121: mu] :
( ~ ( exists_in_world @ SY121 @ SV20 )
| ~ ( qmltpeq @ SV63 @ SY121 @ SV20 )
| ( qmltpeq @ ( product @ SV63 ) @ ( product @ SY121 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(196,plain,
! [SV21: $i,SV64: mu] :
( ( ~ ( exists_in_world @ SV64 @ SV21 )
| ! [SY122: mu] :
( ~ ( exists_in_world @ SY122 @ SV21 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV21 )
| ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SY123 @ SY122 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SY123 @ SV21 )
| ~ ~ ( member @ SV64 @ SY122 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SY123 @ SV21 )
| ~ ~ ( member @ SV64 @ SY122 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SY123 @ SY122 ) @ SV21 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(197,plain,
! [SV22: $i,SV65: mu] :
( ( ~ ( exists_in_world @ SV65 @ SV22 )
| ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV22 )
| ~ ( qmltpeq @ SV65 @ SY124 @ SV22 )
| ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SY124 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(198,plain,
! [SV23: $i,SV66: mu] :
( ( ~ ( exists_in_world @ SV66 @ SV23 )
| ! [SY125: mu] :
( ~ ( exists_in_world @ SY125 @ SV23 )
| ~ ( qmltpeq @ SV66 @ SY125 @ SV23 )
| ( qmltpeq @ SY125 @ SV66 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(199,plain,
! [SV67: $i,SV24: $i] :
( ( ! [SY126: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV24 @ SV67 )
| ~ ( rel_s4 @ SV67 @ SY126 ) )
| ( rel_s4 @ SV24 @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(200,plain,
! [SV25: $i,SV68: mu] :
( ( ~ ( exists_in_world @ SV68 @ SV25 )
| ! [SY127: mu] :
( ~ ( exists_in_world @ SY127 @ SV25 )
| ~ ( qmltpeq @ SV68 @ SY127 @ SV25 )
| ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SY127 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(201,plain,
! [SV26: $i,SV69: mu] :
( ( ~ ( exists_in_world @ SV69 @ SV26 )
| ! [SY128: mu] :
( ~ ( exists_in_world @ SY128 @ SV26 )
| ! [SY129: mu] :
( ~ ( exists_in_world @ SY129 @ SV26 )
| ~ ( qmltpeq @ SV69 @ SY128 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SY129 ) @ ( union @ SY128 @ SY129 ) @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(202,plain,
! [SV27: $i,SV70: mu] :
( ( ~ ( exists_in_world @ SV70 @ SV27 )
| ! [SY130: mu] :
( ~ ( exists_in_world @ SY130 @ SV27 )
| ~ ( qmltpeq @ SV70 @ SY130 @ SV27 )
| ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SY130 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(203,plain,
! [SV28: $i,SV71: mu] :
( ( ~ ( exists_in_world @ SV71 @ SV28 )
| ! [SY131: mu] :
( ~ ( exists_in_world @ SY131 @ SV28 )
| ! [SY132: mu] :
( ~ ( exists_in_world @ SY132 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV71 @ SY131 @ SV28 )
| ~ ( subset @ SY132 @ SV71 @ SV28 ) )
| ( subset @ SY132 @ SY131 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(204,plain,
! [SV29: $i,SV72: mu] :
( ( ~ ( exists_in_world @ SV72 @ SV29 )
| ! [SY133: mu] :
( ~ ( exists_in_world @ SY133 @ SV29 )
| ~ ( ~ ( ~ ( member @ SV72 @ ( power_set @ SY133 ) @ SV29 )
| ( subset @ SV72 @ SY133 @ SV29 ) )
| ~ ( ~ ( subset @ SV72 @ SY133 @ SV29 )
| ( member @ SV72 @ ( power_set @ SY133 ) @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(205,plain,
! [SV30: $i,SV73: mu] :
( ( ~ ( exists_in_world @ SV73 @ SV30 )
| ! [SY134: mu] :
( ~ ( exists_in_world @ SY134 @ SV30 )
| ! [SY135: mu] :
( ~ ( exists_in_world @ SY135 @ SV30 )
| ~ ( qmltpeq @ SV73 @ SY134 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SY135 ) @ ( difference @ SY134 @ SY135 ) @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(206,plain,
! [SV31: $i,SV74: mu] :
( ( ~ ( exists_in_world @ SV74 @ SV31 )
| ~ ( member @ SV74 @ empty_set @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(207,plain,
! [SV32: $i,SV75: mu] :
( ( ~ ( exists_in_world @ SV75 @ SV32 )
| ! [SY136: mu] :
( ~ ( exists_in_world @ SY136 @ SV32 )
| ~ ( ~ ( ~ ( subset @ SV75 @ SY136 @ SV32 )
| ! [SY137: mu] :
( ~ ( exists_in_world @ SY137 @ SV32 )
| ~ ( member @ SY137 @ SV75 @ SV32 )
| ( member @ SY137 @ SY136 @ SV32 ) ) )
| ~ ( ~ ! [SY138: mu] :
( ~ ( exists_in_world @ SY138 @ SV32 )
| ~ ( member @ SY138 @ SV75 @ SV32 )
| ( member @ SY138 @ SY136 @ SV32 ) )
| ( subset @ SV75 @ SY136 @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(208,plain,
! [SV33: $i,SV76: mu] :
( ( ~ ( exists_in_world @ SV76 @ SV33 )
| ! [SY139: mu] :
( ~ ( exists_in_world @ SY139 @ SV33 )
| ! [SY140: mu] :
( ~ ( exists_in_world @ SY140 @ SV33 )
| ~ ( qmltpeq @ SV76 @ SY139 @ SV33 )
| ( qmltpeq @ ( difference @ SY140 @ SV76 ) @ ( difference @ SY140 @ SY139 ) @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(209,plain,
! [SV34: $i,SV77: mu] :
( ( ~ ( exists_in_world @ SV77 @ SV34 )
| ! [SY141: mu] :
( ~ ( exists_in_world @ SY141 @ SV34 )
| ! [SY142: mu] :
( ~ ( exists_in_world @ SY142 @ SV34 )
| ~ ( qmltpeq @ SV77 @ SY141 @ SV34 )
| ( qmltpeq @ ( union @ SY142 @ SV77 ) @ ( union @ SY142 @ SY141 ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(210,plain,
! [SV35: $i,SV78: mu] :
( ( ~ ( exists_in_world @ SV78 @ SV35 )
| ! [SY143: mu] :
( ~ ( exists_in_world @ SY143 @ SV35 )
| ~ ( ~ ( ~ ( member @ SV78 @ ( sum @ SY143 ) @ SV35 )
| ~ ! [SY144: mu] :
( ~ ( exists_in_world @ SY144 @ SV35 )
| ~ ~ ( ~ ( member @ SY144 @ SY143 @ SV35 )
| ~ ( member @ SV78 @ SY144 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY145: mu] :
( ~ ( exists_in_world @ SY145 @ SV35 )
| ~ ~ ( ~ ( member @ SY145 @ SY143 @ SV35 )
| ~ ( member @ SV78 @ SY145 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SY143 ) @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(211,plain,
! [SV36: $i,SV79: mu] :
( ( ~ ( exists_in_world @ SV79 @ SV36 )
| ! [SY146: mu] :
( ~ ( exists_in_world @ SY146 @ SV36 )
| ! [SY147: mu] :
( ~ ( exists_in_world @ SY147 @ SV36 )
| ~ ( qmltpeq @ SV79 @ SY146 @ SV36 )
| ( qmltpeq @ ( intersection @ SY147 @ SV79 ) @ ( intersection @ SY147 @ SY146 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(212,plain,
! [SV37: $i,SV80: mu] :
( ( ~ ( exists_in_world @ SV80 @ SV37 )
| ! [SY148: mu] :
( ~ ( exists_in_world @ SY148 @ SV37 )
| ! [SY149: mu] :
( ~ ( exists_in_world @ SY149 @ SV37 )
| ~ ( qmltpeq @ SV80 @ SY148 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SY149 ) @ ( unordered_pair @ SY148 @ SY149 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(213,plain,
! [SV38: $i,SV81: mu] :
( ( ~ ( exists_in_world @ SV81 @ SV38 )
| ! [SY150: mu] :
( ~ ( exists_in_world @ SY150 @ SV38 )
| ! [SY151: mu] :
( ~ ( exists_in_world @ SY151 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SV81 @ SY150 @ SV38 )
| ~ ( member @ SV81 @ SY151 @ SV38 ) )
| ( member @ SY150 @ SY151 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(214,plain,
! [SV39: $i,SV82: mu] :
( ( ~ ( exists_in_world @ SV82 @ SV39 )
| ! [SY152: mu] :
( ~ ( exists_in_world @ SY152 @ SV39 )
| ! [SY153: mu] :
( ~ ( exists_in_world @ SY153 @ SV39 )
| ~ ( qmltpeq @ SV82 @ SY152 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SY153 @ SV82 ) @ ( unordered_pair @ SY153 @ SY152 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(215,plain,
( ( ! [SY154: mu] :
( ~ ( exists_in_world @ SY154 @ sK2_SX0 )
| ( subset @ empty_set @ SY154 @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(216,plain,
! [SV40: $i,SV83: mu] :
( ( ~ ( exists_in_world @ SV83 @ SV40 )
| ! [SY155: mu] :
( ~ ( exists_in_world @ SY155 @ SV40 )
| ! [SY156: mu] :
( ~ ( exists_in_world @ SY156 @ SV40 )
| ~ ( qmltpeq @ SV83 @ SY155 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SY156 ) @ ( intersection @ SY155 @ SY156 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(217,plain,
! [SV41: $i,SV84: mu] :
( ( ~ ( exists_in_world @ SV84 @ SV41 )
| ! [SY157: mu] :
( ~ ( exists_in_world @ SY157 @ SV41 )
| ! [SY158: mu] :
( ~ ( exists_in_world @ SY158 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SV84 @ SY157 @ SV41 )
| ~ ( equal_set @ SV84 @ SY158 @ SV41 ) )
| ( equal_set @ SY157 @ SY158 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(218,plain,
! [SV42: $i,SV85: mu] :
( ( ~ ( exists_in_world @ SV85 @ SV42 )
| ! [SY159: mu] :
( ~ ( exists_in_world @ SY159 @ SV42 )
| ! [SY160: mu] :
( ~ ( exists_in_world @ SY160 @ SV42 )
| ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SY159 @ SY160 ) @ SV42 )
| ( member @ SV85 @ SY159 @ SV42 )
| ( member @ SV85 @ SY160 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SY159 @ SV42 )
| ( member @ SV85 @ SY160 @ SV42 ) )
| ( member @ SV85 @ ( union @ SY159 @ SY160 ) @ SV42 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(219,plain,
! [SV43: $i,SV86: mu] :
( ( ~ ( exists_in_world @ SV86 @ SV43 )
| ! [SY161: mu] :
( ~ ( exists_in_world @ SY161 @ SV43 )
| ! [SY162: mu] :
( ~ ( exists_in_world @ SY162 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SV86 @ SY161 @ SV43 )
| ~ ( member @ SY162 @ SV86 @ SV43 ) )
| ( member @ SY162 @ SY161 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(220,plain,
! [SV45: $i,SV87: mu] :
( ( ~ ( exists_in_world @ SV87 @ SV45 )
| ! [SY163: mu] :
( ~ ( exists_in_world @ SY163 @ SV45 )
| ! [SY164: mu] :
( ~ ( exists_in_world @ SY164 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SV87 @ SY163 @ SV45 )
| ~ ( equal_set @ SY164 @ SV87 @ SV45 ) )
| ( equal_set @ SY164 @ SY163 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(221,plain,
! [SV88: $i,SV46: $i,SV2: mu] :
( ( ~ ( exists_in_world @ SV2 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SV88 )
| ( exists_in_world @ SV2 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(222,plain,
! [SV4: $i,SV89: mu,SV48: mu] :
( ( exists_in_world @ ( intersection @ SV48 @ SV89 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(223,plain,
! [SV5: $i,SV90: mu,SV49: mu] :
( ( exists_in_world @ ( union @ SV49 @ SV90 ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(224,plain,
! [SV6: $i,SV91: mu,SV50: mu] :
( ( exists_in_world @ ( difference @ SV50 @ SV91 ) @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(225,plain,
! [SV8: $i,SV92: mu,SV52: mu] :
( ( exists_in_world @ ( unordered_pair @ SV52 @ SV92 ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(226,plain,
! [SV12: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV12 ) )
= $true )
| ( ( ! [SY108: mu] :
( ~ ( exists_in_world @ SY108 @ SV12 )
| ~ ( ~ ( ~ ( equal_set @ SV55 @ SY108 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SY108 @ SV12 )
| ~ ( subset @ SY108 @ SV55 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV55 @ SY108 @ SV12 )
| ~ ( subset @ SY108 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SY108 @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(227,plain,
! [SV13: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV13 ) )
= $true )
| ( ( ! [SY109: mu] :
( ~ ( exists_in_world @ SY109 @ SV13 )
| ! [SY110: mu] :
( ~ ( exists_in_world @ SY110 @ SV13 )
| ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SY109 @ SY110 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SY109 @ SV13 )
| ~ ( member @ SV56 @ SY110 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SY109 @ SV13 )
| ~ ( member @ SV56 @ SY110 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SY109 @ SY110 ) @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(228,plain,
! [SV14: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV14 ) )
= $true )
| ( ( ! [SY111: mu] :
( ~ ( exists_in_world @ SY111 @ SV14 )
| ! [SY112: mu] :
( ~ ( exists_in_world @ SY112 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV57 @ SY111 @ SV14 )
| ~ ( subset @ SV57 @ SY112 @ SV14 ) )
| ( subset @ SY111 @ SY112 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(229,plain,
! [SV15: $i,SV58: mu] :
( ( ( ~ ( exists_in_world @ SV58 @ SV15 ) )
= $true )
| ( ( ! [SY113: mu] :
( ~ ( exists_in_world @ SY113 @ SV15 )
| ! [SY114: mu] :
( ~ ( exists_in_world @ SY114 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV58 @ SY113 @ SV15 )
| ~ ( qmltpeq @ SY113 @ SY114 @ SV15 ) )
| ( qmltpeq @ SV58 @ SY114 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(230,plain,
! [SV16: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV16 ) )
= $true )
| ( ( ! [SY115: mu] :
( ~ ( exists_in_world @ SY115 @ SV16 )
| ~ ( ~ ( ~ ( member @ SV59 @ ( singleton @ SY115 ) @ SV16 )
| ( qmltpeq @ SV59 @ SY115 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SV59 @ SY115 @ SV16 )
| ( member @ SV59 @ ( singleton @ SY115 ) @ SV16 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(231,plain,
! [SV17: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV17 ) )
= $true )
| ( ( ! [SY116: mu] :
( ~ ( exists_in_world @ SY116 @ SV17 )
| ~ ( ~ ( ~ ( member @ SV60 @ ( product @ SY116 ) @ SV17 )
| ! [SY117: mu] :
( ~ ( exists_in_world @ SY117 @ SV17 )
| ~ ( member @ SY117 @ SY116 @ SV17 )
| ( member @ SV60 @ SY117 @ SV17 ) ) )
| ~ ( ~ ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ SV17 )
| ~ ( member @ SY118 @ SY116 @ SV17 )
| ( member @ SV60 @ SY118 @ SV17 ) )
| ( member @ SV60 @ ( product @ SY116 ) @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(232,plain,
! [SV18: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV18 ) )
= $true )
| ( ( ! [SY119: mu] :
( ~ ( exists_in_world @ SY119 @ SV18 )
| ! [SY120: mu] :
( ~ ( exists_in_world @ SY120 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SY119 @ SY120 ) @ SV18 )
| ( qmltpeq @ SV61 @ SY119 @ SV18 )
| ( qmltpeq @ SV61 @ SY120 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SY119 @ SV18 )
| ( qmltpeq @ SV61 @ SY120 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SY119 @ SY120 ) @ SV18 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(233,plain,
! [SV19: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV19 ) )
= $true )
| ( ( qmltpeq @ SV62 @ SV62 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(234,plain,
! [SV20: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV20 ) )
= $true )
| ( ( ! [SY121: mu] :
( ~ ( exists_in_world @ SY121 @ SV20 )
| ~ ( qmltpeq @ SV63 @ SY121 @ SV20 )
| ( qmltpeq @ ( product @ SV63 ) @ ( product @ SY121 ) @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(235,plain,
! [SV21: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV21 ) )
= $true )
| ( ( ! [SY122: mu] :
( ~ ( exists_in_world @ SY122 @ SV21 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV21 )
| ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SY123 @ SY122 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SY123 @ SV21 )
| ~ ~ ( member @ SV64 @ SY122 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SY123 @ SV21 )
| ~ ~ ( member @ SV64 @ SY122 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SY123 @ SY122 ) @ SV21 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(236,plain,
! [SV22: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV22 ) )
= $true )
| ( ( ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV22 )
| ~ ( qmltpeq @ SV65 @ SY124 @ SV22 )
| ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SY124 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(237,plain,
! [SV23: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV23 ) )
= $true )
| ( ( ! [SY125: mu] :
( ~ ( exists_in_world @ SY125 @ SV23 )
| ~ ( qmltpeq @ SV66 @ SY125 @ SV23 )
| ( qmltpeq @ SY125 @ SV66 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(238,plain,
! [SV93: $i,SV67: $i,SV24: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV24 @ SV67 )
| ~ ( rel_s4 @ SV67 @ SV93 ) )
| ( rel_s4 @ SV24 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(239,plain,
! [SV25: $i,SV68: mu] :
( ( ( ~ ( exists_in_world @ SV68 @ SV25 ) )
= $true )
| ( ( ! [SY127: mu] :
( ~ ( exists_in_world @ SY127 @ SV25 )
| ~ ( qmltpeq @ SV68 @ SY127 @ SV25 )
| ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SY127 ) @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(240,plain,
! [SV26: $i,SV69: mu] :
( ( ( ~ ( exists_in_world @ SV69 @ SV26 ) )
= $true )
| ( ( ! [SY128: mu] :
( ~ ( exists_in_world @ SY128 @ SV26 )
| ! [SY129: mu] :
( ~ ( exists_in_world @ SY129 @ SV26 )
| ~ ( qmltpeq @ SV69 @ SY128 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SY129 ) @ ( union @ SY128 @ SY129 ) @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(241,plain,
! [SV27: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV27 ) )
= $true )
| ( ( ! [SY130: mu] :
( ~ ( exists_in_world @ SY130 @ SV27 )
| ~ ( qmltpeq @ SV70 @ SY130 @ SV27 )
| ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SY130 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(242,plain,
! [SV28: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV28 ) )
= $true )
| ( ( ! [SY131: mu] :
( ~ ( exists_in_world @ SY131 @ SV28 )
| ! [SY132: mu] :
( ~ ( exists_in_world @ SY132 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV71 @ SY131 @ SV28 )
| ~ ( subset @ SY132 @ SV71 @ SV28 ) )
| ( subset @ SY132 @ SY131 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(243,plain,
! [SV29: $i,SV72: mu] :
( ( ( ~ ( exists_in_world @ SV72 @ SV29 ) )
= $true )
| ( ( ! [SY133: mu] :
( ~ ( exists_in_world @ SY133 @ SV29 )
| ~ ( ~ ( ~ ( member @ SV72 @ ( power_set @ SY133 ) @ SV29 )
| ( subset @ SV72 @ SY133 @ SV29 ) )
| ~ ( ~ ( subset @ SV72 @ SY133 @ SV29 )
| ( member @ SV72 @ ( power_set @ SY133 ) @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(244,plain,
! [SV30: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV30 ) )
= $true )
| ( ( ! [SY134: mu] :
( ~ ( exists_in_world @ SY134 @ SV30 )
| ! [SY135: mu] :
( ~ ( exists_in_world @ SY135 @ SV30 )
| ~ ( qmltpeq @ SV73 @ SY134 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SY135 ) @ ( difference @ SY134 @ SY135 ) @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(245,plain,
! [SV31: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV31 ) )
= $true )
| ( ( ~ ( member @ SV74 @ empty_set @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(246,plain,
! [SV32: $i,SV75: mu] :
( ( ( ~ ( exists_in_world @ SV75 @ SV32 ) )
= $true )
| ( ( ! [SY136: mu] :
( ~ ( exists_in_world @ SY136 @ SV32 )
| ~ ( ~ ( ~ ( subset @ SV75 @ SY136 @ SV32 )
| ! [SY137: mu] :
( ~ ( exists_in_world @ SY137 @ SV32 )
| ~ ( member @ SY137 @ SV75 @ SV32 )
| ( member @ SY137 @ SY136 @ SV32 ) ) )
| ~ ( ~ ! [SY138: mu] :
( ~ ( exists_in_world @ SY138 @ SV32 )
| ~ ( member @ SY138 @ SV75 @ SV32 )
| ( member @ SY138 @ SY136 @ SV32 ) )
| ( subset @ SV75 @ SY136 @ SV32 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(247,plain,
! [SV33: $i,SV76: mu] :
( ( ( ~ ( exists_in_world @ SV76 @ SV33 ) )
= $true )
| ( ( ! [SY139: mu] :
( ~ ( exists_in_world @ SY139 @ SV33 )
| ! [SY140: mu] :
( ~ ( exists_in_world @ SY140 @ SV33 )
| ~ ( qmltpeq @ SV76 @ SY139 @ SV33 )
| ( qmltpeq @ ( difference @ SY140 @ SV76 ) @ ( difference @ SY140 @ SY139 ) @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(248,plain,
! [SV34: $i,SV77: mu] :
( ( ( ~ ( exists_in_world @ SV77 @ SV34 ) )
= $true )
| ( ( ! [SY141: mu] :
( ~ ( exists_in_world @ SY141 @ SV34 )
| ! [SY142: mu] :
( ~ ( exists_in_world @ SY142 @ SV34 )
| ~ ( qmltpeq @ SV77 @ SY141 @ SV34 )
| ( qmltpeq @ ( union @ SY142 @ SV77 ) @ ( union @ SY142 @ SY141 ) @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(249,plain,
! [SV35: $i,SV78: mu] :
( ( ( ~ ( exists_in_world @ SV78 @ SV35 ) )
= $true )
| ( ( ! [SY143: mu] :
( ~ ( exists_in_world @ SY143 @ SV35 )
| ~ ( ~ ( ~ ( member @ SV78 @ ( sum @ SY143 ) @ SV35 )
| ~ ! [SY144: mu] :
( ~ ( exists_in_world @ SY144 @ SV35 )
| ~ ~ ( ~ ( member @ SY144 @ SY143 @ SV35 )
| ~ ( member @ SV78 @ SY144 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY145: mu] :
( ~ ( exists_in_world @ SY145 @ SV35 )
| ~ ~ ( ~ ( member @ SY145 @ SY143 @ SV35 )
| ~ ( member @ SV78 @ SY145 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SY143 ) @ SV35 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(250,plain,
! [SV36: $i,SV79: mu] :
( ( ( ~ ( exists_in_world @ SV79 @ SV36 ) )
= $true )
| ( ( ! [SY146: mu] :
( ~ ( exists_in_world @ SY146 @ SV36 )
| ! [SY147: mu] :
( ~ ( exists_in_world @ SY147 @ SV36 )
| ~ ( qmltpeq @ SV79 @ SY146 @ SV36 )
| ( qmltpeq @ ( intersection @ SY147 @ SV79 ) @ ( intersection @ SY147 @ SY146 ) @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(251,plain,
! [SV37: $i,SV80: mu] :
( ( ( ~ ( exists_in_world @ SV80 @ SV37 ) )
= $true )
| ( ( ! [SY148: mu] :
( ~ ( exists_in_world @ SY148 @ SV37 )
| ! [SY149: mu] :
( ~ ( exists_in_world @ SY149 @ SV37 )
| ~ ( qmltpeq @ SV80 @ SY148 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SY149 ) @ ( unordered_pair @ SY148 @ SY149 ) @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(252,plain,
! [SV38: $i,SV81: mu] :
( ( ( ~ ( exists_in_world @ SV81 @ SV38 ) )
= $true )
| ( ( ! [SY150: mu] :
( ~ ( exists_in_world @ SY150 @ SV38 )
| ! [SY151: mu] :
( ~ ( exists_in_world @ SY151 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SV81 @ SY150 @ SV38 )
| ~ ( member @ SV81 @ SY151 @ SV38 ) )
| ( member @ SY150 @ SY151 @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(253,plain,
! [SV39: $i,SV82: mu] :
( ( ( ~ ( exists_in_world @ SV82 @ SV39 ) )
= $true )
| ( ( ! [SY152: mu] :
( ~ ( exists_in_world @ SY152 @ SV39 )
| ! [SY153: mu] :
( ~ ( exists_in_world @ SY153 @ SV39 )
| ~ ( qmltpeq @ SV82 @ SY152 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SY153 @ SV82 ) @ ( unordered_pair @ SY153 @ SY152 ) @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(254,plain,
( ( ~ ( exists_in_world @ sK3_SY154 @ sK2_SX0 )
| ( subset @ empty_set @ sK3_SY154 @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[215]) ).
thf(255,plain,
! [SV40: $i,SV83: mu] :
( ( ( ~ ( exists_in_world @ SV83 @ SV40 ) )
= $true )
| ( ( ! [SY155: mu] :
( ~ ( exists_in_world @ SY155 @ SV40 )
| ! [SY156: mu] :
( ~ ( exists_in_world @ SY156 @ SV40 )
| ~ ( qmltpeq @ SV83 @ SY155 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SY156 ) @ ( intersection @ SY155 @ SY156 ) @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(256,plain,
! [SV41: $i,SV84: mu] :
( ( ( ~ ( exists_in_world @ SV84 @ SV41 ) )
= $true )
| ( ( ! [SY157: mu] :
( ~ ( exists_in_world @ SY157 @ SV41 )
| ! [SY158: mu] :
( ~ ( exists_in_world @ SY158 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SV84 @ SY157 @ SV41 )
| ~ ( equal_set @ SV84 @ SY158 @ SV41 ) )
| ( equal_set @ SY157 @ SY158 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(257,plain,
! [SV42: $i,SV85: mu] :
( ( ( ~ ( exists_in_world @ SV85 @ SV42 ) )
= $true )
| ( ( ! [SY159: mu] :
( ~ ( exists_in_world @ SY159 @ SV42 )
| ! [SY160: mu] :
( ~ ( exists_in_world @ SY160 @ SV42 )
| ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SY159 @ SY160 ) @ SV42 )
| ( member @ SV85 @ SY159 @ SV42 )
| ( member @ SV85 @ SY160 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SY159 @ SV42 )
| ( member @ SV85 @ SY160 @ SV42 ) )
| ( member @ SV85 @ ( union @ SY159 @ SY160 ) @ SV42 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(258,plain,
! [SV43: $i,SV86: mu] :
( ( ( ~ ( exists_in_world @ SV86 @ SV43 ) )
= $true )
| ( ( ! [SY161: mu] :
( ~ ( exists_in_world @ SY161 @ SV43 )
| ! [SY162: mu] :
( ~ ( exists_in_world @ SY162 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SV86 @ SY161 @ SV43 )
| ~ ( member @ SY162 @ SV86 @ SV43 ) )
| ( member @ SY162 @ SY161 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(259,plain,
! [SV45: $i,SV87: mu] :
( ( ( ~ ( exists_in_world @ SV87 @ SV45 ) )
= $true )
| ( ( ! [SY163: mu] :
( ~ ( exists_in_world @ SY163 @ SV45 )
| ! [SY164: mu] :
( ~ ( exists_in_world @ SY164 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SV87 @ SY163 @ SV45 )
| ~ ( equal_set @ SY164 @ SV87 @ SV45 ) )
| ( equal_set @ SY164 @ SY163 @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(260,plain,
! [SV88: $i,SV46: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV46 )
| ~ ( rel_s4 @ SV46 @ SV88 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(261,plain,
! [SV12: $i,SV55: mu] :
( ( ( exists_in_world @ SV55 @ SV12 )
= $false )
| ( ( ! [SY108: mu] :
( ~ ( exists_in_world @ SY108 @ SV12 )
| ~ ( ~ ( ~ ( equal_set @ SV55 @ SY108 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SY108 @ SV12 )
| ~ ( subset @ SY108 @ SV55 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV55 @ SY108 @ SV12 )
| ~ ( subset @ SY108 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SY108 @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(262,plain,
! [SV13: $i,SV56: mu] :
( ( ( exists_in_world @ SV56 @ SV13 )
= $false )
| ( ( ! [SY109: mu] :
( ~ ( exists_in_world @ SY109 @ SV13 )
| ! [SY110: mu] :
( ~ ( exists_in_world @ SY110 @ SV13 )
| ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SY109 @ SY110 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SY109 @ SV13 )
| ~ ( member @ SV56 @ SY110 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SY109 @ SV13 )
| ~ ( member @ SV56 @ SY110 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SY109 @ SY110 ) @ SV13 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(263,plain,
! [SV14: $i,SV57: mu] :
( ( ( exists_in_world @ SV57 @ SV14 )
= $false )
| ( ( ! [SY111: mu] :
( ~ ( exists_in_world @ SY111 @ SV14 )
| ! [SY112: mu] :
( ~ ( exists_in_world @ SY112 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV57 @ SY111 @ SV14 )
| ~ ( subset @ SV57 @ SY112 @ SV14 ) )
| ( subset @ SY111 @ SY112 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(264,plain,
! [SV15: $i,SV58: mu] :
( ( ( exists_in_world @ SV58 @ SV15 )
= $false )
| ( ( ! [SY113: mu] :
( ~ ( exists_in_world @ SY113 @ SV15 )
| ! [SY114: mu] :
( ~ ( exists_in_world @ SY114 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV58 @ SY113 @ SV15 )
| ~ ( qmltpeq @ SY113 @ SY114 @ SV15 ) )
| ( qmltpeq @ SV58 @ SY114 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(265,plain,
! [SV16: $i,SV59: mu] :
( ( ( exists_in_world @ SV59 @ SV16 )
= $false )
| ( ( ! [SY115: mu] :
( ~ ( exists_in_world @ SY115 @ SV16 )
| ~ ( ~ ( ~ ( member @ SV59 @ ( singleton @ SY115 ) @ SV16 )
| ( qmltpeq @ SV59 @ SY115 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SV59 @ SY115 @ SV16 )
| ( member @ SV59 @ ( singleton @ SY115 ) @ SV16 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(266,plain,
! [SV17: $i,SV60: mu] :
( ( ( exists_in_world @ SV60 @ SV17 )
= $false )
| ( ( ! [SY116: mu] :
( ~ ( exists_in_world @ SY116 @ SV17 )
| ~ ( ~ ( ~ ( member @ SV60 @ ( product @ SY116 ) @ SV17 )
| ! [SY117: mu] :
( ~ ( exists_in_world @ SY117 @ SV17 )
| ~ ( member @ SY117 @ SY116 @ SV17 )
| ( member @ SV60 @ SY117 @ SV17 ) ) )
| ~ ( ~ ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ SV17 )
| ~ ( member @ SY118 @ SY116 @ SV17 )
| ( member @ SV60 @ SY118 @ SV17 ) )
| ( member @ SV60 @ ( product @ SY116 ) @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(267,plain,
! [SV18: $i,SV61: mu] :
( ( ( exists_in_world @ SV61 @ SV18 )
= $false )
| ( ( ! [SY119: mu] :
( ~ ( exists_in_world @ SY119 @ SV18 )
| ! [SY120: mu] :
( ~ ( exists_in_world @ SY120 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SY119 @ SY120 ) @ SV18 )
| ( qmltpeq @ SV61 @ SY119 @ SV18 )
| ( qmltpeq @ SV61 @ SY120 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SY119 @ SV18 )
| ( qmltpeq @ SV61 @ SY120 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SY119 @ SY120 ) @ SV18 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(268,plain,
! [SV19: $i,SV62: mu] :
( ( ( exists_in_world @ SV62 @ SV19 )
= $false )
| ( ( qmltpeq @ SV62 @ SV62 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(269,plain,
! [SV20: $i,SV63: mu] :
( ( ( exists_in_world @ SV63 @ SV20 )
= $false )
| ( ( ! [SY121: mu] :
( ~ ( exists_in_world @ SY121 @ SV20 )
| ~ ( qmltpeq @ SV63 @ SY121 @ SV20 )
| ( qmltpeq @ ( product @ SV63 ) @ ( product @ SY121 ) @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(270,plain,
! [SV21: $i,SV64: mu] :
( ( ( exists_in_world @ SV64 @ SV21 )
= $false )
| ( ( ! [SY122: mu] :
( ~ ( exists_in_world @ SY122 @ SV21 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV21 )
| ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SY123 @ SY122 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SY123 @ SV21 )
| ~ ~ ( member @ SV64 @ SY122 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SY123 @ SV21 )
| ~ ~ ( member @ SV64 @ SY122 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SY123 @ SY122 ) @ SV21 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(271,plain,
! [SV22: $i,SV65: mu] :
( ( ( exists_in_world @ SV65 @ SV22 )
= $false )
| ( ( ! [SY124: mu] :
( ~ ( exists_in_world @ SY124 @ SV22 )
| ~ ( qmltpeq @ SV65 @ SY124 @ SV22 )
| ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SY124 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(272,plain,
! [SV23: $i,SV66: mu] :
( ( ( exists_in_world @ SV66 @ SV23 )
= $false )
| ( ( ! [SY125: mu] :
( ~ ( exists_in_world @ SY125 @ SV23 )
| ~ ( qmltpeq @ SV66 @ SY125 @ SV23 )
| ( qmltpeq @ SY125 @ SV66 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(273,plain,
! [SV93: $i,SV67: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV24 @ SV67 )
| ~ ( rel_s4 @ SV67 @ SV93 ) ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(274,plain,
! [SV25: $i,SV68: mu] :
( ( ( exists_in_world @ SV68 @ SV25 )
= $false )
| ( ( ! [SY127: mu] :
( ~ ( exists_in_world @ SY127 @ SV25 )
| ~ ( qmltpeq @ SV68 @ SY127 @ SV25 )
| ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SY127 ) @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(275,plain,
! [SV26: $i,SV69: mu] :
( ( ( exists_in_world @ SV69 @ SV26 )
= $false )
| ( ( ! [SY128: mu] :
( ~ ( exists_in_world @ SY128 @ SV26 )
| ! [SY129: mu] :
( ~ ( exists_in_world @ SY129 @ SV26 )
| ~ ( qmltpeq @ SV69 @ SY128 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SY129 ) @ ( union @ SY128 @ SY129 ) @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(276,plain,
! [SV27: $i,SV70: mu] :
( ( ( exists_in_world @ SV70 @ SV27 )
= $false )
| ( ( ! [SY130: mu] :
( ~ ( exists_in_world @ SY130 @ SV27 )
| ~ ( qmltpeq @ SV70 @ SY130 @ SV27 )
| ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SY130 ) @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(277,plain,
! [SV28: $i,SV71: mu] :
( ( ( exists_in_world @ SV71 @ SV28 )
= $false )
| ( ( ! [SY131: mu] :
( ~ ( exists_in_world @ SY131 @ SV28 )
| ! [SY132: mu] :
( ~ ( exists_in_world @ SY132 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV71 @ SY131 @ SV28 )
| ~ ( subset @ SY132 @ SV71 @ SV28 ) )
| ( subset @ SY132 @ SY131 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(278,plain,
! [SV29: $i,SV72: mu] :
( ( ( exists_in_world @ SV72 @ SV29 )
= $false )
| ( ( ! [SY133: mu] :
( ~ ( exists_in_world @ SY133 @ SV29 )
| ~ ( ~ ( ~ ( member @ SV72 @ ( power_set @ SY133 ) @ SV29 )
| ( subset @ SV72 @ SY133 @ SV29 ) )
| ~ ( ~ ( subset @ SV72 @ SY133 @ SV29 )
| ( member @ SV72 @ ( power_set @ SY133 ) @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(279,plain,
! [SV30: $i,SV73: mu] :
( ( ( exists_in_world @ SV73 @ SV30 )
= $false )
| ( ( ! [SY134: mu] :
( ~ ( exists_in_world @ SY134 @ SV30 )
| ! [SY135: mu] :
( ~ ( exists_in_world @ SY135 @ SV30 )
| ~ ( qmltpeq @ SV73 @ SY134 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SY135 ) @ ( difference @ SY134 @ SY135 ) @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(280,plain,
! [SV31: $i,SV74: mu] :
( ( ( exists_in_world @ SV74 @ SV31 )
= $false )
| ( ( ~ ( member @ SV74 @ empty_set @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(281,plain,
! [SV32: $i,SV75: mu] :
( ( ( exists_in_world @ SV75 @ SV32 )
= $false )
| ( ( ! [SY136: mu] :
( ~ ( exists_in_world @ SY136 @ SV32 )
| ~ ( ~ ( ~ ( subset @ SV75 @ SY136 @ SV32 )
| ! [SY137: mu] :
( ~ ( exists_in_world @ SY137 @ SV32 )
| ~ ( member @ SY137 @ SV75 @ SV32 )
| ( member @ SY137 @ SY136 @ SV32 ) ) )
| ~ ( ~ ! [SY138: mu] :
( ~ ( exists_in_world @ SY138 @ SV32 )
| ~ ( member @ SY138 @ SV75 @ SV32 )
| ( member @ SY138 @ SY136 @ SV32 ) )
| ( subset @ SV75 @ SY136 @ SV32 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(282,plain,
! [SV33: $i,SV76: mu] :
( ( ( exists_in_world @ SV76 @ SV33 )
= $false )
| ( ( ! [SY139: mu] :
( ~ ( exists_in_world @ SY139 @ SV33 )
| ! [SY140: mu] :
( ~ ( exists_in_world @ SY140 @ SV33 )
| ~ ( qmltpeq @ SV76 @ SY139 @ SV33 )
| ( qmltpeq @ ( difference @ SY140 @ SV76 ) @ ( difference @ SY140 @ SY139 ) @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(283,plain,
! [SV34: $i,SV77: mu] :
( ( ( exists_in_world @ SV77 @ SV34 )
= $false )
| ( ( ! [SY141: mu] :
( ~ ( exists_in_world @ SY141 @ SV34 )
| ! [SY142: mu] :
( ~ ( exists_in_world @ SY142 @ SV34 )
| ~ ( qmltpeq @ SV77 @ SY141 @ SV34 )
| ( qmltpeq @ ( union @ SY142 @ SV77 ) @ ( union @ SY142 @ SY141 ) @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(284,plain,
! [SV35: $i,SV78: mu] :
( ( ( exists_in_world @ SV78 @ SV35 )
= $false )
| ( ( ! [SY143: mu] :
( ~ ( exists_in_world @ SY143 @ SV35 )
| ~ ( ~ ( ~ ( member @ SV78 @ ( sum @ SY143 ) @ SV35 )
| ~ ! [SY144: mu] :
( ~ ( exists_in_world @ SY144 @ SV35 )
| ~ ~ ( ~ ( member @ SY144 @ SY143 @ SV35 )
| ~ ( member @ SV78 @ SY144 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY145: mu] :
( ~ ( exists_in_world @ SY145 @ SV35 )
| ~ ~ ( ~ ( member @ SY145 @ SY143 @ SV35 )
| ~ ( member @ SV78 @ SY145 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SY143 ) @ SV35 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(285,plain,
! [SV36: $i,SV79: mu] :
( ( ( exists_in_world @ SV79 @ SV36 )
= $false )
| ( ( ! [SY146: mu] :
( ~ ( exists_in_world @ SY146 @ SV36 )
| ! [SY147: mu] :
( ~ ( exists_in_world @ SY147 @ SV36 )
| ~ ( qmltpeq @ SV79 @ SY146 @ SV36 )
| ( qmltpeq @ ( intersection @ SY147 @ SV79 ) @ ( intersection @ SY147 @ SY146 ) @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(286,plain,
! [SV37: $i,SV80: mu] :
( ( ( exists_in_world @ SV80 @ SV37 )
= $false )
| ( ( ! [SY148: mu] :
( ~ ( exists_in_world @ SY148 @ SV37 )
| ! [SY149: mu] :
( ~ ( exists_in_world @ SY149 @ SV37 )
| ~ ( qmltpeq @ SV80 @ SY148 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SY149 ) @ ( unordered_pair @ SY148 @ SY149 ) @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(287,plain,
! [SV38: $i,SV81: mu] :
( ( ( exists_in_world @ SV81 @ SV38 )
= $false )
| ( ( ! [SY150: mu] :
( ~ ( exists_in_world @ SY150 @ SV38 )
| ! [SY151: mu] :
( ~ ( exists_in_world @ SY151 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SV81 @ SY150 @ SV38 )
| ~ ( member @ SV81 @ SY151 @ SV38 ) )
| ( member @ SY150 @ SY151 @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(288,plain,
! [SV39: $i,SV82: mu] :
( ( ( exists_in_world @ SV82 @ SV39 )
= $false )
| ( ( ! [SY152: mu] :
( ~ ( exists_in_world @ SY152 @ SV39 )
| ! [SY153: mu] :
( ~ ( exists_in_world @ SY153 @ SV39 )
| ~ ( qmltpeq @ SV82 @ SY152 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SY153 @ SV82 ) @ ( unordered_pair @ SY153 @ SY152 ) @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(289,plain,
( ( ~ ( exists_in_world @ sK3_SY154 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(290,plain,
( ( subset @ empty_set @ sK3_SY154 @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[254]) ).
thf(291,plain,
! [SV40: $i,SV83: mu] :
( ( ( exists_in_world @ SV83 @ SV40 )
= $false )
| ( ( ! [SY155: mu] :
( ~ ( exists_in_world @ SY155 @ SV40 )
| ! [SY156: mu] :
( ~ ( exists_in_world @ SY156 @ SV40 )
| ~ ( qmltpeq @ SV83 @ SY155 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SY156 ) @ ( intersection @ SY155 @ SY156 ) @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(292,plain,
! [SV41: $i,SV84: mu] :
( ( ( exists_in_world @ SV84 @ SV41 )
= $false )
| ( ( ! [SY157: mu] :
( ~ ( exists_in_world @ SY157 @ SV41 )
| ! [SY158: mu] :
( ~ ( exists_in_world @ SY158 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SV84 @ SY157 @ SV41 )
| ~ ( equal_set @ SV84 @ SY158 @ SV41 ) )
| ( equal_set @ SY157 @ SY158 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(293,plain,
! [SV42: $i,SV85: mu] :
( ( ( exists_in_world @ SV85 @ SV42 )
= $false )
| ( ( ! [SY159: mu] :
( ~ ( exists_in_world @ SY159 @ SV42 )
| ! [SY160: mu] :
( ~ ( exists_in_world @ SY160 @ SV42 )
| ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SY159 @ SY160 ) @ SV42 )
| ( member @ SV85 @ SY159 @ SV42 )
| ( member @ SV85 @ SY160 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SY159 @ SV42 )
| ( member @ SV85 @ SY160 @ SV42 ) )
| ( member @ SV85 @ ( union @ SY159 @ SY160 ) @ SV42 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(294,plain,
! [SV43: $i,SV86: mu] :
( ( ( exists_in_world @ SV86 @ SV43 )
= $false )
| ( ( ! [SY161: mu] :
( ~ ( exists_in_world @ SY161 @ SV43 )
| ! [SY162: mu] :
( ~ ( exists_in_world @ SY162 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SV86 @ SY161 @ SV43 )
| ~ ( member @ SY162 @ SV86 @ SV43 ) )
| ( member @ SY162 @ SY161 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(295,plain,
! [SV45: $i,SV87: mu] :
( ( ( exists_in_world @ SV87 @ SV45 )
= $false )
| ( ( ! [SY163: mu] :
( ~ ( exists_in_world @ SY163 @ SV45 )
| ! [SY164: mu] :
( ~ ( exists_in_world @ SY164 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SV87 @ SY163 @ SV45 )
| ~ ( equal_set @ SY164 @ SV87 @ SV45 ) )
| ( equal_set @ SY164 @ SY163 @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(296,plain,
! [SV88: $i,SV46: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV46 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV46 @ SV88 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(297,plain,
! [SV55: mu,SV12: $i,SV94: mu] :
( ( ( ~ ( exists_in_world @ SV94 @ SV12 )
| ~ ( ~ ( ~ ( equal_set @ SV55 @ SV94 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SV94 @ SV12 ) ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(298,plain,
! [SV56: mu,SV13: $i,SV95: mu] :
( ( ( ~ ( exists_in_world @ SV95 @ SV13 )
| ! [SY165: mu] :
( ~ ( exists_in_world @ SY165 @ SV13 )
| ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SY165 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SY165 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SY165 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SY165 ) @ SV13 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(299,plain,
! [SV57: mu,SV14: $i,SV96: mu] :
( ( ( ~ ( exists_in_world @ SV96 @ SV14 )
| ! [SY166: mu] :
( ~ ( exists_in_world @ SY166 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SY166 @ SV14 ) )
| ( subset @ SV96 @ SY166 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(300,plain,
! [SV58: mu,SV15: $i,SV97: mu] :
( ( ( ~ ( exists_in_world @ SV97 @ SV15 )
| ! [SY167: mu] :
( ~ ( exists_in_world @ SY167 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SY167 @ SV15 ) )
| ( qmltpeq @ SV58 @ SY167 @ SV15 ) ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(301,plain,
! [SV59: mu,SV16: $i,SV98: mu] :
( ( ( ~ ( exists_in_world @ SV98 @ SV16 )
| ~ ( ~ ( ~ ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
| ( qmltpeq @ SV59 @ SV98 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SV59 @ SV98 @ SV16 )
| ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(302,plain,
! [SV60: mu,SV17: $i,SV99: mu] :
( ( ( ~ ( exists_in_world @ SV99 @ SV17 )
| ~ ( ~ ( ~ ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) )
| ~ ( ~ ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) )
| ( member @ SV60 @ ( product @ SV99 ) @ SV17 ) ) ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(303,plain,
! [SV61: mu,SV18: $i,SV100: mu] :
( ( ( ~ ( exists_in_world @ SV100 @ SV18 )
| ! [SY170: mu] :
( ~ ( exists_in_world @ SY170 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SY170 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SY170 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SY170 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SY170 ) @ SV18 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(304,plain,
! [SV63: mu,SV20: $i,SV101: mu] :
( ( ( ~ ( exists_in_world @ SV101 @ SV20 )
| ~ ( qmltpeq @ SV63 @ SV101 @ SV20 )
| ( qmltpeq @ ( product @ SV63 ) @ ( product @ SV101 ) @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV63 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(305,plain,
! [SV64: mu,SV21: $i,SV102: mu] :
( ( ( ~ ( exists_in_world @ SV102 @ SV21 )
| ! [SY171: mu] :
( ~ ( exists_in_world @ SY171 @ SV21 )
| ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SY171 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SY171 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SY171 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SY171 @ SV102 ) @ SV21 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(306,plain,
! [SV65: mu,SV22: $i,SV103: mu] :
( ( ( ~ ( exists_in_world @ SV103 @ SV22 )
| ~ ( qmltpeq @ SV65 @ SV103 @ SV22 )
| ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SV103 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV65 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(307,plain,
! [SV66: mu,SV23: $i,SV104: mu] :
( ( ( ~ ( exists_in_world @ SV104 @ SV23 )
| ~ ( qmltpeq @ SV66 @ SV104 @ SV23 )
| ( qmltpeq @ SV104 @ SV66 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(308,plain,
! [SV93: $i,SV67: $i,SV24: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV24 @ SV67 )
| ~ ( rel_s4 @ SV67 @ SV93 ) ) )
= $false )
| ( ( rel_s4 @ SV24 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(309,plain,
! [SV68: mu,SV25: $i,SV105: mu] :
( ( ( ~ ( exists_in_world @ SV105 @ SV25 )
| ~ ( qmltpeq @ SV68 @ SV105 @ SV25 )
| ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SV105 ) @ SV25 ) )
= $true )
| ( ( exists_in_world @ SV68 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(310,plain,
! [SV69: mu,SV26: $i,SV106: mu] :
( ( ( ~ ( exists_in_world @ SV106 @ SV26 )
| ! [SY172: mu] :
( ~ ( exists_in_world @ SY172 @ SV26 )
| ~ ( qmltpeq @ SV69 @ SV106 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SY172 ) @ ( union @ SV106 @ SY172 ) @ SV26 ) ) )
= $true )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(311,plain,
! [SV70: mu,SV27: $i,SV107: mu] :
( ( ( ~ ( exists_in_world @ SV107 @ SV27 )
| ~ ( qmltpeq @ SV70 @ SV107 @ SV27 )
| ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SV107 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(312,plain,
! [SV71: mu,SV28: $i,SV108: mu] :
( ( ( ~ ( exists_in_world @ SV108 @ SV28 )
| ! [SY173: mu] :
( ~ ( exists_in_world @ SY173 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SY173 @ SV71 @ SV28 ) )
| ( subset @ SY173 @ SV108 @ SV28 ) ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(313,plain,
! [SV72: mu,SV29: $i,SV109: mu] :
( ( ( ~ ( exists_in_world @ SV109 @ SV29 )
| ~ ( ~ ( ~ ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
| ( subset @ SV72 @ SV109 @ SV29 ) )
| ~ ( ~ ( subset @ SV72 @ SV109 @ SV29 )
| ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 ) ) ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(314,plain,
! [SV73: mu,SV30: $i,SV110: mu] :
( ( ( ~ ( exists_in_world @ SV110 @ SV30 )
| ! [SY174: mu] :
( ~ ( exists_in_world @ SY174 @ SV30 )
| ~ ( qmltpeq @ SV73 @ SV110 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SY174 ) @ ( difference @ SV110 @ SY174 ) @ SV30 ) ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(315,plain,
! [SV31: $i,SV74: mu] :
( ( ( member @ SV74 @ empty_set @ SV31 )
= $false )
| ( ( exists_in_world @ SV74 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(316,plain,
! [SV75: mu,SV32: $i,SV111: mu] :
( ( ( ~ ( exists_in_world @ SV111 @ SV32 )
| ~ ( ~ ( ~ ( subset @ SV75 @ SV111 @ SV32 )
| ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) )
| ~ ( ~ ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) )
| ( subset @ SV75 @ SV111 @ SV32 ) ) ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(317,plain,
! [SV76: mu,SV33: $i,SV112: mu] :
( ( ( ~ ( exists_in_world @ SV112 @ SV33 )
| ! [SY177: mu] :
( ~ ( exists_in_world @ SY177 @ SV33 )
| ~ ( qmltpeq @ SV76 @ SV112 @ SV33 )
| ( qmltpeq @ ( difference @ SY177 @ SV76 ) @ ( difference @ SY177 @ SV112 ) @ SV33 ) ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(318,plain,
! [SV77: mu,SV34: $i,SV113: mu] :
( ( ( ~ ( exists_in_world @ SV113 @ SV34 )
| ! [SY178: mu] :
( ~ ( exists_in_world @ SY178 @ SV34 )
| ~ ( qmltpeq @ SV77 @ SV113 @ SV34 )
| ( qmltpeq @ ( union @ SY178 @ SV77 ) @ ( union @ SY178 @ SV113 ) @ SV34 ) ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(319,plain,
! [SV78: mu,SV35: $i,SV114: mu] :
( ( ( ~ ( exists_in_world @ SV114 @ SV35 )
| ~ ( ~ ( ~ ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
| ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SV114 ) @ SV35 ) ) ) )
= $true )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(320,plain,
! [SV79: mu,SV36: $i,SV115: mu] :
( ( ( ~ ( exists_in_world @ SV115 @ SV36 )
| ! [SY181: mu] :
( ~ ( exists_in_world @ SY181 @ SV36 )
| ~ ( qmltpeq @ SV79 @ SV115 @ SV36 )
| ( qmltpeq @ ( intersection @ SY181 @ SV79 ) @ ( intersection @ SY181 @ SV115 ) @ SV36 ) ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(321,plain,
! [SV80: mu,SV37: $i,SV116: mu] :
( ( ( ~ ( exists_in_world @ SV116 @ SV37 )
| ! [SY182: mu] :
( ~ ( exists_in_world @ SY182 @ SV37 )
| ~ ( qmltpeq @ SV80 @ SV116 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SY182 ) @ ( unordered_pair @ SV116 @ SY182 ) @ SV37 ) ) )
= $true )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(322,plain,
! [SV81: mu,SV38: $i,SV117: mu] :
( ( ( ~ ( exists_in_world @ SV117 @ SV38 )
| ! [SY183: mu] :
( ~ ( exists_in_world @ SY183 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SY183 @ SV38 ) )
| ( member @ SV117 @ SY183 @ SV38 ) ) )
= $true )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(323,plain,
! [SV82: mu,SV39: $i,SV118: mu] :
( ( ( ~ ( exists_in_world @ SV118 @ SV39 )
| ! [SY184: mu] :
( ~ ( exists_in_world @ SY184 @ SV39 )
| ~ ( qmltpeq @ SV82 @ SV118 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SY184 @ SV82 ) @ ( unordered_pair @ SY184 @ SV118 ) @ SV39 ) ) )
= $true )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(324,plain,
( ( exists_in_world @ sK3_SY154 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(325,plain,
! [SV83: mu,SV40: $i,SV119: mu] :
( ( ( ~ ( exists_in_world @ SV119 @ SV40 )
| ! [SY185: mu] :
( ~ ( exists_in_world @ SY185 @ SV40 )
| ~ ( qmltpeq @ SV83 @ SV119 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SY185 ) @ ( intersection @ SV119 @ SY185 ) @ SV40 ) ) )
= $true )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(326,plain,
! [SV84: mu,SV41: $i,SV120: mu] :
( ( ( ~ ( exists_in_world @ SV120 @ SV41 )
| ! [SY186: mu] :
( ~ ( exists_in_world @ SY186 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SY186 @ SV41 ) )
| ( equal_set @ SV120 @ SY186 @ SV41 ) ) )
= $true )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(327,plain,
! [SV85: mu,SV42: $i,SV121: mu] :
( ( ( ~ ( exists_in_world @ SV121 @ SV42 )
| ! [SY187: mu] :
( ~ ( exists_in_world @ SY187 @ SV42 )
| ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SY187 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SY187 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SY187 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SY187 ) @ SV42 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(328,plain,
! [SV86: mu,SV43: $i,SV122: mu] :
( ( ( ~ ( exists_in_world @ SV122 @ SV43 )
| ! [SY188: mu] :
( ~ ( exists_in_world @ SY188 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SY188 @ SV86 @ SV43 ) )
| ( member @ SY188 @ SV122 @ SV43 ) ) )
= $true )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(329,plain,
! [SV87: mu,SV45: $i,SV123: mu] :
( ( ( ~ ( exists_in_world @ SV123 @ SV45 )
| ! [SY189: mu] :
( ~ ( exists_in_world @ SY189 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SY189 @ SV87 @ SV45 ) )
| ( equal_set @ SY189 @ SV123 @ SV45 ) ) )
= $true )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(330,plain,
! [SV88: $i,SV46: $i,SV2: mu] :
( ( ( exists_in_world @ SV2 @ SV46 )
= $false )
| ( ( ~ ( rel_s4 @ SV46 @ SV88 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(331,plain,
! [SV55: mu,SV12: $i,SV94: mu] :
( ( ( ~ ( exists_in_world @ SV94 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( equal_set @ SV55 @ SV94 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SV94 @ SV12 ) ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(332,plain,
! [SV56: mu,SV13: $i,SV95: mu] :
( ( ( ~ ( exists_in_world @ SV95 @ SV13 ) )
= $true )
| ( ( ! [SY165: mu] :
( ~ ( exists_in_world @ SY165 @ SV13 )
| ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SY165 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SY165 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SY165 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SY165 ) @ SV13 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(333,plain,
! [SV57: mu,SV14: $i,SV96: mu] :
( ( ( ~ ( exists_in_world @ SV96 @ SV14 ) )
= $true )
| ( ( ! [SY166: mu] :
( ~ ( exists_in_world @ SY166 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SY166 @ SV14 ) )
| ( subset @ SV96 @ SY166 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(334,plain,
! [SV58: mu,SV15: $i,SV97: mu] :
( ( ( ~ ( exists_in_world @ SV97 @ SV15 ) )
= $true )
| ( ( ! [SY167: mu] :
( ~ ( exists_in_world @ SY167 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SY167 @ SV15 ) )
| ( qmltpeq @ SV58 @ SY167 @ SV15 ) ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(335,plain,
! [SV59: mu,SV16: $i,SV98: mu] :
( ( ( ~ ( exists_in_world @ SV98 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
| ( qmltpeq @ SV59 @ SV98 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SV59 @ SV98 @ SV16 )
| ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(336,plain,
! [SV60: mu,SV17: $i,SV99: mu] :
( ( ( ~ ( exists_in_world @ SV99 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) )
| ~ ( ~ ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) )
| ( member @ SV60 @ ( product @ SV99 ) @ SV17 ) ) ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(337,plain,
! [SV61: mu,SV18: $i,SV100: mu] :
( ( ( ~ ( exists_in_world @ SV100 @ SV18 ) )
= $true )
| ( ( ! [SY170: mu] :
( ~ ( exists_in_world @ SY170 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SY170 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SY170 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SY170 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SY170 ) @ SV18 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(338,plain,
! [SV63: mu,SV20: $i,SV101: mu] :
( ( ( ~ ( exists_in_world @ SV101 @ SV20 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV63 @ SV101 @ SV20 )
| ( qmltpeq @ ( product @ SV63 ) @ ( product @ SV101 ) @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV63 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(339,plain,
! [SV64: mu,SV21: $i,SV102: mu] :
( ( ( ~ ( exists_in_world @ SV102 @ SV21 ) )
= $true )
| ( ( ! [SY171: mu] :
( ~ ( exists_in_world @ SY171 @ SV21 )
| ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SY171 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SY171 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SY171 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SY171 @ SV102 ) @ SV21 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(340,plain,
! [SV65: mu,SV22: $i,SV103: mu] :
( ( ( ~ ( exists_in_world @ SV103 @ SV22 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV65 @ SV103 @ SV22 )
| ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SV103 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV65 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(341,plain,
! [SV66: mu,SV23: $i,SV104: mu] :
( ( ( ~ ( exists_in_world @ SV104 @ SV23 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV66 @ SV104 @ SV23 )
| ( qmltpeq @ SV104 @ SV66 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(342,plain,
! [SV93: $i,SV67: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV67 )
| ~ ( rel_s4 @ SV67 @ SV93 ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(343,plain,
! [SV68: mu,SV25: $i,SV105: mu] :
( ( ( ~ ( exists_in_world @ SV105 @ SV25 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV68 @ SV105 @ SV25 )
| ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SV105 ) @ SV25 ) )
= $true )
| ( ( exists_in_world @ SV68 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(344,plain,
! [SV69: mu,SV26: $i,SV106: mu] :
( ( ( ~ ( exists_in_world @ SV106 @ SV26 ) )
= $true )
| ( ( ! [SY172: mu] :
( ~ ( exists_in_world @ SY172 @ SV26 )
| ~ ( qmltpeq @ SV69 @ SV106 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SY172 ) @ ( union @ SV106 @ SY172 ) @ SV26 ) ) )
= $true )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(345,plain,
! [SV70: mu,SV27: $i,SV107: mu] :
( ( ( ~ ( exists_in_world @ SV107 @ SV27 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV70 @ SV107 @ SV27 )
| ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SV107 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(346,plain,
! [SV71: mu,SV28: $i,SV108: mu] :
( ( ( ~ ( exists_in_world @ SV108 @ SV28 ) )
= $true )
| ( ( ! [SY173: mu] :
( ~ ( exists_in_world @ SY173 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SY173 @ SV71 @ SV28 ) )
| ( subset @ SY173 @ SV108 @ SV28 ) ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(347,plain,
! [SV72: mu,SV29: $i,SV109: mu] :
( ( ( ~ ( exists_in_world @ SV109 @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
| ( subset @ SV72 @ SV109 @ SV29 ) )
| ~ ( ~ ( subset @ SV72 @ SV109 @ SV29 )
| ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 ) ) ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(348,plain,
! [SV73: mu,SV30: $i,SV110: mu] :
( ( ( ~ ( exists_in_world @ SV110 @ SV30 ) )
= $true )
| ( ( ! [SY174: mu] :
( ~ ( exists_in_world @ SY174 @ SV30 )
| ~ ( qmltpeq @ SV73 @ SV110 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SY174 ) @ ( difference @ SV110 @ SY174 ) @ SV30 ) ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(349,plain,
! [SV75: mu,SV32: $i,SV111: mu] :
( ( ( ~ ( exists_in_world @ SV111 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV75 @ SV111 @ SV32 )
| ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) )
| ~ ( ~ ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) )
| ( subset @ SV75 @ SV111 @ SV32 ) ) ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(350,plain,
! [SV76: mu,SV33: $i,SV112: mu] :
( ( ( ~ ( exists_in_world @ SV112 @ SV33 ) )
= $true )
| ( ( ! [SY177: mu] :
( ~ ( exists_in_world @ SY177 @ SV33 )
| ~ ( qmltpeq @ SV76 @ SV112 @ SV33 )
| ( qmltpeq @ ( difference @ SY177 @ SV76 ) @ ( difference @ SY177 @ SV112 ) @ SV33 ) ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(351,plain,
! [SV77: mu,SV34: $i,SV113: mu] :
( ( ( ~ ( exists_in_world @ SV113 @ SV34 ) )
= $true )
| ( ( ! [SY178: mu] :
( ~ ( exists_in_world @ SY178 @ SV34 )
| ~ ( qmltpeq @ SV77 @ SV113 @ SV34 )
| ( qmltpeq @ ( union @ SY178 @ SV77 ) @ ( union @ SY178 @ SV113 ) @ SV34 ) ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(352,plain,
! [SV78: mu,SV35: $i,SV114: mu] :
( ( ( ~ ( exists_in_world @ SV114 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
| ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SV114 ) @ SV35 ) ) ) )
= $true )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(353,plain,
! [SV79: mu,SV36: $i,SV115: mu] :
( ( ( ~ ( exists_in_world @ SV115 @ SV36 ) )
= $true )
| ( ( ! [SY181: mu] :
( ~ ( exists_in_world @ SY181 @ SV36 )
| ~ ( qmltpeq @ SV79 @ SV115 @ SV36 )
| ( qmltpeq @ ( intersection @ SY181 @ SV79 ) @ ( intersection @ SY181 @ SV115 ) @ SV36 ) ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(354,plain,
! [SV80: mu,SV37: $i,SV116: mu] :
( ( ( ~ ( exists_in_world @ SV116 @ SV37 ) )
= $true )
| ( ( ! [SY182: mu] :
( ~ ( exists_in_world @ SY182 @ SV37 )
| ~ ( qmltpeq @ SV80 @ SV116 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SY182 ) @ ( unordered_pair @ SV116 @ SY182 ) @ SV37 ) ) )
= $true )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(355,plain,
! [SV81: mu,SV38: $i,SV117: mu] :
( ( ( ~ ( exists_in_world @ SV117 @ SV38 ) )
= $true )
| ( ( ! [SY183: mu] :
( ~ ( exists_in_world @ SY183 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SY183 @ SV38 ) )
| ( member @ SV117 @ SY183 @ SV38 ) ) )
= $true )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(356,plain,
! [SV82: mu,SV39: $i,SV118: mu] :
( ( ( ~ ( exists_in_world @ SV118 @ SV39 ) )
= $true )
| ( ( ! [SY184: mu] :
( ~ ( exists_in_world @ SY184 @ SV39 )
| ~ ( qmltpeq @ SV82 @ SV118 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SY184 @ SV82 ) @ ( unordered_pair @ SY184 @ SV118 ) @ SV39 ) ) )
= $true )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(357,plain,
! [SV83: mu,SV40: $i,SV119: mu] :
( ( ( ~ ( exists_in_world @ SV119 @ SV40 ) )
= $true )
| ( ( ! [SY185: mu] :
( ~ ( exists_in_world @ SY185 @ SV40 )
| ~ ( qmltpeq @ SV83 @ SV119 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SY185 ) @ ( intersection @ SV119 @ SY185 ) @ SV40 ) ) )
= $true )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(358,plain,
! [SV84: mu,SV41: $i,SV120: mu] :
( ( ( ~ ( exists_in_world @ SV120 @ SV41 ) )
= $true )
| ( ( ! [SY186: mu] :
( ~ ( exists_in_world @ SY186 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SY186 @ SV41 ) )
| ( equal_set @ SV120 @ SY186 @ SV41 ) ) )
= $true )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(359,plain,
! [SV85: mu,SV42: $i,SV121: mu] :
( ( ( ~ ( exists_in_world @ SV121 @ SV42 ) )
= $true )
| ( ( ! [SY187: mu] :
( ~ ( exists_in_world @ SY187 @ SV42 )
| ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SY187 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SY187 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SY187 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SY187 ) @ SV42 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(360,plain,
! [SV86: mu,SV43: $i,SV122: mu] :
( ( ( ~ ( exists_in_world @ SV122 @ SV43 ) )
= $true )
| ( ( ! [SY188: mu] :
( ~ ( exists_in_world @ SY188 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SY188 @ SV86 @ SV43 ) )
| ( member @ SY188 @ SV122 @ SV43 ) ) )
= $true )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(361,plain,
! [SV87: mu,SV45: $i,SV123: mu] :
( ( ( ~ ( exists_in_world @ SV123 @ SV45 ) )
= $true )
| ( ( ! [SY189: mu] :
( ~ ( exists_in_world @ SY189 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SY189 @ SV87 @ SV45 ) )
| ( equal_set @ SY189 @ SV123 @ SV45 ) ) )
= $true )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(362,plain,
! [SV2: mu,SV88: $i,SV46: $i] :
( ( ( rel_s4 @ SV46 @ SV88 )
= $false )
| ( ( exists_in_world @ SV2 @ SV46 )
= $false )
| ( ( exists_in_world @ SV2 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(363,plain,
! [SV55: mu,SV12: $i,SV94: mu] :
( ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( ~ ( ~ ( ~ ( equal_set @ SV55 @ SV94 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SV94 @ SV12 ) ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(364,plain,
! [SV56: mu,SV13: $i,SV95: mu] :
( ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( ! [SY165: mu] :
( ~ ( exists_in_world @ SY165 @ SV13 )
| ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SY165 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SY165 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SY165 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SY165 ) @ SV13 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(365,plain,
! [SV57: mu,SV14: $i,SV96: mu] :
( ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( ! [SY166: mu] :
( ~ ( exists_in_world @ SY166 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SY166 @ SV14 ) )
| ( subset @ SV96 @ SY166 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(366,plain,
! [SV58: mu,SV15: $i,SV97: mu] :
( ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( ! [SY167: mu] :
( ~ ( exists_in_world @ SY167 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SY167 @ SV15 ) )
| ( qmltpeq @ SV58 @ SY167 @ SV15 ) ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(367,plain,
! [SV59: mu,SV16: $i,SV98: mu] :
( ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
| ( qmltpeq @ SV59 @ SV98 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SV59 @ SV98 @ SV16 )
| ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(368,plain,
! [SV60: mu,SV17: $i,SV99: mu] :
( ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) )
| ~ ( ~ ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) )
| ( member @ SV60 @ ( product @ SV99 ) @ SV17 ) ) ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(369,plain,
! [SV61: mu,SV18: $i,SV100: mu] :
( ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( ! [SY170: mu] :
( ~ ( exists_in_world @ SY170 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SY170 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SY170 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SY170 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SY170 ) @ SV18 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(370,plain,
! [SV63: mu,SV20: $i,SV101: mu] :
( ( ( exists_in_world @ SV101 @ SV20 )
= $false )
| ( ( ~ ( qmltpeq @ SV63 @ SV101 @ SV20 )
| ( qmltpeq @ ( product @ SV63 ) @ ( product @ SV101 ) @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV63 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(371,plain,
! [SV64: mu,SV21: $i,SV102: mu] :
( ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( ! [SY171: mu] :
( ~ ( exists_in_world @ SY171 @ SV21 )
| ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SY171 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SY171 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SY171 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SY171 @ SV102 ) @ SV21 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(372,plain,
! [SV65: mu,SV22: $i,SV103: mu] :
( ( ( exists_in_world @ SV103 @ SV22 )
= $false )
| ( ( ~ ( qmltpeq @ SV65 @ SV103 @ SV22 )
| ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SV103 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV65 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(373,plain,
! [SV66: mu,SV23: $i,SV104: mu] :
( ( ( exists_in_world @ SV104 @ SV23 )
= $false )
| ( ( ~ ( qmltpeq @ SV66 @ SV104 @ SV23 )
| ( qmltpeq @ SV104 @ SV66 @ SV23 ) )
= $true )
| ( ( exists_in_world @ SV66 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(374,plain,
! [SV93: $i,SV67: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV67 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV67 @ SV93 ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(375,plain,
! [SV68: mu,SV25: $i,SV105: mu] :
( ( ( exists_in_world @ SV105 @ SV25 )
= $false )
| ( ( ~ ( qmltpeq @ SV68 @ SV105 @ SV25 )
| ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SV105 ) @ SV25 ) )
= $true )
| ( ( exists_in_world @ SV68 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(376,plain,
! [SV69: mu,SV26: $i,SV106: mu] :
( ( ( exists_in_world @ SV106 @ SV26 )
= $false )
| ( ( ! [SY172: mu] :
( ~ ( exists_in_world @ SY172 @ SV26 )
| ~ ( qmltpeq @ SV69 @ SV106 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SY172 ) @ ( union @ SV106 @ SY172 ) @ SV26 ) ) )
= $true )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(377,plain,
! [SV70: mu,SV27: $i,SV107: mu] :
( ( ( exists_in_world @ SV107 @ SV27 )
= $false )
| ( ( ~ ( qmltpeq @ SV70 @ SV107 @ SV27 )
| ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SV107 ) @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(378,plain,
! [SV71: mu,SV28: $i,SV108: mu] :
( ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( ! [SY173: mu] :
( ~ ( exists_in_world @ SY173 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SY173 @ SV71 @ SV28 ) )
| ( subset @ SY173 @ SV108 @ SV28 ) ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(379,plain,
! [SV72: mu,SV29: $i,SV109: mu] :
( ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
| ( subset @ SV72 @ SV109 @ SV29 ) )
| ~ ( ~ ( subset @ SV72 @ SV109 @ SV29 )
| ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 ) ) ) )
= $true )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(380,plain,
! [SV73: mu,SV30: $i,SV110: mu] :
( ( ( exists_in_world @ SV110 @ SV30 )
= $false )
| ( ( ! [SY174: mu] :
( ~ ( exists_in_world @ SY174 @ SV30 )
| ~ ( qmltpeq @ SV73 @ SV110 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SY174 ) @ ( difference @ SV110 @ SY174 ) @ SV30 ) ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(381,plain,
! [SV75: mu,SV32: $i,SV111: mu] :
( ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV75 @ SV111 @ SV32 )
| ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) )
| ~ ( ~ ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) )
| ( subset @ SV75 @ SV111 @ SV32 ) ) ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(382,plain,
! [SV76: mu,SV33: $i,SV112: mu] :
( ( ( exists_in_world @ SV112 @ SV33 )
= $false )
| ( ( ! [SY177: mu] :
( ~ ( exists_in_world @ SY177 @ SV33 )
| ~ ( qmltpeq @ SV76 @ SV112 @ SV33 )
| ( qmltpeq @ ( difference @ SY177 @ SV76 ) @ ( difference @ SY177 @ SV112 ) @ SV33 ) ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(383,plain,
! [SV77: mu,SV34: $i,SV113: mu] :
( ( ( exists_in_world @ SV113 @ SV34 )
= $false )
| ( ( ! [SY178: mu] :
( ~ ( exists_in_world @ SY178 @ SV34 )
| ~ ( qmltpeq @ SV77 @ SV113 @ SV34 )
| ( qmltpeq @ ( union @ SY178 @ SV77 ) @ ( union @ SY178 @ SV113 ) @ SV34 ) ) )
= $true )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(384,plain,
! [SV78: mu,SV35: $i,SV114: mu] :
( ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
| ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SV114 ) @ SV35 ) ) ) )
= $true )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(385,plain,
! [SV79: mu,SV36: $i,SV115: mu] :
( ( ( exists_in_world @ SV115 @ SV36 )
= $false )
| ( ( ! [SY181: mu] :
( ~ ( exists_in_world @ SY181 @ SV36 )
| ~ ( qmltpeq @ SV79 @ SV115 @ SV36 )
| ( qmltpeq @ ( intersection @ SY181 @ SV79 ) @ ( intersection @ SY181 @ SV115 ) @ SV36 ) ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(386,plain,
! [SV80: mu,SV37: $i,SV116: mu] :
( ( ( exists_in_world @ SV116 @ SV37 )
= $false )
| ( ( ! [SY182: mu] :
( ~ ( exists_in_world @ SY182 @ SV37 )
| ~ ( qmltpeq @ SV80 @ SV116 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SY182 ) @ ( unordered_pair @ SV116 @ SY182 ) @ SV37 ) ) )
= $true )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(387,plain,
! [SV81: mu,SV38: $i,SV117: mu] :
( ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( ! [SY183: mu] :
( ~ ( exists_in_world @ SY183 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SY183 @ SV38 ) )
| ( member @ SV117 @ SY183 @ SV38 ) ) )
= $true )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(388,plain,
! [SV82: mu,SV39: $i,SV118: mu] :
( ( ( exists_in_world @ SV118 @ SV39 )
= $false )
| ( ( ! [SY184: mu] :
( ~ ( exists_in_world @ SY184 @ SV39 )
| ~ ( qmltpeq @ SV82 @ SV118 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SY184 @ SV82 ) @ ( unordered_pair @ SY184 @ SV118 ) @ SV39 ) ) )
= $true )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(389,plain,
! [SV83: mu,SV40: $i,SV119: mu] :
( ( ( exists_in_world @ SV119 @ SV40 )
= $false )
| ( ( ! [SY185: mu] :
( ~ ( exists_in_world @ SY185 @ SV40 )
| ~ ( qmltpeq @ SV83 @ SV119 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SY185 ) @ ( intersection @ SV119 @ SY185 ) @ SV40 ) ) )
= $true )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(390,plain,
! [SV84: mu,SV41: $i,SV120: mu] :
( ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( ! [SY186: mu] :
( ~ ( exists_in_world @ SY186 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SY186 @ SV41 ) )
| ( equal_set @ SV120 @ SY186 @ SV41 ) ) )
= $true )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(391,plain,
! [SV85: mu,SV42: $i,SV121: mu] :
( ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( ! [SY187: mu] :
( ~ ( exists_in_world @ SY187 @ SV42 )
| ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SY187 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SY187 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SY187 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SY187 ) @ SV42 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(392,plain,
! [SV86: mu,SV43: $i,SV122: mu] :
( ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( ! [SY188: mu] :
( ~ ( exists_in_world @ SY188 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SY188 @ SV86 @ SV43 ) )
| ( member @ SY188 @ SV122 @ SV43 ) ) )
= $true )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(393,plain,
! [SV87: mu,SV45: $i,SV123: mu] :
( ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( ! [SY189: mu] :
( ~ ( exists_in_world @ SY189 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SY189 @ SV87 @ SV45 ) )
| ( equal_set @ SY189 @ SV123 @ SV45 ) ) )
= $true )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(394,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( ~ ( equal_set @ SV55 @ SV94 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SV94 @ SV12 ) ) )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(395,plain,
! [SV95: mu,SV56: mu,SV13: $i,SV124: mu] :
( ( ( ~ ( exists_in_world @ SV124 @ SV13 )
| ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 ) ) ) )
= $true )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(396,plain,
! [SV96: mu,SV57: mu,SV14: $i,SV125: mu] :
( ( ( ~ ( exists_in_world @ SV125 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SV125 @ SV14 ) )
| ( subset @ SV96 @ SV125 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(397,plain,
! [SV97: mu,SV58: mu,SV15: $i,SV126: mu] :
( ( ( ~ ( exists_in_world @ SV126 @ SV15 )
| ~ ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) )
| ( qmltpeq @ SV58 @ SV126 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(398,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( ~ ( ~ ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
| ( qmltpeq @ SV59 @ SV98 @ SV16 ) )
| ~ ( ~ ( qmltpeq @ SV59 @ SV98 @ SV16 )
| ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 ) ) )
= $false )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(399,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( ~ ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) )
| ~ ( ~ ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) )
| ( member @ SV60 @ ( product @ SV99 ) @ SV17 ) ) )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(400,plain,
! [SV100: mu,SV61: mu,SV18: $i,SV127: mu] :
( ( ( ~ ( exists_in_world @ SV127 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 ) ) ) )
= $true )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(401,plain,
! [SV20: $i,SV101: mu,SV63: mu] :
( ( ( ~ ( qmltpeq @ SV63 @ SV101 @ SV20 ) )
= $true )
| ( ( qmltpeq @ ( product @ SV63 ) @ ( product @ SV101 ) @ SV20 )
= $true )
| ( ( exists_in_world @ SV101 @ SV20 )
= $false )
| ( ( exists_in_world @ SV63 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(402,plain,
! [SV102: mu,SV64: mu,SV21: $i,SV128: mu] :
( ( ( ~ ( exists_in_world @ SV128 @ SV21 )
| ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 ) ) ) )
= $true )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(403,plain,
! [SV22: $i,SV103: mu,SV65: mu] :
( ( ( ~ ( qmltpeq @ SV65 @ SV103 @ SV22 ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SV103 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV103 @ SV22 )
= $false )
| ( ( exists_in_world @ SV65 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(404,plain,
! [SV23: $i,SV104: mu,SV66: mu] :
( ( ( ~ ( qmltpeq @ SV66 @ SV104 @ SV23 ) )
= $true )
| ( ( qmltpeq @ SV104 @ SV66 @ SV23 )
= $true )
| ( ( exists_in_world @ SV104 @ SV23 )
= $false )
| ( ( exists_in_world @ SV66 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(405,plain,
! [SV93: $i,SV67: $i,SV24: $i] :
( ( ( rel_s4 @ SV24 @ SV67 )
= $false )
| ( ( ~ ( rel_s4 @ SV67 @ SV93 ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(406,plain,
! [SV25: $i,SV105: mu,SV68: mu] :
( ( ( ~ ( qmltpeq @ SV68 @ SV105 @ SV25 ) )
= $true )
| ( ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SV105 ) @ SV25 )
= $true )
| ( ( exists_in_world @ SV105 @ SV25 )
= $false )
| ( ( exists_in_world @ SV68 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(407,plain,
! [SV106: mu,SV69: mu,SV26: $i,SV129: mu] :
( ( ( ~ ( exists_in_world @ SV129 @ SV26 )
| ~ ( qmltpeq @ SV69 @ SV106 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SV129 ) @ ( union @ SV106 @ SV129 ) @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV106 @ SV26 )
= $false )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(408,plain,
! [SV27: $i,SV107: mu,SV70: mu] :
( ( ( ~ ( qmltpeq @ SV70 @ SV107 @ SV27 ) )
= $true )
| ( ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SV107 ) @ SV27 )
= $true )
| ( ( exists_in_world @ SV107 @ SV27 )
= $false )
| ( ( exists_in_world @ SV70 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(409,plain,
! [SV108: mu,SV71: mu,SV28: $i,SV130: mu] :
( ( ( ~ ( exists_in_world @ SV130 @ SV28 )
| ~ ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SV130 @ SV71 @ SV28 ) )
| ( subset @ SV130 @ SV108 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(410,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( ~ ( ~ ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
| ( subset @ SV72 @ SV109 @ SV29 ) )
| ~ ( ~ ( subset @ SV72 @ SV109 @ SV29 )
| ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 ) ) )
= $false )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(411,plain,
! [SV110: mu,SV73: mu,SV30: $i,SV131: mu] :
( ( ( ~ ( exists_in_world @ SV131 @ SV30 )
| ~ ( qmltpeq @ SV73 @ SV110 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SV131 ) @ ( difference @ SV110 @ SV131 ) @ SV30 ) )
= $true )
| ( ( exists_in_world @ SV110 @ SV30 )
= $false )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(412,plain,
! [SV32: $i,SV111: mu,SV75: mu] :
( ( ( ~ ( ~ ( subset @ SV75 @ SV111 @ SV32 )
| ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) )
| ~ ( ~ ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) )
| ( subset @ SV75 @ SV111 @ SV32 ) ) )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(413,plain,
! [SV112: mu,SV76: mu,SV33: $i,SV132: mu] :
( ( ( ~ ( exists_in_world @ SV132 @ SV33 )
| ~ ( qmltpeq @ SV76 @ SV112 @ SV33 )
| ( qmltpeq @ ( difference @ SV132 @ SV76 ) @ ( difference @ SV132 @ SV112 ) @ SV33 ) )
= $true )
| ( ( exists_in_world @ SV112 @ SV33 )
= $false )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(414,plain,
! [SV113: mu,SV77: mu,SV34: $i,SV133: mu] :
( ( ( ~ ( exists_in_world @ SV133 @ SV34 )
| ~ ( qmltpeq @ SV77 @ SV113 @ SV34 )
| ( qmltpeq @ ( union @ SV133 @ SV77 ) @ ( union @ SV133 @ SV113 ) @ SV34 ) )
= $true )
| ( ( exists_in_world @ SV113 @ SV34 )
= $false )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(415,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( ~ ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
| ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
| ~ ( ~ ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SV114 ) @ SV35 ) ) )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(416,plain,
! [SV115: mu,SV79: mu,SV36: $i,SV134: mu] :
( ( ( ~ ( exists_in_world @ SV134 @ SV36 )
| ~ ( qmltpeq @ SV79 @ SV115 @ SV36 )
| ( qmltpeq @ ( intersection @ SV134 @ SV79 ) @ ( intersection @ SV134 @ SV115 ) @ SV36 ) )
= $true )
| ( ( exists_in_world @ SV115 @ SV36 )
= $false )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(417,plain,
! [SV116: mu,SV80: mu,SV37: $i,SV135: mu] :
( ( ( ~ ( exists_in_world @ SV135 @ SV37 )
| ~ ( qmltpeq @ SV80 @ SV116 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SV135 ) @ ( unordered_pair @ SV116 @ SV135 ) @ SV37 ) )
= $true )
| ( ( exists_in_world @ SV116 @ SV37 )
= $false )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(418,plain,
! [SV117: mu,SV81: mu,SV38: $i,SV136: mu] :
( ( ( ~ ( exists_in_world @ SV136 @ SV38 )
| ~ ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SV136 @ SV38 ) )
| ( member @ SV117 @ SV136 @ SV38 ) )
= $true )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(419,plain,
! [SV118: mu,SV82: mu,SV39: $i,SV137: mu] :
( ( ( ~ ( exists_in_world @ SV137 @ SV39 )
| ~ ( qmltpeq @ SV82 @ SV118 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SV137 @ SV82 ) @ ( unordered_pair @ SV137 @ SV118 ) @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV118 @ SV39 )
= $false )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(420,plain,
! [SV119: mu,SV83: mu,SV40: $i,SV138: mu] :
( ( ( ~ ( exists_in_world @ SV138 @ SV40 )
| ~ ( qmltpeq @ SV83 @ SV119 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SV138 ) @ ( intersection @ SV119 @ SV138 ) @ SV40 ) )
= $true )
| ( ( exists_in_world @ SV119 @ SV40 )
= $false )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(421,plain,
! [SV120: mu,SV84: mu,SV41: $i,SV139: mu] :
( ( ( ~ ( exists_in_world @ SV139 @ SV41 )
| ~ ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SV139 @ SV41 ) )
| ( equal_set @ SV120 @ SV139 @ SV41 ) )
= $true )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(422,plain,
! [SV121: mu,SV85: mu,SV42: $i,SV140: mu] :
( ( ( ~ ( exists_in_world @ SV140 @ SV42 )
| ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 ) ) ) )
= $true )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(423,plain,
! [SV122: mu,SV86: mu,SV43: $i,SV141: mu] :
( ( ( ~ ( exists_in_world @ SV141 @ SV43 )
| ~ ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SV141 @ SV86 @ SV43 ) )
| ( member @ SV141 @ SV122 @ SV43 ) )
= $true )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(424,plain,
! [SV123: mu,SV87: mu,SV45: $i,SV142: mu] :
( ( ( ~ ( exists_in_world @ SV142 @ SV45 )
| ~ ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SV142 @ SV87 @ SV45 ) )
| ( equal_set @ SV142 @ SV123 @ SV45 ) )
= $true )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(425,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( ~ ( equal_set @ SV55 @ SV94 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) ) )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(426,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SV94 @ SV12 ) ) )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(427,plain,
! [SV95: mu,SV56: mu,SV13: $i,SV124: mu] :
( ( ( ~ ( exists_in_world @ SV124 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 ) ) ) )
= $true )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(428,plain,
! [SV96: mu,SV57: mu,SV14: $i,SV125: mu] :
( ( ( ~ ( exists_in_world @ SV125 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SV125 @ SV14 ) )
| ( subset @ SV96 @ SV125 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(429,plain,
! [SV97: mu,SV58: mu,SV15: $i,SV126: mu] :
( ( ( ~ ( exists_in_world @ SV126 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) )
| ( qmltpeq @ SV58 @ SV126 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(430,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( ~ ( ~ ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
| ( qmltpeq @ SV59 @ SV98 @ SV16 ) ) )
= $false )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(431,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV59 @ SV98 @ SV16 )
| ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 ) ) )
= $false )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(432,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( ~ ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) ) )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(433,plain,
! [SV60: mu,SV99: mu,SV17: $i] :
( ( ( ~ ( ~ ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) )
| ( member @ SV60 @ ( product @ SV99 ) @ SV17 ) ) )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(434,plain,
! [SV100: mu,SV61: mu,SV18: $i,SV127: mu] :
( ( ( ~ ( exists_in_world @ SV127 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 ) ) ) )
= $true )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(435,plain,
! [SV20: $i,SV101: mu,SV63: mu] :
( ( ( qmltpeq @ SV63 @ SV101 @ SV20 )
= $false )
| ( ( qmltpeq @ ( product @ SV63 ) @ ( product @ SV101 ) @ SV20 )
= $true )
| ( ( exists_in_world @ SV101 @ SV20 )
= $false )
| ( ( exists_in_world @ SV63 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(436,plain,
! [SV102: mu,SV64: mu,SV21: $i,SV128: mu] :
( ( ( ~ ( exists_in_world @ SV128 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 ) ) ) )
= $true )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(437,plain,
! [SV22: $i,SV103: mu,SV65: mu] :
( ( ( qmltpeq @ SV65 @ SV103 @ SV22 )
= $false )
| ( ( qmltpeq @ ( singleton @ SV65 ) @ ( singleton @ SV103 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV103 @ SV22 )
= $false )
| ( ( exists_in_world @ SV65 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(438,plain,
! [SV23: $i,SV104: mu,SV66: mu] :
( ( ( qmltpeq @ SV66 @ SV104 @ SV23 )
= $false )
| ( ( qmltpeq @ SV104 @ SV66 @ SV23 )
= $true )
| ( ( exists_in_world @ SV104 @ SV23 )
= $false )
| ( ( exists_in_world @ SV66 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(439,plain,
! [SV24: $i,SV93: $i,SV67: $i] :
( ( ( rel_s4 @ SV67 @ SV93 )
= $false )
| ( ( rel_s4 @ SV24 @ SV67 )
= $false )
| ( ( rel_s4 @ SV24 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(440,plain,
! [SV25: $i,SV105: mu,SV68: mu] :
( ( ( qmltpeq @ SV68 @ SV105 @ SV25 )
= $false )
| ( ( qmltpeq @ ( power_set @ SV68 ) @ ( power_set @ SV105 ) @ SV25 )
= $true )
| ( ( exists_in_world @ SV105 @ SV25 )
= $false )
| ( ( exists_in_world @ SV68 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(441,plain,
! [SV106: mu,SV69: mu,SV26: $i,SV129: mu] :
( ( ( ~ ( exists_in_world @ SV129 @ SV26 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV69 @ SV106 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SV129 ) @ ( union @ SV106 @ SV129 ) @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV106 @ SV26 )
= $false )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(442,plain,
! [SV27: $i,SV107: mu,SV70: mu] :
( ( ( qmltpeq @ SV70 @ SV107 @ SV27 )
= $false )
| ( ( qmltpeq @ ( sum @ SV70 ) @ ( sum @ SV107 ) @ SV27 )
= $true )
| ( ( exists_in_world @ SV107 @ SV27 )
= $false )
| ( ( exists_in_world @ SV70 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(443,plain,
! [SV108: mu,SV71: mu,SV28: $i,SV130: mu] :
( ( ( ~ ( exists_in_world @ SV130 @ SV28 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SV130 @ SV71 @ SV28 ) )
| ( subset @ SV130 @ SV108 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(444,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( ~ ( ~ ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
| ( subset @ SV72 @ SV109 @ SV29 ) ) )
= $false )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(445,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( ~ ( ~ ( subset @ SV72 @ SV109 @ SV29 )
| ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 ) ) )
= $false )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(446,plain,
! [SV110: mu,SV73: mu,SV30: $i,SV131: mu] :
( ( ( ~ ( exists_in_world @ SV131 @ SV30 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV73 @ SV110 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SV131 ) @ ( difference @ SV110 @ SV131 ) @ SV30 ) )
= $true )
| ( ( exists_in_world @ SV110 @ SV30 )
= $false )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(447,plain,
! [SV32: $i,SV111: mu,SV75: mu] :
( ( ( ~ ( ~ ( subset @ SV75 @ SV111 @ SV32 )
| ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) ) )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(448,plain,
! [SV111: mu,SV75: mu,SV32: $i] :
( ( ( ~ ( ~ ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) )
| ( subset @ SV75 @ SV111 @ SV32 ) ) )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(449,plain,
! [SV112: mu,SV76: mu,SV33: $i,SV132: mu] :
( ( ( ~ ( exists_in_world @ SV132 @ SV33 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV76 @ SV112 @ SV33 )
| ( qmltpeq @ ( difference @ SV132 @ SV76 ) @ ( difference @ SV132 @ SV112 ) @ SV33 ) )
= $true )
| ( ( exists_in_world @ SV112 @ SV33 )
= $false )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(450,plain,
! [SV113: mu,SV77: mu,SV34: $i,SV133: mu] :
( ( ( ~ ( exists_in_world @ SV133 @ SV34 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV77 @ SV113 @ SV34 )
| ( qmltpeq @ ( union @ SV133 @ SV77 ) @ ( union @ SV133 @ SV113 ) @ SV34 ) )
= $true )
| ( ( exists_in_world @ SV113 @ SV34 )
= $false )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(451,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( ~ ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
| ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(452,plain,
! [SV78: mu,SV114: mu,SV35: $i] :
( ( ( ~ ( ~ ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SV114 ) @ SV35 ) ) )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(453,plain,
! [SV115: mu,SV79: mu,SV36: $i,SV134: mu] :
( ( ( ~ ( exists_in_world @ SV134 @ SV36 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV79 @ SV115 @ SV36 )
| ( qmltpeq @ ( intersection @ SV134 @ SV79 ) @ ( intersection @ SV134 @ SV115 ) @ SV36 ) )
= $true )
| ( ( exists_in_world @ SV115 @ SV36 )
= $false )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(454,plain,
! [SV116: mu,SV80: mu,SV37: $i,SV135: mu] :
( ( ( ~ ( exists_in_world @ SV135 @ SV37 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV80 @ SV116 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SV135 ) @ ( unordered_pair @ SV116 @ SV135 ) @ SV37 ) )
= $true )
| ( ( exists_in_world @ SV116 @ SV37 )
= $false )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(455,plain,
! [SV117: mu,SV81: mu,SV38: $i,SV136: mu] :
( ( ( ~ ( exists_in_world @ SV136 @ SV38 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SV136 @ SV38 ) )
| ( member @ SV117 @ SV136 @ SV38 ) )
= $true )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(456,plain,
! [SV118: mu,SV82: mu,SV39: $i,SV137: mu] :
( ( ( ~ ( exists_in_world @ SV137 @ SV39 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV82 @ SV118 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SV137 @ SV82 ) @ ( unordered_pair @ SV137 @ SV118 ) @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV118 @ SV39 )
= $false )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(457,plain,
! [SV119: mu,SV83: mu,SV40: $i,SV138: mu] :
( ( ( ~ ( exists_in_world @ SV138 @ SV40 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV83 @ SV119 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SV138 ) @ ( intersection @ SV119 @ SV138 ) @ SV40 ) )
= $true )
| ( ( exists_in_world @ SV119 @ SV40 )
= $false )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(458,plain,
! [SV120: mu,SV84: mu,SV41: $i,SV139: mu] :
( ( ( ~ ( exists_in_world @ SV139 @ SV41 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SV139 @ SV41 ) )
| ( equal_set @ SV120 @ SV139 @ SV41 ) )
= $true )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(459,plain,
! [SV121: mu,SV85: mu,SV42: $i,SV140: mu] :
( ( ( ~ ( exists_in_world @ SV140 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 ) ) ) )
= $true )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(460,plain,
! [SV122: mu,SV86: mu,SV43: $i,SV141: mu] :
( ( ( ~ ( exists_in_world @ SV141 @ SV43 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SV141 @ SV86 @ SV43 ) )
| ( member @ SV141 @ SV122 @ SV43 ) )
= $true )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(461,plain,
! [SV123: mu,SV87: mu,SV45: $i,SV142: mu] :
( ( ( ~ ( exists_in_world @ SV142 @ SV45 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SV142 @ SV87 @ SV45 ) )
| ( equal_set @ SV142 @ SV123 @ SV45 ) )
= $true )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(462,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( equal_set @ SV55 @ SV94 @ SV12 )
| ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(463,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
| ( equal_set @ SV55 @ SV94 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(464,plain,
! [SV95: mu,SV56: mu,SV13: $i,SV124: mu] :
( ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 ) ) ) )
= $true )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(465,plain,
! [SV96: mu,SV57: mu,SV14: $i,SV125: mu] :
( ( ( exists_in_world @ SV125 @ SV14 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SV125 @ SV14 ) )
| ( subset @ SV96 @ SV125 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(466,plain,
! [SV97: mu,SV58: mu,SV15: $i,SV126: mu] :
( ( ( exists_in_world @ SV126 @ SV15 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) )
| ( qmltpeq @ SV58 @ SV126 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(467,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( ~ ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
| ( qmltpeq @ SV59 @ SV98 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(468,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( ~ ( qmltpeq @ SV59 @ SV98 @ SV16 )
| ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(469,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(470,plain,
! [SV60: mu,SV99: mu,SV17: $i] :
( ( ( ~ ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) )
| ( member @ SV60 @ ( product @ SV99 ) @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(471,plain,
! [SV100: mu,SV61: mu,SV18: $i,SV127: mu] :
( ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 ) ) ) )
= $true )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(472,plain,
! [SV102: mu,SV64: mu,SV21: $i,SV128: mu] :
( ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 ) ) ) )
= $true )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(473,plain,
! [SV106: mu,SV69: mu,SV26: $i,SV129: mu] :
( ( ( exists_in_world @ SV129 @ SV26 )
= $false )
| ( ( ~ ( qmltpeq @ SV69 @ SV106 @ SV26 )
| ( qmltpeq @ ( union @ SV69 @ SV129 ) @ ( union @ SV106 @ SV129 ) @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV106 @ SV26 )
= $false )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(474,plain,
! [SV108: mu,SV71: mu,SV28: $i,SV130: mu] :
( ( ( exists_in_world @ SV130 @ SV28 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SV130 @ SV71 @ SV28 ) )
| ( subset @ SV130 @ SV108 @ SV28 ) )
= $true )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(475,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( ~ ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
| ( subset @ SV72 @ SV109 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(476,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( ~ ( subset @ SV72 @ SV109 @ SV29 )
| ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(477,plain,
! [SV110: mu,SV73: mu,SV30: $i,SV131: mu] :
( ( ( exists_in_world @ SV131 @ SV30 )
= $false )
| ( ( ~ ( qmltpeq @ SV73 @ SV110 @ SV30 )
| ( qmltpeq @ ( difference @ SV73 @ SV131 ) @ ( difference @ SV110 @ SV131 ) @ SV30 ) )
= $true )
| ( ( exists_in_world @ SV110 @ SV30 )
= $false )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(478,plain,
! [SV32: $i,SV111: mu,SV75: mu] :
( ( ( ~ ( subset @ SV75 @ SV111 @ SV32 )
| ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(479,plain,
! [SV111: mu,SV75: mu,SV32: $i] :
( ( ( ~ ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) )
| ( subset @ SV75 @ SV111 @ SV32 ) )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(480,plain,
! [SV112: mu,SV76: mu,SV33: $i,SV132: mu] :
( ( ( exists_in_world @ SV132 @ SV33 )
= $false )
| ( ( ~ ( qmltpeq @ SV76 @ SV112 @ SV33 )
| ( qmltpeq @ ( difference @ SV132 @ SV76 ) @ ( difference @ SV132 @ SV112 ) @ SV33 ) )
= $true )
| ( ( exists_in_world @ SV112 @ SV33 )
= $false )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(481,plain,
! [SV113: mu,SV77: mu,SV34: $i,SV133: mu] :
( ( ( exists_in_world @ SV133 @ SV34 )
= $false )
| ( ( ~ ( qmltpeq @ SV77 @ SV113 @ SV34 )
| ( qmltpeq @ ( union @ SV133 @ SV77 ) @ ( union @ SV133 @ SV113 ) @ SV34 ) )
= $true )
| ( ( exists_in_world @ SV113 @ SV34 )
= $false )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(482,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
| ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(483,plain,
! [SV78: mu,SV114: mu,SV35: $i] :
( ( ( ~ ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) )
| ( member @ SV78 @ ( sum @ SV114 ) @ SV35 ) )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(484,plain,
! [SV115: mu,SV79: mu,SV36: $i,SV134: mu] :
( ( ( exists_in_world @ SV134 @ SV36 )
= $false )
| ( ( ~ ( qmltpeq @ SV79 @ SV115 @ SV36 )
| ( qmltpeq @ ( intersection @ SV134 @ SV79 ) @ ( intersection @ SV134 @ SV115 ) @ SV36 ) )
= $true )
| ( ( exists_in_world @ SV115 @ SV36 )
= $false )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(485,plain,
! [SV116: mu,SV80: mu,SV37: $i,SV135: mu] :
( ( ( exists_in_world @ SV135 @ SV37 )
= $false )
| ( ( ~ ( qmltpeq @ SV80 @ SV116 @ SV37 )
| ( qmltpeq @ ( unordered_pair @ SV80 @ SV135 ) @ ( unordered_pair @ SV116 @ SV135 ) @ SV37 ) )
= $true )
| ( ( exists_in_world @ SV116 @ SV37 )
= $false )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(486,plain,
! [SV117: mu,SV81: mu,SV38: $i,SV136: mu] :
( ( ( exists_in_world @ SV136 @ SV38 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SV136 @ SV38 ) )
| ( member @ SV117 @ SV136 @ SV38 ) )
= $true )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(487,plain,
! [SV118: mu,SV82: mu,SV39: $i,SV137: mu] :
( ( ( exists_in_world @ SV137 @ SV39 )
= $false )
| ( ( ~ ( qmltpeq @ SV82 @ SV118 @ SV39 )
| ( qmltpeq @ ( unordered_pair @ SV137 @ SV82 ) @ ( unordered_pair @ SV137 @ SV118 ) @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV118 @ SV39 )
= $false )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(488,plain,
! [SV119: mu,SV83: mu,SV40: $i,SV138: mu] :
( ( ( exists_in_world @ SV138 @ SV40 )
= $false )
| ( ( ~ ( qmltpeq @ SV83 @ SV119 @ SV40 )
| ( qmltpeq @ ( intersection @ SV83 @ SV138 ) @ ( intersection @ SV119 @ SV138 ) @ SV40 ) )
= $true )
| ( ( exists_in_world @ SV119 @ SV40 )
= $false )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(489,plain,
! [SV120: mu,SV84: mu,SV41: $i,SV139: mu] :
( ( ( exists_in_world @ SV139 @ SV41 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SV139 @ SV41 ) )
| ( equal_set @ SV120 @ SV139 @ SV41 ) )
= $true )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(490,plain,
! [SV121: mu,SV85: mu,SV42: $i,SV140: mu] :
( ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 ) ) ) )
= $true )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(491,plain,
! [SV122: mu,SV86: mu,SV43: $i,SV141: mu] :
( ( ( exists_in_world @ SV141 @ SV43 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SV141 @ SV86 @ SV43 ) )
| ( member @ SV141 @ SV122 @ SV43 ) )
= $true )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(492,plain,
! [SV123: mu,SV87: mu,SV45: $i,SV142: mu] :
( ( ( exists_in_world @ SV142 @ SV45 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SV142 @ SV87 @ SV45 ) )
| ( equal_set @ SV142 @ SV123 @ SV45 ) )
= $true )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(493,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( equal_set @ SV55 @ SV94 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(494,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
= $true )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(495,plain,
! [SV13: $i,SV124: mu,SV95: mu,SV56: mu] :
( ( ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 ) ) )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(496,plain,
! [SV125: mu,SV14: $i,SV96: mu,SV57: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SV125 @ SV14 ) ) )
= $true )
| ( ( subset @ SV96 @ SV125 @ SV14 )
= $true )
| ( ( exists_in_world @ SV125 @ SV14 )
= $false )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(497,plain,
! [SV126: mu,SV15: $i,SV97: mu,SV58: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) ) )
= $true )
| ( ( qmltpeq @ SV58 @ SV126 @ SV15 )
= $true )
| ( ( exists_in_world @ SV126 @ SV15 )
= $false )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(498,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( ~ ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 ) )
= $true )
| ( ( qmltpeq @ SV59 @ SV98 @ SV16 )
= $true )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(499,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( ~ ( qmltpeq @ SV59 @ SV98 @ SV16 ) )
= $true )
| ( ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
= $true )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(500,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( member @ SV60 @ ( product @ SV99 ) @ SV17 ) )
= $true )
| ( ( ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(501,plain,
! [SV60: mu,SV99: mu,SV17: $i] :
( ( ( ~ ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) ) )
= $true )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(502,plain,
! [SV18: $i,SV127: mu,SV100: mu,SV61: mu] :
( ( ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 ) ) )
= $false )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(503,plain,
! [SV21: $i,SV102: mu,SV128: mu,SV64: mu] :
( ( ( ~ ( ~ ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 ) ) )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(504,plain,
! [SV129: mu,SV26: $i,SV106: mu,SV69: mu] :
( ( ( ~ ( qmltpeq @ SV69 @ SV106 @ SV26 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV69 @ SV129 ) @ ( union @ SV106 @ SV129 ) @ SV26 )
= $true )
| ( ( exists_in_world @ SV129 @ SV26 )
= $false )
| ( ( exists_in_world @ SV106 @ SV26 )
= $false )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(505,plain,
! [SV130: mu,SV28: $i,SV108: mu,SV71: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SV130 @ SV71 @ SV28 ) ) )
= $true )
| ( ( subset @ SV130 @ SV108 @ SV28 )
= $true )
| ( ( exists_in_world @ SV130 @ SV28 )
= $false )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(506,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( ~ ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 ) )
= $true )
| ( ( subset @ SV72 @ SV109 @ SV29 )
= $true )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(507,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( ~ ( subset @ SV72 @ SV109 @ SV29 ) )
= $true )
| ( ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
= $true )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(508,plain,
! [SV131: mu,SV30: $i,SV110: mu,SV73: mu] :
( ( ( ~ ( qmltpeq @ SV73 @ SV110 @ SV30 ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV73 @ SV131 ) @ ( difference @ SV110 @ SV131 ) @ SV30 )
= $true )
| ( ( exists_in_world @ SV131 @ SV30 )
= $false )
| ( ( exists_in_world @ SV110 @ SV30 )
= $false )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(509,plain,
! [SV32: $i,SV111: mu,SV75: mu] :
( ( ( ~ ( subset @ SV75 @ SV111 @ SV32 ) )
= $true )
| ( ( ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(510,plain,
! [SV111: mu,SV75: mu,SV32: $i] :
( ( ( ~ ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) ) )
= $true )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(511,plain,
! [SV132: mu,SV33: $i,SV112: mu,SV76: mu] :
( ( ( ~ ( qmltpeq @ SV76 @ SV112 @ SV33 ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV132 @ SV76 ) @ ( difference @ SV132 @ SV112 ) @ SV33 )
= $true )
| ( ( exists_in_world @ SV132 @ SV33 )
= $false )
| ( ( exists_in_world @ SV112 @ SV33 )
= $false )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(512,plain,
! [SV133: mu,SV34: $i,SV113: mu,SV77: mu] :
( ( ( ~ ( qmltpeq @ SV77 @ SV113 @ SV34 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV133 @ SV77 ) @ ( union @ SV133 @ SV113 ) @ SV34 )
= $true )
| ( ( exists_in_world @ SV133 @ SV34 )
= $false )
| ( ( exists_in_world @ SV113 @ SV34 )
= $false )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(513,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( member @ SV78 @ ( sum @ SV114 ) @ SV35 ) )
= $true )
| ( ( ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(514,plain,
! [SV78: mu,SV114: mu,SV35: $i] :
( ( ( ~ ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) ) )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(515,plain,
! [SV134: mu,SV36: $i,SV115: mu,SV79: mu] :
( ( ( ~ ( qmltpeq @ SV79 @ SV115 @ SV36 ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV134 @ SV79 ) @ ( intersection @ SV134 @ SV115 ) @ SV36 )
= $true )
| ( ( exists_in_world @ SV134 @ SV36 )
= $false )
| ( ( exists_in_world @ SV115 @ SV36 )
= $false )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(516,plain,
! [SV135: mu,SV37: $i,SV116: mu,SV80: mu] :
( ( ( ~ ( qmltpeq @ SV80 @ SV116 @ SV37 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV80 @ SV135 ) @ ( unordered_pair @ SV116 @ SV135 ) @ SV37 )
= $true )
| ( ( exists_in_world @ SV135 @ SV37 )
= $false )
| ( ( exists_in_world @ SV116 @ SV37 )
= $false )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(517,plain,
! [SV136: mu,SV38: $i,SV117: mu,SV81: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SV136 @ SV38 ) ) )
= $true )
| ( ( member @ SV117 @ SV136 @ SV38 )
= $true )
| ( ( exists_in_world @ SV136 @ SV38 )
= $false )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(518,plain,
! [SV137: mu,SV39: $i,SV118: mu,SV82: mu] :
( ( ( ~ ( qmltpeq @ SV82 @ SV118 @ SV39 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV137 @ SV82 ) @ ( unordered_pair @ SV137 @ SV118 ) @ SV39 )
= $true )
| ( ( exists_in_world @ SV137 @ SV39 )
= $false )
| ( ( exists_in_world @ SV118 @ SV39 )
= $false )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(519,plain,
! [SV138: mu,SV40: $i,SV119: mu,SV83: mu] :
( ( ( ~ ( qmltpeq @ SV83 @ SV119 @ SV40 ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV83 @ SV138 ) @ ( intersection @ SV119 @ SV138 ) @ SV40 )
= $true )
| ( ( exists_in_world @ SV138 @ SV40 )
= $false )
| ( ( exists_in_world @ SV119 @ SV40 )
= $false )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(520,plain,
! [SV139: mu,SV41: $i,SV120: mu,SV84: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SV139 @ SV41 ) ) )
= $true )
| ( ( equal_set @ SV120 @ SV139 @ SV41 )
= $true )
| ( ( exists_in_world @ SV139 @ SV41 )
= $false )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(521,plain,
! [SV42: $i,SV140: mu,SV121: mu,SV85: mu] :
( ( ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 ) ) )
= $false )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(522,plain,
! [SV141: mu,SV43: $i,SV122: mu,SV86: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SV141 @ SV86 @ SV43 ) ) )
= $true )
| ( ( member @ SV141 @ SV122 @ SV43 )
= $true )
| ( ( exists_in_world @ SV141 @ SV43 )
= $false )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(523,plain,
! [SV142: mu,SV45: $i,SV123: mu,SV87: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SV142 @ SV87 @ SV45 ) ) )
= $true )
| ( ( equal_set @ SV142 @ SV123 @ SV45 )
= $true )
| ( ( exists_in_world @ SV142 @ SV45 )
= $false )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(524,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(525,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) ) )
= $false )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(526,plain,
! [SV13: $i,SV124: mu,SV95: mu,SV56: mu] :
( ( ( ~ ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) ) )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(527,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 ) ) )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(528,plain,
! [SV125: mu,SV14: $i,SV96: mu,SV57: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SV125 @ SV14 ) ) )
= $false )
| ( ( subset @ SV96 @ SV125 @ SV14 )
= $true )
| ( ( exists_in_world @ SV125 @ SV14 )
= $false )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(529,plain,
! [SV126: mu,SV15: $i,SV97: mu,SV58: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) ) )
= $false )
| ( ( qmltpeq @ SV58 @ SV126 @ SV15 )
= $true )
| ( ( exists_in_world @ SV126 @ SV15 )
= $false )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(530,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
= $false )
| ( ( qmltpeq @ SV59 @ SV98 @ SV16 )
= $true )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(531,plain,
! [SV16: $i,SV98: mu,SV59: mu] :
( ( ( qmltpeq @ SV59 @ SV98 @ SV16 )
= $false )
| ( ( member @ SV59 @ ( singleton @ SV98 ) @ SV16 )
= $true )
| ( ( exists_in_world @ SV98 @ SV16 )
= $false )
| ( ( exists_in_world @ SV59 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(532,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $false )
| ( ( ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SV17 )
| ~ ( member @ SY168 @ SV99 @ SV17 )
| ( member @ SV60 @ SY168 @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(533,plain,
! [SV60: mu,SV99: mu,SV17: $i] :
( ( ( ! [SY169: mu] :
( ~ ( exists_in_world @ SY169 @ SV17 )
| ~ ( member @ SY169 @ SV99 @ SV17 )
| ( member @ SV60 @ SY169 @ SV17 ) ) )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(534,plain,
! [SV18: $i,SV127: mu,SV100: mu,SV61: mu] :
( ( ( ~ ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) ) )
= $false )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(535,plain,
! [SV127: mu,SV18: $i,SV100: mu,SV61: mu] :
( ( ( ~ ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 ) ) )
= $false )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(536,plain,
! [SV21: $i,SV102: mu,SV128: mu,SV64: mu] :
( ( ( ~ ( ~ ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) ) )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(537,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ( ~ ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 ) ) )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(538,plain,
! [SV129: mu,SV26: $i,SV106: mu,SV69: mu] :
( ( ( qmltpeq @ SV69 @ SV106 @ SV26 )
= $false )
| ( ( qmltpeq @ ( union @ SV69 @ SV129 ) @ ( union @ SV106 @ SV129 ) @ SV26 )
= $true )
| ( ( exists_in_world @ SV129 @ SV26 )
= $false )
| ( ( exists_in_world @ SV106 @ SV26 )
= $false )
| ( ( exists_in_world @ SV69 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(539,plain,
! [SV130: mu,SV28: $i,SV108: mu,SV71: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SV130 @ SV71 @ SV28 ) ) )
= $false )
| ( ( subset @ SV130 @ SV108 @ SV28 )
= $true )
| ( ( exists_in_world @ SV130 @ SV28 )
= $false )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(540,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
= $false )
| ( ( subset @ SV72 @ SV109 @ SV29 )
= $true )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(541,plain,
! [SV29: $i,SV109: mu,SV72: mu] :
( ( ( subset @ SV72 @ SV109 @ SV29 )
= $false )
| ( ( member @ SV72 @ ( power_set @ SV109 ) @ SV29 )
= $true )
| ( ( exists_in_world @ SV109 @ SV29 )
= $false )
| ( ( exists_in_world @ SV72 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(542,plain,
! [SV131: mu,SV30: $i,SV110: mu,SV73: mu] :
( ( ( qmltpeq @ SV73 @ SV110 @ SV30 )
= $false )
| ( ( qmltpeq @ ( difference @ SV73 @ SV131 ) @ ( difference @ SV110 @ SV131 ) @ SV30 )
= $true )
| ( ( exists_in_world @ SV131 @ SV30 )
= $false )
| ( ( exists_in_world @ SV110 @ SV30 )
= $false )
| ( ( exists_in_world @ SV73 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(543,plain,
! [SV32: $i,SV111: mu,SV75: mu] :
( ( ( subset @ SV75 @ SV111 @ SV32 )
= $false )
| ( ( ! [SY175: mu] :
( ~ ( exists_in_world @ SY175 @ SV32 )
| ~ ( member @ SY175 @ SV75 @ SV32 )
| ( member @ SY175 @ SV111 @ SV32 ) ) )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(544,plain,
! [SV111: mu,SV75: mu,SV32: $i] :
( ( ( ! [SY176: mu] :
( ~ ( exists_in_world @ SY176 @ SV32 )
| ~ ( member @ SY176 @ SV75 @ SV32 )
| ( member @ SY176 @ SV111 @ SV32 ) ) )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(545,plain,
! [SV132: mu,SV33: $i,SV112: mu,SV76: mu] :
( ( ( qmltpeq @ SV76 @ SV112 @ SV33 )
= $false )
| ( ( qmltpeq @ ( difference @ SV132 @ SV76 ) @ ( difference @ SV132 @ SV112 ) @ SV33 )
= $true )
| ( ( exists_in_world @ SV132 @ SV33 )
= $false )
| ( ( exists_in_world @ SV112 @ SV33 )
= $false )
| ( ( exists_in_world @ SV76 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(546,plain,
! [SV133: mu,SV34: $i,SV113: mu,SV77: mu] :
( ( ( qmltpeq @ SV77 @ SV113 @ SV34 )
= $false )
| ( ( qmltpeq @ ( union @ SV133 @ SV77 ) @ ( union @ SV133 @ SV113 ) @ SV34 )
= $true )
| ( ( exists_in_world @ SV133 @ SV34 )
= $false )
| ( ( exists_in_world @ SV113 @ SV34 )
= $false )
| ( ( exists_in_world @ SV77 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(547,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( ~ ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(548,plain,
! [SV78: mu,SV114: mu,SV35: $i] :
( ( ( ~ ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(549,plain,
! [SV134: mu,SV36: $i,SV115: mu,SV79: mu] :
( ( ( qmltpeq @ SV79 @ SV115 @ SV36 )
= $false )
| ( ( qmltpeq @ ( intersection @ SV134 @ SV79 ) @ ( intersection @ SV134 @ SV115 ) @ SV36 )
= $true )
| ( ( exists_in_world @ SV134 @ SV36 )
= $false )
| ( ( exists_in_world @ SV115 @ SV36 )
= $false )
| ( ( exists_in_world @ SV79 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(550,plain,
! [SV135: mu,SV37: $i,SV116: mu,SV80: mu] :
( ( ( qmltpeq @ SV80 @ SV116 @ SV37 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV80 @ SV135 ) @ ( unordered_pair @ SV116 @ SV135 ) @ SV37 )
= $true )
| ( ( exists_in_world @ SV135 @ SV37 )
= $false )
| ( ( exists_in_world @ SV116 @ SV37 )
= $false )
| ( ( exists_in_world @ SV80 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(551,plain,
! [SV136: mu,SV38: $i,SV117: mu,SV81: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SV136 @ SV38 ) ) )
= $false )
| ( ( member @ SV117 @ SV136 @ SV38 )
= $true )
| ( ( exists_in_world @ SV136 @ SV38 )
= $false )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(552,plain,
! [SV137: mu,SV39: $i,SV118: mu,SV82: mu] :
( ( ( qmltpeq @ SV82 @ SV118 @ SV39 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV137 @ SV82 ) @ ( unordered_pair @ SV137 @ SV118 ) @ SV39 )
= $true )
| ( ( exists_in_world @ SV137 @ SV39 )
= $false )
| ( ( exists_in_world @ SV118 @ SV39 )
= $false )
| ( ( exists_in_world @ SV82 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(553,plain,
! [SV138: mu,SV40: $i,SV119: mu,SV83: mu] :
( ( ( qmltpeq @ SV83 @ SV119 @ SV40 )
= $false )
| ( ( qmltpeq @ ( intersection @ SV83 @ SV138 ) @ ( intersection @ SV119 @ SV138 ) @ SV40 )
= $true )
| ( ( exists_in_world @ SV138 @ SV40 )
= $false )
| ( ( exists_in_world @ SV119 @ SV40 )
= $false )
| ( ( exists_in_world @ SV83 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(554,plain,
! [SV139: mu,SV41: $i,SV120: mu,SV84: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SV139 @ SV41 ) ) )
= $false )
| ( ( equal_set @ SV120 @ SV139 @ SV41 )
= $true )
| ( ( exists_in_world @ SV139 @ SV41 )
= $false )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(555,plain,
! [SV42: $i,SV140: mu,SV121: mu,SV85: mu] :
( ( ( ~ ( ~ ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) ) )
= $false )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(556,plain,
! [SV140: mu,SV42: $i,SV121: mu,SV85: mu] :
( ( ( ~ ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 ) ) )
= $false )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(557,plain,
! [SV141: mu,SV43: $i,SV122: mu,SV86: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SV141 @ SV86 @ SV43 ) ) )
= $false )
| ( ( member @ SV141 @ SV122 @ SV43 )
= $true )
| ( ( exists_in_world @ SV141 @ SV43 )
= $false )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(558,plain,
! [SV142: mu,SV45: $i,SV123: mu,SV87: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SV142 @ SV87 @ SV45 ) ) )
= $false )
| ( ( equal_set @ SV142 @ SV123 @ SV45 )
= $true )
| ( ( exists_in_world @ SV142 @ SV45 )
= $false )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(559,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
= $false )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(560,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( subset @ SV55 @ SV94 @ SV12 )
| ~ ( subset @ SV94 @ SV55 @ SV12 ) )
= $true )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(561,plain,
! [SV13: $i,SV124: mu,SV95: mu,SV56: mu] :
( ( ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
| ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(562,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
| ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(563,plain,
! [SV125: mu,SV14: $i,SV96: mu,SV57: mu] :
( ( ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 )
| ~ ( subset @ SV57 @ SV125 @ SV14 ) )
= $true )
| ( ( subset @ SV96 @ SV125 @ SV14 )
= $true )
| ( ( exists_in_world @ SV125 @ SV14 )
= $false )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(564,plain,
! [SV126: mu,SV15: $i,SV97: mu,SV58: mu] :
( ( ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 )
| ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) )
= $true )
| ( ( qmltpeq @ SV58 @ SV126 @ SV15 )
= $true )
| ( ( exists_in_world @ SV126 @ SV15 )
= $false )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(565,plain,
! [SV60: mu,SV99: mu,SV17: $i,SV143: mu] :
( ( ( ~ ( exists_in_world @ SV143 @ SV17 )
| ~ ( member @ SV143 @ SV99 @ SV17 )
| ( member @ SV60 @ SV143 @ SV17 ) )
= $true )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(566,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV17 )
| ~ ( member @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV99 @ SV17 )
| ( member @ SV60 @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV17 ) )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[533]) ).
thf(567,plain,
! [SV18: $i,SV127: mu,SV100: mu,SV61: mu] :
( ( ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
| ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(568,plain,
! [SV127: mu,SV18: $i,SV100: mu,SV61: mu] :
( ( ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
| ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(569,plain,
! [SV21: $i,SV102: mu,SV128: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
| ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(570,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
| ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 ) )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(571,plain,
! [SV130: mu,SV28: $i,SV108: mu,SV71: mu] :
( ( ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 )
| ~ ( subset @ SV130 @ SV71 @ SV28 ) )
= $true )
| ( ( subset @ SV130 @ SV108 @ SV28 )
= $true )
| ( ( exists_in_world @ SV130 @ SV28 )
= $false )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(572,plain,
! [SV111: mu,SV75: mu,SV32: $i,SV144: mu] :
( ( ( ~ ( exists_in_world @ SV144 @ SV32 )
| ~ ( member @ SV144 @ SV75 @ SV32 )
| ( member @ SV144 @ SV111 @ SV32 ) )
= $true )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(573,plain,
! [SV32: $i,SV75: mu,SV111: mu] :
( ( ( ~ ( exists_in_world @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV32 )
| ~ ( member @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV75 @ SV32 )
| ( member @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV111 @ SV32 ) )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[544]) ).
thf(574,plain,
! [SV78: mu,SV114: mu,SV35: $i] :
( ( ( ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SV35 )
| ~ ~ ( ~ ( member @ SY179 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY179 @ SV35 ) ) ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(575,plain,
! [SV78: mu,SV114: mu,SV35: $i] :
( ( ( ! [SY180: mu] :
( ~ ( exists_in_world @ SY180 @ SV35 )
| ~ ~ ( ~ ( member @ SY180 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SY180 @ SV35 ) ) ) )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(576,plain,
! [SV136: mu,SV38: $i,SV117: mu,SV81: mu] :
( ( ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 )
| ~ ( member @ SV81 @ SV136 @ SV38 ) )
= $true )
| ( ( member @ SV117 @ SV136 @ SV38 )
= $true )
| ( ( exists_in_world @ SV136 @ SV38 )
= $false )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(577,plain,
! [SV139: mu,SV41: $i,SV120: mu,SV84: mu] :
( ( ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 )
| ~ ( equal_set @ SV84 @ SV139 @ SV41 ) )
= $true )
| ( ( equal_set @ SV120 @ SV139 @ SV41 )
= $true )
| ( ( exists_in_world @ SV139 @ SV41 )
= $false )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(578,plain,
! [SV42: $i,SV140: mu,SV121: mu,SV85: mu] :
( ( ( ~ ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
| ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(579,plain,
! [SV140: mu,SV42: $i,SV121: mu,SV85: mu] :
( ( ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
| ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 ) )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(580,plain,
! [SV141: mu,SV43: $i,SV122: mu,SV86: mu] :
( ( ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 )
| ~ ( member @ SV141 @ SV86 @ SV43 ) )
= $true )
| ( ( member @ SV141 @ SV122 @ SV43 )
= $true )
| ( ( exists_in_world @ SV141 @ SV43 )
= $false )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(581,plain,
! [SV142: mu,SV45: $i,SV123: mu,SV87: mu] :
( ( ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 )
| ~ ( equal_set @ SV142 @ SV87 @ SV45 ) )
= $true )
| ( ( equal_set @ SV142 @ SV123 @ SV45 )
= $true )
| ( ( exists_in_world @ SV142 @ SV45 )
= $false )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(582,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( subset @ SV55 @ SV94 @ SV12 ) )
= $false )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(583,plain,
! [SV12: $i,SV55: mu,SV94: mu] :
( ( ( ~ ( subset @ SV94 @ SV55 @ SV12 ) )
= $false )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(584,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( ~ ( subset @ SV55 @ SV94 @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV94 @ SV55 @ SV12 ) )
= $true )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(585,plain,
! [SV13: $i,SV124: mu,SV95: mu,SV56: mu] :
( ( ( ~ ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(586,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
= $true )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(587,plain,
! [SV125: mu,SV14: $i,SV96: mu,SV57: mu] :
( ( ( ~ ( qmltpeq @ SV57 @ SV96 @ SV14 ) )
= $true )
| ( ( ~ ( subset @ SV57 @ SV125 @ SV14 ) )
= $true )
| ( ( subset @ SV96 @ SV125 @ SV14 )
= $true )
| ( ( exists_in_world @ SV125 @ SV14 )
= $false )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(588,plain,
! [SV126: mu,SV15: $i,SV97: mu,SV58: mu] :
( ( ( ~ ( qmltpeq @ SV58 @ SV97 @ SV15 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) )
= $true )
| ( ( qmltpeq @ SV58 @ SV126 @ SV15 )
= $true )
| ( ( exists_in_world @ SV126 @ SV15 )
= $false )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(589,plain,
! [SV60: mu,SV99: mu,SV17: $i,SV143: mu] :
( ( ( ~ ( exists_in_world @ SV143 @ SV17 ) )
= $true )
| ( ( ~ ( member @ SV143 @ SV99 @ SV17 )
| ( member @ SV60 @ SV143 @ SV17 ) )
= $true )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(590,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV17 ) )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(591,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( member @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV99 @ SV17 )
| ( member @ SV60 @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV17 ) )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(592,plain,
! [SV18: $i,SV127: mu,SV100: mu,SV61: mu] :
( ( ( ~ ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 ) )
= $true )
| ( ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(593,plain,
! [SV127: mu,SV18: $i,SV100: mu,SV61: mu] :
( ( ( ~ ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) ) )
= $true )
| ( ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(594,plain,
! [SV21: $i,SV102: mu,SV128: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(595,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
= $true )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(596,plain,
! [SV130: mu,SV28: $i,SV108: mu,SV71: mu] :
( ( ( ~ ( qmltpeq @ SV71 @ SV108 @ SV28 ) )
= $true )
| ( ( ~ ( subset @ SV130 @ SV71 @ SV28 ) )
= $true )
| ( ( subset @ SV130 @ SV108 @ SV28 )
= $true )
| ( ( exists_in_world @ SV130 @ SV28 )
= $false )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(597,plain,
! [SV111: mu,SV75: mu,SV32: $i,SV144: mu] :
( ( ( ~ ( exists_in_world @ SV144 @ SV32 ) )
= $true )
| ( ( ~ ( member @ SV144 @ SV75 @ SV32 )
| ( member @ SV144 @ SV111 @ SV32 ) )
= $true )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(598,plain,
! [SV32: $i,SV75: mu,SV111: mu] :
( ( ( ~ ( exists_in_world @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV32 ) )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(599,plain,
! [SV32: $i,SV75: mu,SV111: mu] :
( ( ( ~ ( member @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV75 @ SV32 )
| ( member @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV111 @ SV32 ) )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(600,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( exists_in_world @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 )
| ~ ~ ( ~ ( member @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV114 @ SV35 )
| ~ ( member @ SV78 @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 ) ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[574]) ).
thf(601,plain,
! [SV78: mu,SV114: mu,SV35: $i,SV145: mu] :
( ( ( ~ ( exists_in_world @ SV145 @ SV35 )
| ~ ~ ( ~ ( member @ SV145 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SV145 @ SV35 ) ) )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(602,plain,
! [SV136: mu,SV38: $i,SV117: mu,SV81: mu] :
( ( ( ~ ( qmltpeq @ SV81 @ SV117 @ SV38 ) )
= $true )
| ( ( ~ ( member @ SV81 @ SV136 @ SV38 ) )
= $true )
| ( ( member @ SV117 @ SV136 @ SV38 )
= $true )
| ( ( exists_in_world @ SV136 @ SV38 )
= $false )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(603,plain,
! [SV139: mu,SV41: $i,SV120: mu,SV84: mu] :
( ( ( ~ ( qmltpeq @ SV84 @ SV120 @ SV41 ) )
= $true )
| ( ( ~ ( equal_set @ SV84 @ SV139 @ SV41 ) )
= $true )
| ( ( equal_set @ SV120 @ SV139 @ SV41 )
= $true )
| ( ( exists_in_world @ SV139 @ SV41 )
= $false )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(604,plain,
! [SV42: $i,SV140: mu,SV121: mu,SV85: mu] :
( ( ( ~ ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 ) )
= $true )
| ( ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(605,plain,
! [SV140: mu,SV42: $i,SV121: mu,SV85: mu] :
( ( ( ~ ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) ) )
= $true )
| ( ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(606,plain,
! [SV141: mu,SV43: $i,SV122: mu,SV86: mu] :
( ( ( ~ ( qmltpeq @ SV86 @ SV122 @ SV43 ) )
= $true )
| ( ( ~ ( member @ SV141 @ SV86 @ SV43 ) )
= $true )
| ( ( member @ SV141 @ SV122 @ SV43 )
= $true )
| ( ( exists_in_world @ SV141 @ SV43 )
= $false )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(607,plain,
! [SV142: mu,SV45: $i,SV123: mu,SV87: mu] :
( ( ( ~ ( qmltpeq @ SV87 @ SV123 @ SV45 ) )
= $true )
| ( ( ~ ( equal_set @ SV142 @ SV87 @ SV45 ) )
= $true )
| ( ( equal_set @ SV142 @ SV123 @ SV45 )
= $true )
| ( ( exists_in_world @ SV142 @ SV45 )
= $false )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(608,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( subset @ SV55 @ SV94 @ SV12 )
= $true )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(609,plain,
! [SV12: $i,SV55: mu,SV94: mu] :
( ( ( subset @ SV94 @ SV55 @ SV12 )
= $true )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(610,plain,
! [SV12: $i,SV94: mu,SV55: mu] :
( ( ( subset @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( ~ ( subset @ SV94 @ SV55 @ SV12 ) )
= $true )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(611,plain,
! [SV13: $i,SV124: mu,SV95: mu,SV56: mu] :
( ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $false )
| ( ( ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(612,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) ) )
= $false )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(613,plain,
! [SV125: mu,SV14: $i,SV96: mu,SV57: mu] :
( ( ( qmltpeq @ SV57 @ SV96 @ SV14 )
= $false )
| ( ( ~ ( subset @ SV57 @ SV125 @ SV14 ) )
= $true )
| ( ( subset @ SV96 @ SV125 @ SV14 )
= $true )
| ( ( exists_in_world @ SV125 @ SV14 )
= $false )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(614,plain,
! [SV126: mu,SV15: $i,SV97: mu,SV58: mu] :
( ( ( qmltpeq @ SV58 @ SV97 @ SV15 )
= $false )
| ( ( ~ ( qmltpeq @ SV97 @ SV126 @ SV15 ) )
= $true )
| ( ( qmltpeq @ SV58 @ SV126 @ SV15 )
= $true )
| ( ( exists_in_world @ SV126 @ SV15 )
= $false )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(615,plain,
! [SV60: mu,SV99: mu,SV17: $i,SV143: mu] :
( ( ( exists_in_world @ SV143 @ SV17 )
= $false )
| ( ( ~ ( member @ SV143 @ SV99 @ SV17 )
| ( member @ SV60 @ SV143 @ SV17 ) )
= $true )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(616,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( exists_in_world @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV17 )
= $true )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(617,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( ~ ( member @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV99 @ SV17 ) )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(618,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( member @ SV60 @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV17 )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(619,plain,
! [SV18: $i,SV127: mu,SV100: mu,SV61: mu] :
( ( ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
= $false )
| ( ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(620,plain,
! [SV127: mu,SV18: $i,SV100: mu,SV61: mu] :
( ( ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
| ( qmltpeq @ SV61 @ SV127 @ SV18 ) )
= $false )
| ( ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(621,plain,
! [SV21: $i,SV102: mu,SV128: mu,SV64: mu] :
( ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $false )
| ( ( ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(622,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) ) )
= $false )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(623,plain,
! [SV130: mu,SV28: $i,SV108: mu,SV71: mu] :
( ( ( qmltpeq @ SV71 @ SV108 @ SV28 )
= $false )
| ( ( ~ ( subset @ SV130 @ SV71 @ SV28 ) )
= $true )
| ( ( subset @ SV130 @ SV108 @ SV28 )
= $true )
| ( ( exists_in_world @ SV130 @ SV28 )
= $false )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(624,plain,
! [SV111: mu,SV75: mu,SV32: $i,SV144: mu] :
( ( ( exists_in_world @ SV144 @ SV32 )
= $false )
| ( ( ~ ( member @ SV144 @ SV75 @ SV32 )
| ( member @ SV144 @ SV111 @ SV32 ) )
= $true )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(625,plain,
! [SV32: $i,SV75: mu,SV111: mu] :
( ( ( exists_in_world @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV32 )
= $true )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(626,plain,
! [SV32: $i,SV75: mu,SV111: mu] :
( ( ( ~ ( member @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV75 @ SV32 ) )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(627,plain,
! [SV32: $i,SV75: mu,SV111: mu] :
( ( ( member @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV111 @ SV32 )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(628,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( exists_in_world @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[600]) ).
thf(629,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ~ ( ~ ( member @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV114 @ SV35 )
| ~ ( member @ SV78 @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 ) ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[600]) ).
thf(630,plain,
! [SV78: mu,SV114: mu,SV35: $i,SV145: mu] :
( ( ( ~ ( exists_in_world @ SV145 @ SV35 ) )
= $true )
| ( ( ~ ~ ( ~ ( member @ SV145 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SV145 @ SV35 ) ) )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(631,plain,
! [SV136: mu,SV38: $i,SV117: mu,SV81: mu] :
( ( ( qmltpeq @ SV81 @ SV117 @ SV38 )
= $false )
| ( ( ~ ( member @ SV81 @ SV136 @ SV38 ) )
= $true )
| ( ( member @ SV117 @ SV136 @ SV38 )
= $true )
| ( ( exists_in_world @ SV136 @ SV38 )
= $false )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(632,plain,
! [SV139: mu,SV41: $i,SV120: mu,SV84: mu] :
( ( ( qmltpeq @ SV84 @ SV120 @ SV41 )
= $false )
| ( ( ~ ( equal_set @ SV84 @ SV139 @ SV41 ) )
= $true )
| ( ( equal_set @ SV120 @ SV139 @ SV41 )
= $true )
| ( ( exists_in_world @ SV139 @ SV41 )
= $false )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(633,plain,
! [SV42: $i,SV140: mu,SV121: mu,SV85: mu] :
( ( ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
= $false )
| ( ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(634,plain,
! [SV140: mu,SV42: $i,SV121: mu,SV85: mu] :
( ( ( ( member @ SV85 @ SV121 @ SV42 )
| ( member @ SV85 @ SV140 @ SV42 ) )
= $false )
| ( ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(635,plain,
! [SV141: mu,SV43: $i,SV122: mu,SV86: mu] :
( ( ( qmltpeq @ SV86 @ SV122 @ SV43 )
= $false )
| ( ( ~ ( member @ SV141 @ SV86 @ SV43 ) )
= $true )
| ( ( member @ SV141 @ SV122 @ SV43 )
= $true )
| ( ( exists_in_world @ SV141 @ SV43 )
= $false )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(636,plain,
! [SV142: mu,SV45: $i,SV123: mu,SV87: mu] :
( ( ( qmltpeq @ SV87 @ SV123 @ SV45 )
= $false )
| ( ( ~ ( equal_set @ SV142 @ SV87 @ SV45 ) )
= $true )
| ( ( equal_set @ SV142 @ SV123 @ SV45 )
= $true )
| ( ( exists_in_world @ SV142 @ SV45 )
= $false )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(637,plain,
! [SV12: $i,SV55: mu,SV94: mu] :
( ( ( subset @ SV94 @ SV55 @ SV12 )
= $false )
| ( ( subset @ SV55 @ SV94 @ SV12 )
= $false )
| ( ( equal_set @ SV55 @ SV94 @ SV12 )
= $true )
| ( ( exists_in_world @ SV94 @ SV12 )
= $false )
| ( ( exists_in_world @ SV55 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(638,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
= $false )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(639,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ( member @ SV56 @ SV95 @ SV13 )
| ~ ( member @ SV56 @ SV124 @ SV13 ) )
= $true )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(640,plain,
! [SV96: mu,SV14: $i,SV125: mu,SV57: mu] :
( ( ( subset @ SV57 @ SV125 @ SV14 )
= $false )
| ( ( qmltpeq @ SV57 @ SV96 @ SV14 )
= $false )
| ( ( subset @ SV96 @ SV125 @ SV14 )
= $true )
| ( ( exists_in_world @ SV125 @ SV14 )
= $false )
| ( ( exists_in_world @ SV96 @ SV14 )
= $false )
| ( ( exists_in_world @ SV57 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(641,plain,
! [SV58: mu,SV15: $i,SV126: mu,SV97: mu] :
( ( ( qmltpeq @ SV97 @ SV126 @ SV15 )
= $false )
| ( ( qmltpeq @ SV58 @ SV97 @ SV15 )
= $false )
| ( ( qmltpeq @ SV58 @ SV126 @ SV15 )
= $true )
| ( ( exists_in_world @ SV126 @ SV15 )
= $false )
| ( ( exists_in_world @ SV97 @ SV15 )
= $false )
| ( ( exists_in_world @ SV58 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(642,plain,
! [SV60: mu,SV17: $i,SV99: mu,SV143: mu] :
( ( ( ~ ( member @ SV143 @ SV99 @ SV17 ) )
= $true )
| ( ( member @ SV60 @ SV143 @ SV17 )
= $true )
| ( ( exists_in_world @ SV143 @ SV17 )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(643,plain,
! [SV17: $i,SV99: mu,SV60: mu] :
( ( ( member @ ( sK4_SY169 @ SV60 @ SV99 @ SV17 ) @ SV99 @ SV17 )
= $true )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(644,plain,
! [SV127: mu,SV18: $i,SV100: mu,SV61: mu] :
( ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
= $true )
| ( ( qmltpeq @ SV61 @ SV127 @ SV18 )
= $true )
| ( ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
= $false )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(645,plain,
! [SV127: mu,SV18: $i,SV100: mu,SV61: mu] :
( ( ( qmltpeq @ SV61 @ SV100 @ SV18 )
= $false )
| ( ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(646,plain,
! [SV100: mu,SV18: $i,SV127: mu,SV61: mu] :
( ( ( qmltpeq @ SV61 @ SV127 @ SV18 )
= $false )
| ( ( member @ SV61 @ ( unordered_pair @ SV100 @ SV127 ) @ SV18 )
= $true )
| ( ( exists_in_world @ SV127 @ SV18 )
= $false )
| ( ( exists_in_world @ SV100 @ SV18 )
= $false )
| ( ( exists_in_world @ SV61 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(647,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
= $false )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(648,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ SV128 @ SV21 )
| ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
= $true )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(649,plain,
! [SV108: mu,SV28: $i,SV71: mu,SV130: mu] :
( ( ( subset @ SV130 @ SV71 @ SV28 )
= $false )
| ( ( qmltpeq @ SV71 @ SV108 @ SV28 )
= $false )
| ( ( subset @ SV130 @ SV108 @ SV28 )
= $true )
| ( ( exists_in_world @ SV130 @ SV28 )
= $false )
| ( ( exists_in_world @ SV108 @ SV28 )
= $false )
| ( ( exists_in_world @ SV71 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(650,plain,
! [SV111: mu,SV32: $i,SV75: mu,SV144: mu] :
( ( ( ~ ( member @ SV144 @ SV75 @ SV32 ) )
= $true )
| ( ( member @ SV144 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV144 @ SV32 )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(651,plain,
! [SV32: $i,SV75: mu,SV111: mu] :
( ( ( member @ ( sK5_SY176 @ SV111 @ SV75 @ SV32 ) @ SV75 @ SV32 )
= $true )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(652,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( exists_in_world @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(653,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( ~ ( member @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV114 @ SV35 )
| ~ ( member @ SV78 @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(654,plain,
! [SV78: mu,SV114: mu,SV35: $i,SV145: mu] :
( ( ( exists_in_world @ SV145 @ SV35 )
= $false )
| ( ( ~ ~ ( ~ ( member @ SV145 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SV145 @ SV35 ) ) )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(655,plain,
! [SV117: mu,SV38: $i,SV136: mu,SV81: mu] :
( ( ( member @ SV81 @ SV136 @ SV38 )
= $false )
| ( ( qmltpeq @ SV81 @ SV117 @ SV38 )
= $false )
| ( ( member @ SV117 @ SV136 @ SV38 )
= $true )
| ( ( exists_in_world @ SV136 @ SV38 )
= $false )
| ( ( exists_in_world @ SV117 @ SV38 )
= $false )
| ( ( exists_in_world @ SV81 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(656,plain,
! [SV120: mu,SV41: $i,SV139: mu,SV84: mu] :
( ( ( equal_set @ SV84 @ SV139 @ SV41 )
= $false )
| ( ( qmltpeq @ SV84 @ SV120 @ SV41 )
= $false )
| ( ( equal_set @ SV120 @ SV139 @ SV41 )
= $true )
| ( ( exists_in_world @ SV139 @ SV41 )
= $false )
| ( ( exists_in_world @ SV120 @ SV41 )
= $false )
| ( ( exists_in_world @ SV84 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(657,plain,
! [SV140: mu,SV42: $i,SV121: mu,SV85: mu] :
( ( ( member @ SV85 @ SV121 @ SV42 )
= $true )
| ( ( member @ SV85 @ SV140 @ SV42 )
= $true )
| ( ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
= $false )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(658,plain,
! [SV140: mu,SV42: $i,SV121: mu,SV85: mu] :
( ( ( member @ SV85 @ SV121 @ SV42 )
= $false )
| ( ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(659,plain,
! [SV121: mu,SV42: $i,SV140: mu,SV85: mu] :
( ( ( member @ SV85 @ SV140 @ SV42 )
= $false )
| ( ( member @ SV85 @ ( union @ SV121 @ SV140 ) @ SV42 )
= $true )
| ( ( exists_in_world @ SV140 @ SV42 )
= $false )
| ( ( exists_in_world @ SV121 @ SV42 )
= $false )
| ( ( exists_in_world @ SV85 @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(660,plain,
! [SV122: mu,SV43: $i,SV86: mu,SV141: mu] :
( ( ( member @ SV141 @ SV86 @ SV43 )
= $false )
| ( ( qmltpeq @ SV86 @ SV122 @ SV43 )
= $false )
| ( ( member @ SV141 @ SV122 @ SV43 )
= $true )
| ( ( exists_in_world @ SV141 @ SV43 )
= $false )
| ( ( exists_in_world @ SV122 @ SV43 )
= $false )
| ( ( exists_in_world @ SV86 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(661,plain,
! [SV123: mu,SV45: $i,SV87: mu,SV142: mu] :
( ( ( equal_set @ SV142 @ SV87 @ SV45 )
= $false )
| ( ( qmltpeq @ SV87 @ SV123 @ SV45 )
= $false )
| ( ( equal_set @ SV142 @ SV123 @ SV45 )
= $true )
| ( ( exists_in_world @ SV142 @ SV45 )
= $false )
| ( ( exists_in_world @ SV123 @ SV45 )
= $false )
| ( ( exists_in_world @ SV87 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(662,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ( member @ SV56 @ SV95 @ SV13 ) )
= $false )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(663,plain,
! [SV95: mu,SV13: $i,SV124: mu,SV56: mu] :
( ( ( ~ ( member @ SV56 @ SV124 @ SV13 ) )
= $false )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(664,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( ~ ( member @ SV56 @ SV95 @ SV13 ) )
= $true )
| ( ( ~ ( member @ SV56 @ SV124 @ SV13 ) )
= $true )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(665,plain,
! [SV60: mu,SV17: $i,SV99: mu,SV143: mu] :
( ( ( member @ SV143 @ SV99 @ SV17 )
= $false )
| ( ( member @ SV60 @ SV143 @ SV17 )
= $true )
| ( ( exists_in_world @ SV143 @ SV17 )
= $false )
| ( ( member @ SV60 @ ( product @ SV99 ) @ SV17 )
= $false )
| ( ( exists_in_world @ SV99 @ SV17 )
= $false )
| ( ( exists_in_world @ SV60 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(666,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ SV128 @ SV21 ) )
= $false )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(667,plain,
! [SV128: mu,SV21: $i,SV102: mu,SV64: mu] :
( ( ( ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
= $false )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(668,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ SV128 @ SV21 ) )
= $true )
| ( ( ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
= $true )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(669,plain,
! [SV111: mu,SV32: $i,SV75: mu,SV144: mu] :
( ( ( member @ SV144 @ SV75 @ SV32 )
= $false )
| ( ( member @ SV144 @ SV111 @ SV32 )
= $true )
| ( ( exists_in_world @ SV144 @ SV32 )
= $false )
| ( ( subset @ SV75 @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV111 @ SV32 )
= $false )
| ( ( exists_in_world @ SV75 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(670,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( member @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV114 @ SV35 )
| ~ ( member @ SV78 @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(671,plain,
! [SV78: mu,SV35: $i,SV114: mu,SV145: mu] :
( ( ( ~ ( ~ ( member @ SV145 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SV145 @ SV35 ) ) )
= $false )
| ( ( exists_in_world @ SV145 @ SV35 )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(672,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( member @ SV56 @ SV95 @ SV13 )
= $true )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(673,plain,
! [SV95: mu,SV13: $i,SV124: mu,SV56: mu] :
( ( ( member @ SV56 @ SV124 @ SV13 )
= $true )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $false )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(674,plain,
! [SV124: mu,SV13: $i,SV95: mu,SV56: mu] :
( ( ( member @ SV56 @ SV95 @ SV13 )
= $false )
| ( ( ~ ( member @ SV56 @ SV124 @ SV13 ) )
= $true )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(675,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( member @ SV64 @ SV128 @ SV21 )
= $true )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(676,plain,
! [SV128: mu,SV21: $i,SV102: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ SV102 @ SV21 ) )
= $true )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(677,plain,
! [SV102: mu,SV21: $i,SV128: mu,SV64: mu] :
( ( ( member @ SV64 @ SV128 @ SV21 )
= $false )
| ( ( ~ ~ ( member @ SV64 @ SV102 @ SV21 ) )
= $true )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(678,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( member @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV114 @ SV35 ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(679,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( ~ ( member @ SV78 @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 ) )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(680,plain,
! [SV78: mu,SV35: $i,SV114: mu,SV145: mu] :
( ( ( ~ ( member @ SV145 @ SV114 @ SV35 )
| ~ ( member @ SV78 @ SV145 @ SV35 ) )
= $true )
| ( ( exists_in_world @ SV145 @ SV35 )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(681,plain,
! [SV95: mu,SV13: $i,SV124: mu,SV56: mu] :
( ( ( member @ SV56 @ SV124 @ SV13 )
= $false )
| ( ( member @ SV56 @ SV95 @ SV13 )
= $false )
| ( ( member @ SV56 @ ( intersection @ SV95 @ SV124 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV124 @ SV13 )
= $false )
| ( ( exists_in_world @ SV95 @ SV13 )
= $false )
| ( ( exists_in_world @ SV56 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(682,plain,
! [SV128: mu,SV21: $i,SV102: mu,SV64: mu] :
( ( ( member @ SV64 @ SV102 @ SV21 )
= $false )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $false )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(683,plain,
! [SV128: mu,SV21: $i,SV102: mu,SV64: mu] :
( ( ( ~ ( member @ SV64 @ SV102 @ SV21 ) )
= $false )
| ( ( member @ SV64 @ SV128 @ SV21 )
= $false )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(684,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( member @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV114 @ SV35 )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(685,plain,
! [SV35: $i,SV114: mu,SV78: mu] :
( ( ( member @ SV78 @ ( sK6_SY179 @ SV78 @ SV114 @ SV35 ) @ SV35 )
= $true )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $false )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(686,plain,
! [SV78: mu,SV35: $i,SV114: mu,SV145: mu] :
( ( ( ~ ( member @ SV145 @ SV114 @ SV35 ) )
= $true )
| ( ( ~ ( member @ SV78 @ SV145 @ SV35 ) )
= $true )
| ( ( exists_in_world @ SV145 @ SV35 )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(687,plain,
! [SV128: mu,SV21: $i,SV102: mu,SV64: mu] :
( ( ( member @ SV64 @ SV102 @ SV21 )
= $true )
| ( ( member @ SV64 @ SV128 @ SV21 )
= $false )
| ( ( member @ SV64 @ ( difference @ SV128 @ SV102 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV128 @ SV21 )
= $false )
| ( ( exists_in_world @ SV102 @ SV21 )
= $false )
| ( ( exists_in_world @ SV64 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(688,plain,
! [SV78: mu,SV35: $i,SV114: mu,SV145: mu] :
( ( ( member @ SV145 @ SV114 @ SV35 )
= $false )
| ( ( ~ ( member @ SV78 @ SV145 @ SV35 ) )
= $true )
| ( ( exists_in_world @ SV145 @ SV35 )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(689,plain,
! [SV114: mu,SV35: $i,SV145: mu,SV78: mu] :
( ( ( member @ SV78 @ SV145 @ SV35 )
= $false )
| ( ( member @ SV145 @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV145 @ SV35 )
= $false )
| ( ( member @ SV78 @ ( sum @ SV114 ) @ SV35 )
= $true )
| ( ( exists_in_world @ SV114 @ SV35 )
= $false )
| ( ( exists_in_world @ SV78 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(690,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[132,689,687,685,684,682,681,675,673,672,669,665,661,660,659,658,657,656,655,652,651,649,646,645,644,643,641,640,637,627,625,618,616,609,608,553,552,550,549,546,545,542,541,540,538,531,530,442,440,439,438,437,435,362,324,315,290,268,225,224,223,222,186,185,183,179,176,142]) ).
thf(691,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET062^7 : TPTP v8.1.0. Released v5.5.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 15:33:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.39
% 0.19/0.39 No.of.Axioms: 45
% 0.19/0.39
% 0.19/0.39 Length.of.Defs: 5540
% 0.19/0.39
% 0.19/0.39 Contains.Choice.Funs: false
% 0.19/0.42 .
% 0.19/0.43 (rf:0,axioms:45,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:47,loop_count:0,foatp_calls:0,translation:fof_full)..........................................
% 0.59/0.83
% 0.59/0.83 ********************************
% 0.59/0.83 * All subproblems solved! *
% 0.59/0.83 ********************************
% 0.59/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:45,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:690,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.80/1.00
% 0.80/1.00 %**** Beginning of derivation protocol ****
% 0.80/1.00 % SZS output start CNFRefutation
% See solution above
% 0.80/1.01
% 0.80/1.01 %**** End of derivation protocol ****
% 0.80/1.01 %**** no. of clauses in derivation: 691 ****
% 0.80/1.01 %**** clause counter: 690 ****
% 0.80/1.01
% 0.80/1.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:45,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:690,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------