%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET062^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:39:15 AM UTC 2026
% Result : Theorem 1.39s 0.61s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 55
% Syntax : Number of formulae : 400 ( 153 unt; 0 typ; 32 def)
% Number of atoms : 3729 ( 919 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 7722 (1052 ~;1267 |; 8 &;5277 @)
% ( 0 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 5 con; 0-3 aty)
% Number of variables : 1333 ( 103 ^;1224 !; 6 ?;1333 :)
% 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_SY3,type,
sK1_SY3: $i ).
thf(tp_sK2_SY656,type,
sK2_SY656: mu ).
thf(tp_sK3_SY749,type,
sK3_SY749: 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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(6,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( member @ X @ empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [A: mu] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',subset_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(32,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(33,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(46,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] : ( subset @ empty_set @ A ) ) ),
file('/export/starexec/sandbox/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,
( ( ! [SY3: $i,SY4: mu] :
( ( exists_in_world @ SY4 @ SY3 )
=> ( subset @ empty_set @ SY4 @ SY3 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[47,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(49,plain,
( ( ! [SY12: $i,SY13: mu] :
( ( exists_in_world @ SY13 @ SY12 )
=> ~ ( member @ SY13 @ empty_set @ SY12 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,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(50,plain,
( ( ! [SY48: $i,SY49: mu] :
( ( exists_in_world @ SY49 @ SY48 )
=> ! [SY50: mu] :
( ( exists_in_world @ SY50 @ SY48 )
=> ~ ( ~ ( ~ ( member @ SY49 @ ( power_set @ SY50 ) @ SY48 )
| ( subset @ SY49 @ SY50 @ SY48 ) )
| ~ ( ~ ( subset @ SY49 @ SY50 @ SY48 )
| ( member @ SY49 @ ( power_set @ SY50 ) @ SY48 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,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(51,plain,
( ( ! [SY94: $i,SY95: mu] :
( ( exists_in_world @ SY95 @ SY94 )
=> ! [SY96: mu] :
( ( exists_in_world @ SY96 @ SY94 )
=> ~ ( ~ ( ~ ( equal_set @ SY95 @ SY96 @ SY94 )
| ~ ( ~ ( subset @ SY95 @ SY96 @ SY94 )
| ~ ( subset @ SY96 @ SY95 @ SY94 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY95 @ SY96 @ SY94 )
| ~ ( subset @ SY96 @ SY95 @ SY94 ) )
| ( equal_set @ SY95 @ SY96 @ SY94 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,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(52,plain,
( ( ! [SY152: $i,SY153: mu] :
( ( exists_in_world @ SY153 @ SY152 )
=> ! [SY154: mu] :
( ( exists_in_world @ SY154 @ SY152 )
=> ~ ( ~ ( ~ ( subset @ SY153 @ SY154 @ SY152 )
| ! [SY155: mu] :
( ( exists_in_world @ SY155 @ SY152 )
=> ( ~ ( member @ SY155 @ SY153 @ SY152 )
| ( member @ SY155 @ SY154 @ SY152 ) ) ) )
| ~ ( ~ ! [SY156: mu] :
( ( exists_in_world @ SY156 @ SY152 )
=> ( ~ ( member @ SY156 @ SY153 @ SY152 )
| ( member @ SY156 @ SY154 @ SY152 ) ) )
| ( subset @ SY153 @ SY154 @ SY152 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,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(53,plain,
( ( ! [SY194: $i,SY195: mu] :
( ( exists_in_world @ SY195 @ SY194 )
=> ! [SY196: mu] :
( ( exists_in_world @ SY196 @ SY194 )
=> ! [SY197: mu] :
( ( exists_in_world @ SY197 @ SY194 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY195 @ SY196 @ SY194 )
| ~ ( subset @ SY197 @ SY195 @ SY194 ) )
| ( subset @ SY197 @ SY196 @ SY194 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,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(54,plain,
( ( ! [SY234: $i,SY235: mu] :
( ( exists_in_world @ SY235 @ SY234 )
=> ! [SY236: mu] :
( ( exists_in_world @ SY236 @ SY234 )
=> ! [SY237: mu] :
( ( exists_in_world @ SY237 @ SY234 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY235 @ SY236 @ SY234 )
| ~ ( subset @ SY235 @ SY237 @ SY234 ) )
| ( subset @ SY236 @ SY237 @ SY234 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,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(55,plain,
( ( ! [SY266: $i,SY267: mu] :
( ( exists_in_world @ SY267 @ SY266 )
=> ! [SY268: mu] :
( ( exists_in_world @ SY268 @ SY266 )
=> ! [SY269: mu] :
( ( exists_in_world @ SY269 @ SY266 )
=> ( ~ ( qmltpeq @ SY267 @ SY268 @ SY266 )
| ( qmltpeq @ ( unordered_pair @ SY269 @ SY267 ) @ ( unordered_pair @ SY269 @ SY268 ) @ SY266 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,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(56,plain,
( ( ! [SY298: $i,SY299: mu] :
( ( exists_in_world @ SY299 @ SY298 )
=> ! [SY300: mu] :
( ( exists_in_world @ SY300 @ SY298 )
=> ! [SY301: mu] :
( ( exists_in_world @ SY301 @ SY298 )
=> ( ~ ( qmltpeq @ SY299 @ SY300 @ SY298 )
| ( qmltpeq @ ( unordered_pair @ SY299 @ SY301 ) @ ( unordered_pair @ SY300 @ SY301 ) @ SY298 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,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(57,plain,
( ( ! [SY330: $i,SY331: mu] :
( ( exists_in_world @ SY331 @ SY330 )
=> ! [SY332: mu] :
( ( exists_in_world @ SY332 @ SY330 )
=> ! [SY333: mu] :
( ( exists_in_world @ SY333 @ SY330 )
=> ( ~ ( qmltpeq @ SY331 @ SY332 @ SY330 )
| ( qmltpeq @ ( union @ SY333 @ SY331 ) @ ( union @ SY333 @ SY332 ) @ SY330 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,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(58,plain,
( ( ! [SY362: $i,SY363: mu] :
( ( exists_in_world @ SY363 @ SY362 )
=> ! [SY364: mu] :
( ( exists_in_world @ SY364 @ SY362 )
=> ! [SY365: mu] :
( ( exists_in_world @ SY365 @ SY362 )
=> ( ~ ( qmltpeq @ SY363 @ SY364 @ SY362 )
| ( qmltpeq @ ( union @ SY363 @ SY365 ) @ ( union @ SY364 @ SY365 ) @ SY362 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,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(59,plain,
( ( ! [SY386: $i,SY387: mu] :
( ( exists_in_world @ SY387 @ SY386 )
=> ! [SY388: mu] :
( ( exists_in_world @ SY388 @ SY386 )
=> ( ~ ( qmltpeq @ SY387 @ SY388 @ SY386 )
| ( qmltpeq @ ( sum @ SY387 ) @ ( sum @ SY388 ) @ SY386 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,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(60,plain,
( ( ! [SY408: $i,SY409: mu] :
( ( exists_in_world @ SY409 @ SY408 )
=> ! [SY410: mu] :
( ( exists_in_world @ SY410 @ SY408 )
=> ( ~ ( qmltpeq @ SY409 @ SY410 @ SY408 )
| ( qmltpeq @ ( singleton @ SY409 ) @ ( singleton @ SY410 ) @ SY408 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,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(61,plain,
( ( ! [SY430: $i,SY431: mu] :
( ( exists_in_world @ SY431 @ SY430 )
=> ! [SY432: mu] :
( ( exists_in_world @ SY432 @ SY430 )
=> ( ~ ( qmltpeq @ SY431 @ SY432 @ SY430 )
| ( qmltpeq @ ( product @ SY431 ) @ ( product @ SY432 ) @ SY430 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,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(62,plain,
( ( ! [SY452: $i,SY453: mu] :
( ( exists_in_world @ SY453 @ SY452 )
=> ! [SY454: mu] :
( ( exists_in_world @ SY454 @ SY452 )
=> ( ~ ( qmltpeq @ SY453 @ SY454 @ SY452 )
| ( qmltpeq @ ( power_set @ SY453 ) @ ( power_set @ SY454 ) @ SY452 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,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(63,plain,
( ( ! [SY482: $i,SY483: mu] :
( ( exists_in_world @ SY483 @ SY482 )
=> ! [SY484: mu] :
( ( exists_in_world @ SY484 @ SY482 )
=> ! [SY485: mu] :
( ( exists_in_world @ SY485 @ SY482 )
=> ( ~ ( qmltpeq @ SY483 @ SY484 @ SY482 )
| ( qmltpeq @ ( intersection @ SY485 @ SY483 ) @ ( intersection @ SY485 @ SY484 ) @ SY482 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,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(64,plain,
( ( ! [SY514: $i,SY515: mu] :
( ( exists_in_world @ SY515 @ SY514 )
=> ! [SY516: mu] :
( ( exists_in_world @ SY516 @ SY514 )
=> ! [SY517: mu] :
( ( exists_in_world @ SY517 @ SY514 )
=> ( ~ ( qmltpeq @ SY515 @ SY516 @ SY514 )
| ( qmltpeq @ ( intersection @ SY515 @ SY517 ) @ ( intersection @ SY516 @ SY517 ) @ SY514 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,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(65,plain,
( ( ! [SY546: $i,SY547: mu] :
( ( exists_in_world @ SY547 @ SY546 )
=> ! [SY548: mu] :
( ( exists_in_world @ SY548 @ SY546 )
=> ! [SY549: mu] :
( ( exists_in_world @ SY549 @ SY546 )
=> ( ~ ( qmltpeq @ SY547 @ SY548 @ SY546 )
| ( qmltpeq @ ( difference @ SY549 @ SY547 ) @ ( difference @ SY549 @ SY548 ) @ SY546 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,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(66,plain,
( ( ! [SY578: $i,SY579: mu] :
( ( exists_in_world @ SY579 @ SY578 )
=> ! [SY580: mu] :
( ( exists_in_world @ SY580 @ SY578 )
=> ! [SY581: mu] :
( ( exists_in_world @ SY581 @ SY578 )
=> ( ~ ( qmltpeq @ SY579 @ SY580 @ SY578 )
| ( qmltpeq @ ( difference @ SY579 @ SY581 ) @ ( difference @ SY580 @ SY581 ) @ SY578 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,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(67,plain,
( ( ! [SY618: $i,SY619: mu] :
( ( exists_in_world @ SY619 @ SY618 )
=> ! [SY620: mu] :
( ( exists_in_world @ SY620 @ SY618 )
=> ! [SY621: mu] :
( ( exists_in_world @ SY621 @ SY618 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY619 @ SY620 @ SY618 )
| ~ ( qmltpeq @ SY620 @ SY621 @ SY618 ) )
| ( qmltpeq @ SY619 @ SY621 @ SY618 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,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(68,plain,
( ( ! [SY642: $i,SY643: mu] :
( ( exists_in_world @ SY643 @ SY642 )
=> ! [SY644: mu] :
( ( exists_in_world @ SY644 @ SY642 )
=> ( ~ ( qmltpeq @ SY643 @ SY644 @ SY642 )
| ( qmltpeq @ SY644 @ SY643 @ SY642 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,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(69,plain,
( ( ! [SY651: $i,SY652: mu] :
( ( exists_in_world @ SY652 @ SY651 )
=> ( qmltpeq @ SY652 @ SY652 @ SY651 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32,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(70,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[33,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(71,plain,
( ( ! [SY656: mu] :
( ( exists_in_world @ SY656 @ sK1_SY3 )
=> ( subset @ empty_set @ SY656 @ sK1_SY3 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(72,plain,
( ( ( exists_in_world @ sK2_SY656 @ sK1_SY3 )
=> ( subset @ empty_set @ sK2_SY656 @ sK1_SY3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(73,plain,
( ( exists_in_world @ sK2_SY656 @ sK1_SY3 )
= $true ),
inference(standard_cnf,[status(thm)],[72]) ).
thf(74,plain,
( ( subset @ empty_set @ sK2_SY656 @ sK1_SY3 )
= $false ),
inference(standard_cnf,[status(thm)],[72]) ).
thf(75,plain,
( ( ~ ( subset @ empty_set @ sK2_SY656 @ sK1_SY3 ) )
= $true ),
inference(polarity_switch,[status(thm)],[74]) ).
thf(76,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(77,plain,
( ( ! [SY651: $i,SY652: mu] :
( ( exists_in_world @ SY652 @ SY651 )
=> ( qmltpeq @ SY652 @ SY652 @ SY651 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(78,plain,
( ( ! [SY642: $i,SY643: mu] :
( ( exists_in_world @ SY643 @ SY642 )
=> ! [SY644: mu] :
( ( exists_in_world @ SY644 @ SY642 )
=> ( ~ ( qmltpeq @ SY643 @ SY644 @ SY642 )
| ( qmltpeq @ SY644 @ SY643 @ SY642 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(79,plain,
( ( ! [SY618: $i,SY619: mu] :
( ( exists_in_world @ SY619 @ SY618 )
=> ! [SY620: mu] :
( ( exists_in_world @ SY620 @ SY618 )
=> ! [SY621: mu] :
( ( exists_in_world @ SY621 @ SY618 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY619 @ SY620 @ SY618 )
| ~ ( qmltpeq @ SY620 @ SY621 @ SY618 ) )
| ( qmltpeq @ SY619 @ SY621 @ SY618 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(80,plain,
( ( ! [SY578: $i,SY579: mu] :
( ( exists_in_world @ SY579 @ SY578 )
=> ! [SY580: mu] :
( ( exists_in_world @ SY580 @ SY578 )
=> ! [SY581: mu] :
( ( exists_in_world @ SY581 @ SY578 )
=> ( ~ ( qmltpeq @ SY579 @ SY580 @ SY578 )
| ( qmltpeq @ ( difference @ SY579 @ SY581 ) @ ( difference @ SY580 @ SY581 ) @ SY578 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(81,plain,
( ( ! [SY546: $i,SY547: mu] :
( ( exists_in_world @ SY547 @ SY546 )
=> ! [SY548: mu] :
( ( exists_in_world @ SY548 @ SY546 )
=> ! [SY549: mu] :
( ( exists_in_world @ SY549 @ SY546 )
=> ( ~ ( qmltpeq @ SY547 @ SY548 @ SY546 )
| ( qmltpeq @ ( difference @ SY549 @ SY547 ) @ ( difference @ SY549 @ SY548 ) @ SY546 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(82,plain,
( ( ! [SY514: $i,SY515: mu] :
( ( exists_in_world @ SY515 @ SY514 )
=> ! [SY516: mu] :
( ( exists_in_world @ SY516 @ SY514 )
=> ! [SY517: mu] :
( ( exists_in_world @ SY517 @ SY514 )
=> ( ~ ( qmltpeq @ SY515 @ SY516 @ SY514 )
| ( qmltpeq @ ( intersection @ SY515 @ SY517 ) @ ( intersection @ SY516 @ SY517 ) @ SY514 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(83,plain,
( ( ! [SY482: $i,SY483: mu] :
( ( exists_in_world @ SY483 @ SY482 )
=> ! [SY484: mu] :
( ( exists_in_world @ SY484 @ SY482 )
=> ! [SY485: mu] :
( ( exists_in_world @ SY485 @ SY482 )
=> ( ~ ( qmltpeq @ SY483 @ SY484 @ SY482 )
| ( qmltpeq @ ( intersection @ SY485 @ SY483 ) @ ( intersection @ SY485 @ SY484 ) @ SY482 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(84,plain,
( ( ! [SY452: $i,SY453: mu] :
( ( exists_in_world @ SY453 @ SY452 )
=> ! [SY454: mu] :
( ( exists_in_world @ SY454 @ SY452 )
=> ( ~ ( qmltpeq @ SY453 @ SY454 @ SY452 )
| ( qmltpeq @ ( power_set @ SY453 ) @ ( power_set @ SY454 ) @ SY452 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(85,plain,
( ( ! [SY430: $i,SY431: mu] :
( ( exists_in_world @ SY431 @ SY430 )
=> ! [SY432: mu] :
( ( exists_in_world @ SY432 @ SY430 )
=> ( ~ ( qmltpeq @ SY431 @ SY432 @ SY430 )
| ( qmltpeq @ ( product @ SY431 ) @ ( product @ SY432 ) @ SY430 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(86,plain,
( ( ! [SY408: $i,SY409: mu] :
( ( exists_in_world @ SY409 @ SY408 )
=> ! [SY410: mu] :
( ( exists_in_world @ SY410 @ SY408 )
=> ( ~ ( qmltpeq @ SY409 @ SY410 @ SY408 )
| ( qmltpeq @ ( singleton @ SY409 ) @ ( singleton @ SY410 ) @ SY408 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(87,plain,
( ( ! [SY386: $i,SY387: mu] :
( ( exists_in_world @ SY387 @ SY386 )
=> ! [SY388: mu] :
( ( exists_in_world @ SY388 @ SY386 )
=> ( ~ ( qmltpeq @ SY387 @ SY388 @ SY386 )
| ( qmltpeq @ ( sum @ SY387 ) @ ( sum @ SY388 ) @ SY386 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(88,plain,
( ( ! [SY362: $i,SY363: mu] :
( ( exists_in_world @ SY363 @ SY362 )
=> ! [SY364: mu] :
( ( exists_in_world @ SY364 @ SY362 )
=> ! [SY365: mu] :
( ( exists_in_world @ SY365 @ SY362 )
=> ( ~ ( qmltpeq @ SY363 @ SY364 @ SY362 )
| ( qmltpeq @ ( union @ SY363 @ SY365 ) @ ( union @ SY364 @ SY365 ) @ SY362 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(89,plain,
( ( ! [SY330: $i,SY331: mu] :
( ( exists_in_world @ SY331 @ SY330 )
=> ! [SY332: mu] :
( ( exists_in_world @ SY332 @ SY330 )
=> ! [SY333: mu] :
( ( exists_in_world @ SY333 @ SY330 )
=> ( ~ ( qmltpeq @ SY331 @ SY332 @ SY330 )
| ( qmltpeq @ ( union @ SY333 @ SY331 ) @ ( union @ SY333 @ SY332 ) @ SY330 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(90,plain,
( ( ! [SY298: $i,SY299: mu] :
( ( exists_in_world @ SY299 @ SY298 )
=> ! [SY300: mu] :
( ( exists_in_world @ SY300 @ SY298 )
=> ! [SY301: mu] :
( ( exists_in_world @ SY301 @ SY298 )
=> ( ~ ( qmltpeq @ SY299 @ SY300 @ SY298 )
| ( qmltpeq @ ( unordered_pair @ SY299 @ SY301 ) @ ( unordered_pair @ SY300 @ SY301 ) @ SY298 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(91,plain,
( ( ! [SY266: $i,SY267: mu] :
( ( exists_in_world @ SY267 @ SY266 )
=> ! [SY268: mu] :
( ( exists_in_world @ SY268 @ SY266 )
=> ! [SY269: mu] :
( ( exists_in_world @ SY269 @ SY266 )
=> ( ~ ( qmltpeq @ SY267 @ SY268 @ SY266 )
| ( qmltpeq @ ( unordered_pair @ SY269 @ SY267 ) @ ( unordered_pair @ SY269 @ SY268 ) @ SY266 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(92,plain,
( ( ! [SY234: $i,SY235: mu] :
( ( exists_in_world @ SY235 @ SY234 )
=> ! [SY236: mu] :
( ( exists_in_world @ SY236 @ SY234 )
=> ! [SY237: mu] :
( ( exists_in_world @ SY237 @ SY234 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY235 @ SY236 @ SY234 )
| ~ ( subset @ SY235 @ SY237 @ SY234 ) )
| ( subset @ SY236 @ SY237 @ SY234 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(93,plain,
( ( ! [SY194: $i,SY195: mu] :
( ( exists_in_world @ SY195 @ SY194 )
=> ! [SY196: mu] :
( ( exists_in_world @ SY196 @ SY194 )
=> ! [SY197: mu] :
( ( exists_in_world @ SY197 @ SY194 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY195 @ SY196 @ SY194 )
| ~ ( subset @ SY197 @ SY195 @ SY194 ) )
| ( subset @ SY197 @ SY196 @ SY194 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(94,plain,
( ( ! [SY152: $i,SY153: mu] :
( ( exists_in_world @ SY153 @ SY152 )
=> ! [SY154: mu] :
( ( exists_in_world @ SY154 @ SY152 )
=> ~ ( ~ ( ~ ( subset @ SY153 @ SY154 @ SY152 )
| ! [SY155: mu] :
( ( exists_in_world @ SY155 @ SY152 )
=> ( ~ ( member @ SY155 @ SY153 @ SY152 )
| ( member @ SY155 @ SY154 @ SY152 ) ) ) )
| ~ ( ~ ! [SY156: mu] :
( ( exists_in_world @ SY156 @ SY152 )
=> ( ~ ( member @ SY156 @ SY153 @ SY152 )
| ( member @ SY156 @ SY154 @ SY152 ) ) )
| ( subset @ SY153 @ SY154 @ SY152 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(95,plain,
( ( ! [SY94: $i,SY95: mu] :
( ( exists_in_world @ SY95 @ SY94 )
=> ! [SY96: mu] :
( ( exists_in_world @ SY96 @ SY94 )
=> ~ ( ~ ( ~ ( equal_set @ SY95 @ SY96 @ SY94 )
| ~ ( ~ ( subset @ SY95 @ SY96 @ SY94 )
| ~ ( subset @ SY96 @ SY95 @ SY94 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY95 @ SY96 @ SY94 )
| ~ ( subset @ SY96 @ SY95 @ SY94 ) )
| ( equal_set @ SY95 @ SY96 @ SY94 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(96,plain,
( ( ! [SY48: $i,SY49: mu] :
( ( exists_in_world @ SY49 @ SY48 )
=> ! [SY50: mu] :
( ( exists_in_world @ SY50 @ SY48 )
=> ~ ( ~ ( ~ ( member @ SY49 @ ( power_set @ SY50 ) @ SY48 )
| ( subset @ SY49 @ SY50 @ SY48 ) )
| ~ ( ~ ( subset @ SY49 @ SY50 @ SY48 )
| ( member @ SY49 @ ( power_set @ SY50 ) @ SY48 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(97,plain,
( ( ! [SY12: $i,SY13: mu] :
( ( exists_in_world @ SY13 @ SY12 )
=> ~ ( member @ SY13 @ empty_set @ SY12 ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(98,plain,
( ( exists_in_world @ sK2_SY656 @ sK1_SY3 )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(99,plain,
( ( ~ ( subset @ empty_set @ sK2_SY656 @ sK1_SY3 ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(100,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)],[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(101,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)],[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(102,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)],[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(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 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( subset @ SX1 @ SX3 @ SX0 ) )
| ( subset @ SX2 @ SX3 @ 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(104,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)],[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(105,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)],[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(106,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ( member @ SX1 @ empty_set @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97,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 )
| ! [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)],[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(108,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)],[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(109,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)],[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(110,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)],[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(111,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)],[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(112,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)],[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(113,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX1 @ 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(114,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)],[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(115,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)],[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(116,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)],[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(117,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)],[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(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 @ ( union @ SX3 @ SX1 ) @ ( union @ SX3 @ SX2 ) @ 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(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 @ ( intersection @ SX1 @ SX3 ) @ ( intersection @ SX2 @ SX3 ) @ 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(120,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)],[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(121,plain,
! [SV1: $i] :
( ( exists_in_world @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(122,plain,
( ( subset @ empty_set @ sK2_SY656 @ sK1_SY3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(123,plain,
! [SV2: $i] :
( ( ! [SY657: mu] :
( ~ ( exists_in_world @ SY657 @ SV2 )
| ! [SY658: mu] :
( ~ ( exists_in_world @ SY658 @ SV2 )
| ~ ( qmltpeq @ SY657 @ SY658 @ SV2 )
| ( qmltpeq @ ( singleton @ SY657 ) @ ( singleton @ SY658 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(124,plain,
! [SV3: $i] :
( ( ! [SY659: mu] :
( ~ ( exists_in_world @ SY659 @ SV3 )
| ! [SY660: mu] :
( ~ ( exists_in_world @ SY660 @ SV3 )
| ! [SY661: mu] :
( ~ ( exists_in_world @ SY661 @ SV3 )
| ~ ( qmltpeq @ SY659 @ SY660 @ SV3 )
| ( qmltpeq @ ( union @ SY659 @ SY661 ) @ ( union @ SY660 @ SY661 ) @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(125,plain,
! [SV4: $i] :
( ( ! [SY662: mu] :
( ~ ( exists_in_world @ SY662 @ SV4 )
| ! [SY663: mu] :
( ~ ( exists_in_world @ SY663 @ SV4 )
| ! [SY664: mu] :
( ~ ( exists_in_world @ SY664 @ SV4 )
| ~ ( qmltpeq @ SY662 @ SY663 @ SV4 )
| ( qmltpeq @ ( intersection @ SY664 @ SY662 ) @ ( intersection @ SY664 @ SY663 ) @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(126,plain,
! [SV5: $i] :
( ( ! [SY665: mu] :
( ~ ( exists_in_world @ SY665 @ SV5 )
| ! [SY666: mu] :
( ~ ( exists_in_world @ SY666 @ SV5 )
| ! [SY667: mu] :
( ~ ( exists_in_world @ SY667 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SY665 @ SY666 @ SV5 )
| ~ ( subset @ SY665 @ SY667 @ SV5 ) )
| ( subset @ SY666 @ SY667 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(127,plain,
! [SV6: $i] :
( ( ! [SY668: mu] :
( ~ ( exists_in_world @ SY668 @ SV6 )
| ! [SY669: mu] :
( ~ ( exists_in_world @ SY669 @ SV6 )
| ~ ( ~ ( ~ ( equal_set @ SY668 @ SY669 @ SV6 )
| ~ ( ~ ( subset @ SY668 @ SY669 @ SV6 )
| ~ ( subset @ SY669 @ SY668 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SY668 @ SY669 @ SV6 )
| ~ ( subset @ SY669 @ SY668 @ SV6 ) )
| ( equal_set @ SY668 @ SY669 @ SV6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(128,plain,
! [SV7: $i] :
( ( ! [SY670: mu] :
( ~ ( exists_in_world @ SY670 @ SV7 )
| ! [SY671: mu] :
( ~ ( exists_in_world @ SY671 @ SV7 )
| ! [SY672: mu] :
( ~ ( exists_in_world @ SY672 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SY670 @ SY671 @ SV7 )
| ~ ( subset @ SY672 @ SY670 @ SV7 ) )
| ( subset @ SY672 @ SY671 @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(129,plain,
! [SV8: $i] :
( ( ! [SY673: mu] :
( ~ ( exists_in_world @ SY673 @ SV8 )
| ~ ( member @ SY673 @ empty_set @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(130,plain,
! [SV9: $i] :
( ( ! [SY674: mu] :
( ~ ( exists_in_world @ SY674 @ SV9 )
| ! [SY675: mu] :
( ~ ( exists_in_world @ SY675 @ SV9 )
| ! [SY676: mu] :
( ~ ( exists_in_world @ SY676 @ SV9 )
| ~ ( qmltpeq @ SY674 @ SY675 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SY676 @ SY674 ) @ ( unordered_pair @ SY676 @ SY675 ) @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(131,plain,
! [SV10: $i] :
( ( ! [SY677: mu] :
( ~ ( exists_in_world @ SY677 @ SV10 )
| ! [SY678: mu] :
( ~ ( exists_in_world @ SY678 @ SV10 )
| ~ ( qmltpeq @ SY677 @ SY678 @ SV10 )
| ( qmltpeq @ ( power_set @ SY677 ) @ ( power_set @ SY678 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(132,plain,
! [SV11: $i] :
( ( ! [SY679: mu] :
( ~ ( exists_in_world @ SY679 @ SV11 )
| ! [SY680: mu] :
( ~ ( exists_in_world @ SY680 @ SV11 )
| ~ ( qmltpeq @ SY679 @ SY680 @ SV11 )
| ( qmltpeq @ ( sum @ SY679 ) @ ( sum @ SY680 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(133,plain,
! [SV12: $i] :
( ( ! [SY681: mu] :
( ~ ( exists_in_world @ SY681 @ SV12 )
| ! [SY682: mu] :
( ~ ( exists_in_world @ SY682 @ SV12 )
| ! [SY683: mu] :
( ~ ( exists_in_world @ SY683 @ SV12 )
| ~ ( qmltpeq @ SY681 @ SY682 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SY681 @ SY683 ) @ ( unordered_pair @ SY682 @ SY683 ) @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(134,plain,
! [SV13: $i] :
( ( ! [SY684: mu] :
( ~ ( exists_in_world @ SY684 @ SV13 )
| ! [SY685: mu] :
( ~ ( exists_in_world @ SY685 @ SV13 )
| ~ ( qmltpeq @ SY684 @ SY685 @ SV13 )
| ( qmltpeq @ ( product @ SY684 ) @ ( product @ SY685 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(135,plain,
! [SV14: $i] :
( ( ! [SY686: mu] :
( ~ ( exists_in_world @ SY686 @ SV14 )
| ! [SY687: mu] :
( ~ ( exists_in_world @ SY687 @ SV14 )
| ~ ( ~ ( ~ ( subset @ SY686 @ SY687 @ SV14 )
| ! [SY688: mu] :
( ~ ( exists_in_world @ SY688 @ SV14 )
| ~ ( member @ SY688 @ SY686 @ SV14 )
| ( member @ SY688 @ SY687 @ SV14 ) ) )
| ~ ( ~ ! [SY689: mu] :
( ~ ( exists_in_world @ SY689 @ SV14 )
| ~ ( member @ SY689 @ SY686 @ SV14 )
| ( member @ SY689 @ SY687 @ SV14 ) )
| ( subset @ SY686 @ SY687 @ SV14 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(136,plain,
! [SV15: $i] :
( ( ! [SY690: mu] :
( ~ ( exists_in_world @ SY690 @ SV15 )
| ( qmltpeq @ SY690 @ SY690 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(137,plain,
! [SV16: $i] :
( ( ! [SY691: mu] :
( ~ ( exists_in_world @ SY691 @ SV16 )
| ! [SY692: mu] :
( ~ ( exists_in_world @ SY692 @ SV16 )
| ! [SY693: mu] :
( ~ ( exists_in_world @ SY693 @ SV16 )
| ~ ( qmltpeq @ SY691 @ SY692 @ SV16 )
| ( qmltpeq @ ( difference @ SY693 @ SY691 ) @ ( difference @ SY693 @ SY692 ) @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(138,plain,
! [SV17: $i] :
( ( ! [SY694: mu] :
( ~ ( exists_in_world @ SY694 @ SV17 )
| ! [SY695: mu] :
( ~ ( exists_in_world @ SY695 @ SV17 )
| ~ ( qmltpeq @ SY694 @ SY695 @ SV17 )
| ( qmltpeq @ SY695 @ SY694 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(139,plain,
! [SV18: $i] :
( ( ! [SY696: mu] :
( ~ ( exists_in_world @ SY696 @ SV18 )
| ! [SY697: mu] :
( ~ ( exists_in_world @ SY697 @ SV18 )
| ~ ( ~ ( ~ ( member @ SY696 @ ( power_set @ SY697 ) @ SV18 )
| ( subset @ SY696 @ SY697 @ SV18 ) )
| ~ ( ~ ( subset @ SY696 @ SY697 @ SV18 )
| ( member @ SY696 @ ( power_set @ SY697 ) @ SV18 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(140,plain,
! [SV19: $i] :
( ( ! [SY698: mu] :
( ~ ( exists_in_world @ SY698 @ SV19 )
| ! [SY699: mu] :
( ~ ( exists_in_world @ SY699 @ SV19 )
| ! [SY700: mu] :
( ~ ( exists_in_world @ SY700 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SY698 @ SY699 @ SV19 )
| ~ ( qmltpeq @ SY699 @ SY700 @ SV19 ) )
| ( qmltpeq @ SY698 @ SY700 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(141,plain,
! [SV20: $i] :
( ( ! [SY701: mu] :
( ~ ( exists_in_world @ SY701 @ SV20 )
| ! [SY702: mu] :
( ~ ( exists_in_world @ SY702 @ SV20 )
| ! [SY703: mu] :
( ~ ( exists_in_world @ SY703 @ SV20 )
| ~ ( qmltpeq @ SY701 @ SY702 @ SV20 )
| ( qmltpeq @ ( union @ SY703 @ SY701 ) @ ( union @ SY703 @ SY702 ) @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(142,plain,
! [SV21: $i] :
( ( ! [SY704: mu] :
( ~ ( exists_in_world @ SY704 @ SV21 )
| ! [SY705: mu] :
( ~ ( exists_in_world @ SY705 @ SV21 )
| ! [SY706: mu] :
( ~ ( exists_in_world @ SY706 @ SV21 )
| ~ ( qmltpeq @ SY704 @ SY705 @ SV21 )
| ( qmltpeq @ ( intersection @ SY704 @ SY706 ) @ ( intersection @ SY705 @ SY706 ) @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(143,plain,
! [SV22: $i] :
( ( ! [SY707: mu] :
( ~ ( exists_in_world @ SY707 @ SV22 )
| ! [SY708: mu] :
( ~ ( exists_in_world @ SY708 @ SV22 )
| ! [SY709: mu] :
( ~ ( exists_in_world @ SY709 @ SV22 )
| ~ ( qmltpeq @ SY707 @ SY708 @ SV22 )
| ( qmltpeq @ ( difference @ SY707 @ SY709 ) @ ( difference @ SY708 @ SY709 ) @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(144,plain,
! [SV2: $i,SV23: mu] :
( ( ~ ( exists_in_world @ SV23 @ SV2 )
| ! [SY710: mu] :
( ~ ( exists_in_world @ SY710 @ SV2 )
| ~ ( qmltpeq @ SV23 @ SY710 @ SV2 )
| ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SY710 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(145,plain,
! [SV3: $i,SV24: mu] :
( ( ~ ( exists_in_world @ SV24 @ SV3 )
| ! [SY711: mu] :
( ~ ( exists_in_world @ SY711 @ SV3 )
| ! [SY712: mu] :
( ~ ( exists_in_world @ SY712 @ SV3 )
| ~ ( qmltpeq @ SV24 @ SY711 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SY712 ) @ ( union @ SY711 @ SY712 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(146,plain,
! [SV4: $i,SV25: mu] :
( ( ~ ( exists_in_world @ SV25 @ SV4 )
| ! [SY713: mu] :
( ~ ( exists_in_world @ SY713 @ SV4 )
| ! [SY714: mu] :
( ~ ( exists_in_world @ SY714 @ SV4 )
| ~ ( qmltpeq @ SV25 @ SY713 @ SV4 )
| ( qmltpeq @ ( intersection @ SY714 @ SV25 ) @ ( intersection @ SY714 @ SY713 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(147,plain,
! [SV5: $i,SV26: mu] :
( ( ~ ( exists_in_world @ SV26 @ SV5 )
| ! [SY715: mu] :
( ~ ( exists_in_world @ SY715 @ SV5 )
| ! [SY716: mu] :
( ~ ( exists_in_world @ SY716 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY715 @ SV5 )
| ~ ( subset @ SV26 @ SY716 @ SV5 ) )
| ( subset @ SY715 @ SY716 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV6: $i,SV27: mu] :
( ( ~ ( exists_in_world @ SV27 @ SV6 )
| ! [SY717: mu] :
( ~ ( exists_in_world @ SY717 @ SV6 )
| ~ ( ~ ( ~ ( equal_set @ SV27 @ SY717 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SY717 @ SV6 )
| ~ ( subset @ SY717 @ SV27 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV27 @ SY717 @ SV6 )
| ~ ( subset @ SY717 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SY717 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV7: $i,SV28: mu] :
( ( ~ ( exists_in_world @ SV28 @ SV7 )
| ! [SY718: mu] :
( ~ ( exists_in_world @ SY718 @ SV7 )
| ! [SY719: mu] :
( ~ ( exists_in_world @ SY719 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV28 @ SY718 @ SV7 )
| ~ ( subset @ SY719 @ SV28 @ SV7 ) )
| ( subset @ SY719 @ SY718 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV8: $i,SV29: mu] :
( ( ~ ( exists_in_world @ SV29 @ SV8 )
| ~ ( member @ SV29 @ empty_set @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
! [SV9: $i,SV30: mu] :
( ( ~ ( exists_in_world @ SV30 @ SV9 )
| ! [SY720: mu] :
( ~ ( exists_in_world @ SY720 @ SV9 )
| ! [SY721: mu] :
( ~ ( exists_in_world @ SY721 @ SV9 )
| ~ ( qmltpeq @ SV30 @ SY720 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SY721 @ SV30 ) @ ( unordered_pair @ SY721 @ SY720 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV10: $i,SV31: mu] :
( ( ~ ( exists_in_world @ SV31 @ SV10 )
| ! [SY722: mu] :
( ~ ( exists_in_world @ SY722 @ SV10 )
| ~ ( qmltpeq @ SV31 @ SY722 @ SV10 )
| ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SY722 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV11: $i,SV32: mu] :
( ( ~ ( exists_in_world @ SV32 @ SV11 )
| ! [SY723: mu] :
( ~ ( exists_in_world @ SY723 @ SV11 )
| ~ ( qmltpeq @ SV32 @ SY723 @ SV11 )
| ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SY723 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV12: $i,SV33: mu] :
( ( ~ ( exists_in_world @ SV33 @ SV12 )
| ! [SY724: mu] :
( ~ ( exists_in_world @ SY724 @ SV12 )
| ! [SY725: mu] :
( ~ ( exists_in_world @ SY725 @ SV12 )
| ~ ( qmltpeq @ SV33 @ SY724 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SY725 ) @ ( unordered_pair @ SY724 @ SY725 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV13: $i,SV34: mu] :
( ( ~ ( exists_in_world @ SV34 @ SV13 )
| ! [SY726: mu] :
( ~ ( exists_in_world @ SY726 @ SV13 )
| ~ ( qmltpeq @ SV34 @ SY726 @ SV13 )
| ( qmltpeq @ ( product @ SV34 ) @ ( product @ SY726 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(156,plain,
! [SV14: $i,SV35: mu] :
( ( ~ ( exists_in_world @ SV35 @ SV14 )
| ! [SY727: mu] :
( ~ ( exists_in_world @ SY727 @ SV14 )
| ~ ( ~ ( ~ ( subset @ SV35 @ SY727 @ SV14 )
| ! [SY728: mu] :
( ~ ( exists_in_world @ SY728 @ SV14 )
| ~ ( member @ SY728 @ SV35 @ SV14 )
| ( member @ SY728 @ SY727 @ SV14 ) ) )
| ~ ( ~ ! [SY729: mu] :
( ~ ( exists_in_world @ SY729 @ SV14 )
| ~ ( member @ SY729 @ SV35 @ SV14 )
| ( member @ SY729 @ SY727 @ SV14 ) )
| ( subset @ SV35 @ SY727 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(157,plain,
! [SV15: $i,SV36: mu] :
( ( ~ ( exists_in_world @ SV36 @ SV15 )
| ( qmltpeq @ SV36 @ SV36 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(158,plain,
! [SV16: $i,SV37: mu] :
( ( ~ ( exists_in_world @ SV37 @ SV16 )
| ! [SY730: mu] :
( ~ ( exists_in_world @ SY730 @ SV16 )
| ! [SY731: mu] :
( ~ ( exists_in_world @ SY731 @ SV16 )
| ~ ( qmltpeq @ SV37 @ SY730 @ SV16 )
| ( qmltpeq @ ( difference @ SY731 @ SV37 ) @ ( difference @ SY731 @ SY730 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(159,plain,
! [SV17: $i,SV38: mu] :
( ( ~ ( exists_in_world @ SV38 @ SV17 )
| ! [SY732: mu] :
( ~ ( exists_in_world @ SY732 @ SV17 )
| ~ ( qmltpeq @ SV38 @ SY732 @ SV17 )
| ( qmltpeq @ SY732 @ SV38 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(160,plain,
! [SV18: $i,SV39: mu] :
( ( ~ ( exists_in_world @ SV39 @ SV18 )
| ! [SY733: mu] :
( ~ ( exists_in_world @ SY733 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV39 @ ( power_set @ SY733 ) @ SV18 )
| ( subset @ SV39 @ SY733 @ SV18 ) )
| ~ ( ~ ( subset @ SV39 @ SY733 @ SV18 )
| ( member @ SV39 @ ( power_set @ SY733 ) @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(161,plain,
! [SV19: $i,SV40: mu] :
( ( ~ ( exists_in_world @ SV40 @ SV19 )
| ! [SY734: mu] :
( ~ ( exists_in_world @ SY734 @ SV19 )
| ! [SY735: mu] :
( ~ ( exists_in_world @ SY735 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SY734 @ SV19 )
| ~ ( qmltpeq @ SY734 @ SY735 @ SV19 ) )
| ( qmltpeq @ SV40 @ SY735 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(162,plain,
! [SV20: $i,SV41: mu] :
( ( ~ ( exists_in_world @ SV41 @ SV20 )
| ! [SY736: mu] :
( ~ ( exists_in_world @ SY736 @ SV20 )
| ! [SY737: mu] :
( ~ ( exists_in_world @ SY737 @ SV20 )
| ~ ( qmltpeq @ SV41 @ SY736 @ SV20 )
| ( qmltpeq @ ( union @ SY737 @ SV41 ) @ ( union @ SY737 @ SY736 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(163,plain,
! [SV21: $i,SV42: mu] :
( ( ~ ( exists_in_world @ SV42 @ SV21 )
| ! [SY738: mu] :
( ~ ( exists_in_world @ SY738 @ SV21 )
| ! [SY739: mu] :
( ~ ( exists_in_world @ SY739 @ SV21 )
| ~ ( qmltpeq @ SV42 @ SY738 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SY739 ) @ ( intersection @ SY738 @ SY739 ) @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(164,plain,
! [SV22: $i,SV43: mu] :
( ( ~ ( exists_in_world @ SV43 @ SV22 )
| ! [SY740: mu] :
( ~ ( exists_in_world @ SY740 @ SV22 )
| ! [SY741: mu] :
( ~ ( exists_in_world @ SY741 @ SV22 )
| ~ ( qmltpeq @ SV43 @ SY740 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SY741 ) @ ( difference @ SY740 @ SY741 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(165,plain,
! [SV2: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV2 ) )
= $true )
| ( ( ! [SY710: mu] :
( ~ ( exists_in_world @ SY710 @ SV2 )
| ~ ( qmltpeq @ SV23 @ SY710 @ SV2 )
| ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SY710 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(166,plain,
! [SV3: $i,SV24: mu] :
( ( ( ~ ( exists_in_world @ SV24 @ SV3 ) )
= $true )
| ( ( ! [SY711: mu] :
( ~ ( exists_in_world @ SY711 @ SV3 )
| ! [SY712: mu] :
( ~ ( exists_in_world @ SY712 @ SV3 )
| ~ ( qmltpeq @ SV24 @ SY711 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SY712 ) @ ( union @ SY711 @ SY712 ) @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(167,plain,
! [SV4: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV4 ) )
= $true )
| ( ( ! [SY713: mu] :
( ~ ( exists_in_world @ SY713 @ SV4 )
| ! [SY714: mu] :
( ~ ( exists_in_world @ SY714 @ SV4 )
| ~ ( qmltpeq @ SV25 @ SY713 @ SV4 )
| ( qmltpeq @ ( intersection @ SY714 @ SV25 ) @ ( intersection @ SY714 @ SY713 ) @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(168,plain,
! [SV5: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV5 ) )
= $true )
| ( ( ! [SY715: mu] :
( ~ ( exists_in_world @ SY715 @ SV5 )
| ! [SY716: mu] :
( ~ ( exists_in_world @ SY716 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY715 @ SV5 )
| ~ ( subset @ SV26 @ SY716 @ SV5 ) )
| ( subset @ SY715 @ SY716 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV6: $i,SV27: mu] :
( ( ( ~ ( exists_in_world @ SV27 @ SV6 ) )
= $true )
| ( ( ! [SY717: mu] :
( ~ ( exists_in_world @ SY717 @ SV6 )
| ~ ( ~ ( ~ ( equal_set @ SV27 @ SY717 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SY717 @ SV6 )
| ~ ( subset @ SY717 @ SV27 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV27 @ SY717 @ SV6 )
| ~ ( subset @ SY717 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SY717 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(170,plain,
! [SV7: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV7 ) )
= $true )
| ( ( ! [SY718: mu] :
( ~ ( exists_in_world @ SY718 @ SV7 )
| ! [SY719: mu] :
( ~ ( exists_in_world @ SY719 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV28 @ SY718 @ SV7 )
| ~ ( subset @ SY719 @ SV28 @ SV7 ) )
| ( subset @ SY719 @ SY718 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(171,plain,
! [SV8: $i,SV29: mu] :
( ( ( ~ ( exists_in_world @ SV29 @ SV8 ) )
= $true )
| ( ( ~ ( member @ SV29 @ empty_set @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(172,plain,
! [SV9: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV9 ) )
= $true )
| ( ( ! [SY720: mu] :
( ~ ( exists_in_world @ SY720 @ SV9 )
| ! [SY721: mu] :
( ~ ( exists_in_world @ SY721 @ SV9 )
| ~ ( qmltpeq @ SV30 @ SY720 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SY721 @ SV30 ) @ ( unordered_pair @ SY721 @ SY720 ) @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(173,plain,
! [SV10: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV10 ) )
= $true )
| ( ( ! [SY722: mu] :
( ~ ( exists_in_world @ SY722 @ SV10 )
| ~ ( qmltpeq @ SV31 @ SY722 @ SV10 )
| ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SY722 ) @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(174,plain,
! [SV11: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV11 ) )
= $true )
| ( ( ! [SY723: mu] :
( ~ ( exists_in_world @ SY723 @ SV11 )
| ~ ( qmltpeq @ SV32 @ SY723 @ SV11 )
| ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SY723 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(175,plain,
! [SV12: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV12 ) )
= $true )
| ( ( ! [SY724: mu] :
( ~ ( exists_in_world @ SY724 @ SV12 )
| ! [SY725: mu] :
( ~ ( exists_in_world @ SY725 @ SV12 )
| ~ ( qmltpeq @ SV33 @ SY724 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SY725 ) @ ( unordered_pair @ SY724 @ SY725 ) @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(176,plain,
! [SV13: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV13 ) )
= $true )
| ( ( ! [SY726: mu] :
( ~ ( exists_in_world @ SY726 @ SV13 )
| ~ ( qmltpeq @ SV34 @ SY726 @ SV13 )
| ( qmltpeq @ ( product @ SV34 ) @ ( product @ SY726 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(177,plain,
! [SV14: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV14 ) )
= $true )
| ( ( ! [SY727: mu] :
( ~ ( exists_in_world @ SY727 @ SV14 )
| ~ ( ~ ( ~ ( subset @ SV35 @ SY727 @ SV14 )
| ! [SY728: mu] :
( ~ ( exists_in_world @ SY728 @ SV14 )
| ~ ( member @ SY728 @ SV35 @ SV14 )
| ( member @ SY728 @ SY727 @ SV14 ) ) )
| ~ ( ~ ! [SY729: mu] :
( ~ ( exists_in_world @ SY729 @ SV14 )
| ~ ( member @ SY729 @ SV35 @ SV14 )
| ( member @ SY729 @ SY727 @ SV14 ) )
| ( subset @ SV35 @ SY727 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(178,plain,
! [SV15: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV15 ) )
= $true )
| ( ( qmltpeq @ SV36 @ SV36 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(179,plain,
! [SV16: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV16 ) )
= $true )
| ( ( ! [SY730: mu] :
( ~ ( exists_in_world @ SY730 @ SV16 )
| ! [SY731: mu] :
( ~ ( exists_in_world @ SY731 @ SV16 )
| ~ ( qmltpeq @ SV37 @ SY730 @ SV16 )
| ( qmltpeq @ ( difference @ SY731 @ SV37 ) @ ( difference @ SY731 @ SY730 ) @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(180,plain,
! [SV17: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV17 ) )
= $true )
| ( ( ! [SY732: mu] :
( ~ ( exists_in_world @ SY732 @ SV17 )
| ~ ( qmltpeq @ SV38 @ SY732 @ SV17 )
| ( qmltpeq @ SY732 @ SV38 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(181,plain,
! [SV18: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV18 ) )
= $true )
| ( ( ! [SY733: mu] :
( ~ ( exists_in_world @ SY733 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV39 @ ( power_set @ SY733 ) @ SV18 )
| ( subset @ SV39 @ SY733 @ SV18 ) )
| ~ ( ~ ( subset @ SV39 @ SY733 @ SV18 )
| ( member @ SV39 @ ( power_set @ SY733 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(182,plain,
! [SV19: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV19 ) )
= $true )
| ( ( ! [SY734: mu] :
( ~ ( exists_in_world @ SY734 @ SV19 )
| ! [SY735: mu] :
( ~ ( exists_in_world @ SY735 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SY734 @ SV19 )
| ~ ( qmltpeq @ SY734 @ SY735 @ SV19 ) )
| ( qmltpeq @ SV40 @ SY735 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(183,plain,
! [SV20: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV20 ) )
= $true )
| ( ( ! [SY736: mu] :
( ~ ( exists_in_world @ SY736 @ SV20 )
| ! [SY737: mu] :
( ~ ( exists_in_world @ SY737 @ SV20 )
| ~ ( qmltpeq @ SV41 @ SY736 @ SV20 )
| ( qmltpeq @ ( union @ SY737 @ SV41 ) @ ( union @ SY737 @ SY736 ) @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(184,plain,
! [SV21: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV21 ) )
= $true )
| ( ( ! [SY738: mu] :
( ~ ( exists_in_world @ SY738 @ SV21 )
| ! [SY739: mu] :
( ~ ( exists_in_world @ SY739 @ SV21 )
| ~ ( qmltpeq @ SV42 @ SY738 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SY739 ) @ ( intersection @ SY738 @ SY739 ) @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(185,plain,
! [SV22: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV22 ) )
= $true )
| ( ( ! [SY740: mu] :
( ~ ( exists_in_world @ SY740 @ SV22 )
| ! [SY741: mu] :
( ~ ( exists_in_world @ SY741 @ SV22 )
| ~ ( qmltpeq @ SV43 @ SY740 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SY741 ) @ ( difference @ SY740 @ SY741 ) @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(186,plain,
! [SV2: $i,SV23: mu] :
( ( ( exists_in_world @ SV23 @ SV2 )
= $false )
| ( ( ! [SY710: mu] :
( ~ ( exists_in_world @ SY710 @ SV2 )
| ~ ( qmltpeq @ SV23 @ SY710 @ SV2 )
| ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SY710 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(187,plain,
! [SV3: $i,SV24: mu] :
( ( ( exists_in_world @ SV24 @ SV3 )
= $false )
| ( ( ! [SY711: mu] :
( ~ ( exists_in_world @ SY711 @ SV3 )
| ! [SY712: mu] :
( ~ ( exists_in_world @ SY712 @ SV3 )
| ~ ( qmltpeq @ SV24 @ SY711 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SY712 ) @ ( union @ SY711 @ SY712 ) @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(188,plain,
! [SV4: $i,SV25: mu] :
( ( ( exists_in_world @ SV25 @ SV4 )
= $false )
| ( ( ! [SY713: mu] :
( ~ ( exists_in_world @ SY713 @ SV4 )
| ! [SY714: mu] :
( ~ ( exists_in_world @ SY714 @ SV4 )
| ~ ( qmltpeq @ SV25 @ SY713 @ SV4 )
| ( qmltpeq @ ( intersection @ SY714 @ SV25 ) @ ( intersection @ SY714 @ SY713 ) @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(189,plain,
! [SV5: $i,SV26: mu] :
( ( ( exists_in_world @ SV26 @ SV5 )
= $false )
| ( ( ! [SY715: mu] :
( ~ ( exists_in_world @ SY715 @ SV5 )
| ! [SY716: mu] :
( ~ ( exists_in_world @ SY716 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY715 @ SV5 )
| ~ ( subset @ SV26 @ SY716 @ SV5 ) )
| ( subset @ SY715 @ SY716 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(190,plain,
! [SV6: $i,SV27: mu] :
( ( ( exists_in_world @ SV27 @ SV6 )
= $false )
| ( ( ! [SY717: mu] :
( ~ ( exists_in_world @ SY717 @ SV6 )
| ~ ( ~ ( ~ ( equal_set @ SV27 @ SY717 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SY717 @ SV6 )
| ~ ( subset @ SY717 @ SV27 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV27 @ SY717 @ SV6 )
| ~ ( subset @ SY717 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SY717 @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(191,plain,
! [SV7: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV7 )
= $false )
| ( ( ! [SY718: mu] :
( ~ ( exists_in_world @ SY718 @ SV7 )
| ! [SY719: mu] :
( ~ ( exists_in_world @ SY719 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV28 @ SY718 @ SV7 )
| ~ ( subset @ SY719 @ SV28 @ SV7 ) )
| ( subset @ SY719 @ SY718 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(192,plain,
! [SV8: $i,SV29: mu] :
( ( ( exists_in_world @ SV29 @ SV8 )
= $false )
| ( ( ~ ( member @ SV29 @ empty_set @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(193,plain,
! [SV9: $i,SV30: mu] :
( ( ( exists_in_world @ SV30 @ SV9 )
= $false )
| ( ( ! [SY720: mu] :
( ~ ( exists_in_world @ SY720 @ SV9 )
| ! [SY721: mu] :
( ~ ( exists_in_world @ SY721 @ SV9 )
| ~ ( qmltpeq @ SV30 @ SY720 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SY721 @ SV30 ) @ ( unordered_pair @ SY721 @ SY720 ) @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(194,plain,
! [SV10: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV10 )
= $false )
| ( ( ! [SY722: mu] :
( ~ ( exists_in_world @ SY722 @ SV10 )
| ~ ( qmltpeq @ SV31 @ SY722 @ SV10 )
| ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SY722 ) @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(195,plain,
! [SV11: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV11 )
= $false )
| ( ( ! [SY723: mu] :
( ~ ( exists_in_world @ SY723 @ SV11 )
| ~ ( qmltpeq @ SV32 @ SY723 @ SV11 )
| ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SY723 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(196,plain,
! [SV12: $i,SV33: mu] :
( ( ( exists_in_world @ SV33 @ SV12 )
= $false )
| ( ( ! [SY724: mu] :
( ~ ( exists_in_world @ SY724 @ SV12 )
| ! [SY725: mu] :
( ~ ( exists_in_world @ SY725 @ SV12 )
| ~ ( qmltpeq @ SV33 @ SY724 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SY725 ) @ ( unordered_pair @ SY724 @ SY725 ) @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(197,plain,
! [SV13: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV13 )
= $false )
| ( ( ! [SY726: mu] :
( ~ ( exists_in_world @ SY726 @ SV13 )
| ~ ( qmltpeq @ SV34 @ SY726 @ SV13 )
| ( qmltpeq @ ( product @ SV34 ) @ ( product @ SY726 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(198,plain,
! [SV14: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV14 )
= $false )
| ( ( ! [SY727: mu] :
( ~ ( exists_in_world @ SY727 @ SV14 )
| ~ ( ~ ( ~ ( subset @ SV35 @ SY727 @ SV14 )
| ! [SY728: mu] :
( ~ ( exists_in_world @ SY728 @ SV14 )
| ~ ( member @ SY728 @ SV35 @ SV14 )
| ( member @ SY728 @ SY727 @ SV14 ) ) )
| ~ ( ~ ! [SY729: mu] :
( ~ ( exists_in_world @ SY729 @ SV14 )
| ~ ( member @ SY729 @ SV35 @ SV14 )
| ( member @ SY729 @ SY727 @ SV14 ) )
| ( subset @ SV35 @ SY727 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(199,plain,
! [SV15: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV15 )
= $false )
| ( ( qmltpeq @ SV36 @ SV36 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(200,plain,
! [SV16: $i,SV37: mu] :
( ( ( exists_in_world @ SV37 @ SV16 )
= $false )
| ( ( ! [SY730: mu] :
( ~ ( exists_in_world @ SY730 @ SV16 )
| ! [SY731: mu] :
( ~ ( exists_in_world @ SY731 @ SV16 )
| ~ ( qmltpeq @ SV37 @ SY730 @ SV16 )
| ( qmltpeq @ ( difference @ SY731 @ SV37 ) @ ( difference @ SY731 @ SY730 ) @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(201,plain,
! [SV17: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV17 )
= $false )
| ( ( ! [SY732: mu] :
( ~ ( exists_in_world @ SY732 @ SV17 )
| ~ ( qmltpeq @ SV38 @ SY732 @ SV17 )
| ( qmltpeq @ SY732 @ SV38 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(202,plain,
! [SV18: $i,SV39: mu] :
( ( ( exists_in_world @ SV39 @ SV18 )
= $false )
| ( ( ! [SY733: mu] :
( ~ ( exists_in_world @ SY733 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV39 @ ( power_set @ SY733 ) @ SV18 )
| ( subset @ SV39 @ SY733 @ SV18 ) )
| ~ ( ~ ( subset @ SV39 @ SY733 @ SV18 )
| ( member @ SV39 @ ( power_set @ SY733 ) @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(203,plain,
! [SV19: $i,SV40: mu] :
( ( ( exists_in_world @ SV40 @ SV19 )
= $false )
| ( ( ! [SY734: mu] :
( ~ ( exists_in_world @ SY734 @ SV19 )
| ! [SY735: mu] :
( ~ ( exists_in_world @ SY735 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SY734 @ SV19 )
| ~ ( qmltpeq @ SY734 @ SY735 @ SV19 ) )
| ( qmltpeq @ SV40 @ SY735 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(204,plain,
! [SV20: $i,SV41: mu] :
( ( ( exists_in_world @ SV41 @ SV20 )
= $false )
| ( ( ! [SY736: mu] :
( ~ ( exists_in_world @ SY736 @ SV20 )
| ! [SY737: mu] :
( ~ ( exists_in_world @ SY737 @ SV20 )
| ~ ( qmltpeq @ SV41 @ SY736 @ SV20 )
| ( qmltpeq @ ( union @ SY737 @ SV41 ) @ ( union @ SY737 @ SY736 ) @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(205,plain,
! [SV21: $i,SV42: mu] :
( ( ( exists_in_world @ SV42 @ SV21 )
= $false )
| ( ( ! [SY738: mu] :
( ~ ( exists_in_world @ SY738 @ SV21 )
| ! [SY739: mu] :
( ~ ( exists_in_world @ SY739 @ SV21 )
| ~ ( qmltpeq @ SV42 @ SY738 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SY739 ) @ ( intersection @ SY738 @ SY739 ) @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(206,plain,
! [SV22: $i,SV43: mu] :
( ( ( exists_in_world @ SV43 @ SV22 )
= $false )
| ( ( ! [SY740: mu] :
( ~ ( exists_in_world @ SY740 @ SV22 )
| ! [SY741: mu] :
( ~ ( exists_in_world @ SY741 @ SV22 )
| ~ ( qmltpeq @ SV43 @ SY740 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SY741 ) @ ( difference @ SY740 @ SY741 ) @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(207,plain,
! [SV23: mu,SV2: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV2 )
| ~ ( qmltpeq @ SV23 @ SV44 @ SV2 )
| ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SV44 ) @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(208,plain,
! [SV24: mu,SV3: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV3 )
| ! [SY742: mu] :
( ~ ( exists_in_world @ SY742 @ SV3 )
| ~ ( qmltpeq @ SV24 @ SV45 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SY742 ) @ ( union @ SV45 @ SY742 ) @ SV3 ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(209,plain,
! [SV25: mu,SV4: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV4 )
| ! [SY743: mu] :
( ~ ( exists_in_world @ SY743 @ SV4 )
| ~ ( qmltpeq @ SV25 @ SV46 @ SV4 )
| ( qmltpeq @ ( intersection @ SY743 @ SV25 ) @ ( intersection @ SY743 @ SV46 ) @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(210,plain,
! [SV26: mu,SV5: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV5 )
| ! [SY744: mu] :
( ~ ( exists_in_world @ SY744 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SY744 @ SV5 ) )
| ( subset @ SV47 @ SY744 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(211,plain,
! [SV27: mu,SV6: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV6 )
| ~ ( ~ ( ~ ( equal_set @ SV27 @ SV48 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SV48 @ SV6 ) ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(212,plain,
! [SV28: mu,SV7: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV7 )
| ! [SY745: mu] :
( ~ ( exists_in_world @ SY745 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SY745 @ SV28 @ SV7 ) )
| ( subset @ SY745 @ SV49 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(213,plain,
! [SV8: $i,SV29: mu] :
( ( ( member @ SV29 @ empty_set @ SV8 )
= $false )
| ( ( exists_in_world @ SV29 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(214,plain,
! [SV30: mu,SV9: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV9 )
| ! [SY746: mu] :
( ~ ( exists_in_world @ SY746 @ SV9 )
| ~ ( qmltpeq @ SV30 @ SV50 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SY746 @ SV30 ) @ ( unordered_pair @ SY746 @ SV50 ) @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(215,plain,
! [SV31: mu,SV10: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV10 )
| ~ ( qmltpeq @ SV31 @ SV51 @ SV10 )
| ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SV51 ) @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(216,plain,
! [SV32: mu,SV11: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV11 )
| ~ ( qmltpeq @ SV32 @ SV52 @ SV11 )
| ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SV52 ) @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(217,plain,
! [SV33: mu,SV12: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV12 )
| ! [SY747: mu] :
( ~ ( exists_in_world @ SY747 @ SV12 )
| ~ ( qmltpeq @ SV33 @ SV53 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SY747 ) @ ( unordered_pair @ SV53 @ SY747 ) @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(218,plain,
! [SV34: mu,SV13: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV13 )
| ~ ( qmltpeq @ SV34 @ SV54 @ SV13 )
| ( qmltpeq @ ( product @ SV34 ) @ ( product @ SV54 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(219,plain,
! [SV35: mu,SV14: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV14 )
| ~ ( ~ ( ~ ( subset @ SV35 @ SV55 @ SV14 )
| ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) )
| ~ ( ~ ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) )
| ( subset @ SV35 @ SV55 @ SV14 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(220,plain,
! [SV37: mu,SV16: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV16 )
| ! [SY750: mu] :
( ~ ( exists_in_world @ SY750 @ SV16 )
| ~ ( qmltpeq @ SV37 @ SV56 @ SV16 )
| ( qmltpeq @ ( difference @ SY750 @ SV37 ) @ ( difference @ SY750 @ SV56 ) @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV38: mu,SV17: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV17 )
| ~ ( qmltpeq @ SV38 @ SV57 @ SV17 )
| ( qmltpeq @ SV57 @ SV38 @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV39: mu,SV18: $i,SV58: mu] :
( ( ( ~ ( exists_in_world @ SV58 @ SV18 )
| ~ ( ~ ( ~ ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
| ( subset @ SV39 @ SV58 @ SV18 ) )
| ~ ( ~ ( subset @ SV39 @ SV58 @ SV18 )
| ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 ) ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(223,plain,
! [SV40: mu,SV19: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV19 )
| ! [SY751: mu] :
( ~ ( exists_in_world @ SY751 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SY751 @ SV19 ) )
| ( qmltpeq @ SV40 @ SY751 @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(224,plain,
! [SV41: mu,SV20: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV20 )
| ! [SY752: mu] :
( ~ ( exists_in_world @ SY752 @ SV20 )
| ~ ( qmltpeq @ SV41 @ SV60 @ SV20 )
| ( qmltpeq @ ( union @ SY752 @ SV41 ) @ ( union @ SY752 @ SV60 ) @ SV20 ) ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(225,plain,
! [SV42: mu,SV21: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV21 )
| ! [SY753: mu] :
( ~ ( exists_in_world @ SY753 @ SV21 )
| ~ ( qmltpeq @ SV42 @ SV61 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SY753 ) @ ( intersection @ SV61 @ SY753 ) @ SV21 ) ) )
= $true )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(226,plain,
! [SV43: mu,SV22: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV22 )
| ! [SY754: mu] :
( ~ ( exists_in_world @ SY754 @ SV22 )
| ~ ( qmltpeq @ SV43 @ SV62 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SY754 ) @ ( difference @ SV62 @ SY754 ) @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(227,plain,
! [SV23: mu,SV2: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV2 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV23 @ SV44 @ SV2 )
| ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SV44 ) @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(228,plain,
! [SV24: mu,SV3: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV3 ) )
= $true )
| ( ( ! [SY742: mu] :
( ~ ( exists_in_world @ SY742 @ SV3 )
| ~ ( qmltpeq @ SV24 @ SV45 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SY742 ) @ ( union @ SV45 @ SY742 ) @ SV3 ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(229,plain,
! [SV25: mu,SV4: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV4 ) )
= $true )
| ( ( ! [SY743: mu] :
( ~ ( exists_in_world @ SY743 @ SV4 )
| ~ ( qmltpeq @ SV25 @ SV46 @ SV4 )
| ( qmltpeq @ ( intersection @ SY743 @ SV25 ) @ ( intersection @ SY743 @ SV46 ) @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(230,plain,
! [SV26: mu,SV5: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV5 ) )
= $true )
| ( ( ! [SY744: mu] :
( ~ ( exists_in_world @ SY744 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SY744 @ SV5 ) )
| ( subset @ SV47 @ SY744 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(231,plain,
! [SV27: mu,SV6: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( equal_set @ SV27 @ SV48 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SV48 @ SV6 ) ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(232,plain,
! [SV28: mu,SV7: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV7 ) )
= $true )
| ( ( ! [SY745: mu] :
( ~ ( exists_in_world @ SY745 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SY745 @ SV28 @ SV7 ) )
| ( subset @ SY745 @ SV49 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(233,plain,
! [SV30: mu,SV9: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV9 ) )
= $true )
| ( ( ! [SY746: mu] :
( ~ ( exists_in_world @ SY746 @ SV9 )
| ~ ( qmltpeq @ SV30 @ SV50 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SY746 @ SV30 ) @ ( unordered_pair @ SY746 @ SV50 ) @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(234,plain,
! [SV31: mu,SV10: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV10 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV31 @ SV51 @ SV10 )
| ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SV51 ) @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(235,plain,
! [SV32: mu,SV11: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV11 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV32 @ SV52 @ SV11 )
| ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SV52 ) @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(236,plain,
! [SV33: mu,SV12: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV12 ) )
= $true )
| ( ( ! [SY747: mu] :
( ~ ( exists_in_world @ SY747 @ SV12 )
| ~ ( qmltpeq @ SV33 @ SV53 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SY747 ) @ ( unordered_pair @ SV53 @ SY747 ) @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(237,plain,
! [SV34: mu,SV13: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV13 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV34 @ SV54 @ SV13 )
| ( qmltpeq @ ( product @ SV34 ) @ ( product @ SV54 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(238,plain,
! [SV35: mu,SV14: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subset @ SV35 @ SV55 @ SV14 )
| ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) )
| ~ ( ~ ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) )
| ( subset @ SV35 @ SV55 @ SV14 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(239,plain,
! [SV37: mu,SV16: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV16 ) )
= $true )
| ( ( ! [SY750: mu] :
( ~ ( exists_in_world @ SY750 @ SV16 )
| ~ ( qmltpeq @ SV37 @ SV56 @ SV16 )
| ( qmltpeq @ ( difference @ SY750 @ SV37 ) @ ( difference @ SY750 @ SV56 ) @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(240,plain,
! [SV38: mu,SV17: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV17 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV38 @ SV57 @ SV17 )
| ( qmltpeq @ SV57 @ SV38 @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(241,plain,
! [SV39: mu,SV18: $i,SV58: mu] :
( ( ( ~ ( exists_in_world @ SV58 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
| ( subset @ SV39 @ SV58 @ SV18 ) )
| ~ ( ~ ( subset @ SV39 @ SV58 @ SV18 )
| ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 ) ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(242,plain,
! [SV40: mu,SV19: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV19 ) )
= $true )
| ( ( ! [SY751: mu] :
( ~ ( exists_in_world @ SY751 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SY751 @ SV19 ) )
| ( qmltpeq @ SV40 @ SY751 @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(243,plain,
! [SV41: mu,SV20: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV20 ) )
= $true )
| ( ( ! [SY752: mu] :
( ~ ( exists_in_world @ SY752 @ SV20 )
| ~ ( qmltpeq @ SV41 @ SV60 @ SV20 )
| ( qmltpeq @ ( union @ SY752 @ SV41 ) @ ( union @ SY752 @ SV60 ) @ SV20 ) ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(244,plain,
! [SV42: mu,SV21: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV21 ) )
= $true )
| ( ( ! [SY753: mu] :
( ~ ( exists_in_world @ SY753 @ SV21 )
| ~ ( qmltpeq @ SV42 @ SV61 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SY753 ) @ ( intersection @ SV61 @ SY753 ) @ SV21 ) ) )
= $true )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(245,plain,
! [SV43: mu,SV22: $i,SV62: mu] :
( ( ( ~ ( exists_in_world @ SV62 @ SV22 ) )
= $true )
| ( ( ! [SY754: mu] :
( ~ ( exists_in_world @ SY754 @ SV22 )
| ~ ( qmltpeq @ SV43 @ SV62 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SY754 ) @ ( difference @ SV62 @ SY754 ) @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(246,plain,
! [SV23: mu,SV2: $i,SV44: mu] :
( ( ( exists_in_world @ SV44 @ SV2 )
= $false )
| ( ( ~ ( qmltpeq @ SV23 @ SV44 @ SV2 )
| ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SV44 ) @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(247,plain,
! [SV24: mu,SV3: $i,SV45: mu] :
( ( ( exists_in_world @ SV45 @ SV3 )
= $false )
| ( ( ! [SY742: mu] :
( ~ ( exists_in_world @ SY742 @ SV3 )
| ~ ( qmltpeq @ SV24 @ SV45 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SY742 ) @ ( union @ SV45 @ SY742 ) @ SV3 ) ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(248,plain,
! [SV25: mu,SV4: $i,SV46: mu] :
( ( ( exists_in_world @ SV46 @ SV4 )
= $false )
| ( ( ! [SY743: mu] :
( ~ ( exists_in_world @ SY743 @ SV4 )
| ~ ( qmltpeq @ SV25 @ SV46 @ SV4 )
| ( qmltpeq @ ( intersection @ SY743 @ SV25 ) @ ( intersection @ SY743 @ SV46 ) @ SV4 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(249,plain,
! [SV26: mu,SV5: $i,SV47: mu] :
( ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( ! [SY744: mu] :
( ~ ( exists_in_world @ SY744 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SY744 @ SV5 ) )
| ( subset @ SV47 @ SY744 @ SV5 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(250,plain,
! [SV27: mu,SV6: $i,SV48: mu] :
( ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( ~ ( ~ ( ~ ( equal_set @ SV27 @ SV48 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SV48 @ SV6 ) ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(251,plain,
! [SV28: mu,SV7: $i,SV49: mu] :
( ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( ! [SY745: mu] :
( ~ ( exists_in_world @ SY745 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SY745 @ SV28 @ SV7 ) )
| ( subset @ SY745 @ SV49 @ SV7 ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(252,plain,
! [SV30: mu,SV9: $i,SV50: mu] :
( ( ( exists_in_world @ SV50 @ SV9 )
= $false )
| ( ( ! [SY746: mu] :
( ~ ( exists_in_world @ SY746 @ SV9 )
| ~ ( qmltpeq @ SV30 @ SV50 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SY746 @ SV30 ) @ ( unordered_pair @ SY746 @ SV50 ) @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(253,plain,
! [SV31: mu,SV10: $i,SV51: mu] :
( ( ( exists_in_world @ SV51 @ SV10 )
= $false )
| ( ( ~ ( qmltpeq @ SV31 @ SV51 @ SV10 )
| ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SV51 ) @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(254,plain,
! [SV32: mu,SV11: $i,SV52: mu] :
( ( ( exists_in_world @ SV52 @ SV11 )
= $false )
| ( ( ~ ( qmltpeq @ SV32 @ SV52 @ SV11 )
| ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SV52 ) @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(255,plain,
! [SV33: mu,SV12: $i,SV53: mu] :
( ( ( exists_in_world @ SV53 @ SV12 )
= $false )
| ( ( ! [SY747: mu] :
( ~ ( exists_in_world @ SY747 @ SV12 )
| ~ ( qmltpeq @ SV33 @ SV53 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SY747 ) @ ( unordered_pair @ SV53 @ SY747 ) @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(256,plain,
! [SV34: mu,SV13: $i,SV54: mu] :
( ( ( exists_in_world @ SV54 @ SV13 )
= $false )
| ( ( ~ ( qmltpeq @ SV34 @ SV54 @ SV13 )
| ( qmltpeq @ ( product @ SV34 ) @ ( product @ SV54 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(257,plain,
! [SV35: mu,SV14: $i,SV55: mu] :
( ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( ~ ( ~ ( ~ ( subset @ SV35 @ SV55 @ SV14 )
| ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) )
| ~ ( ~ ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) )
| ( subset @ SV35 @ SV55 @ SV14 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(258,plain,
! [SV37: mu,SV16: $i,SV56: mu] :
( ( ( exists_in_world @ SV56 @ SV16 )
= $false )
| ( ( ! [SY750: mu] :
( ~ ( exists_in_world @ SY750 @ SV16 )
| ~ ( qmltpeq @ SV37 @ SV56 @ SV16 )
| ( qmltpeq @ ( difference @ SY750 @ SV37 ) @ ( difference @ SY750 @ SV56 ) @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(259,plain,
! [SV38: mu,SV17: $i,SV57: mu] :
( ( ( exists_in_world @ SV57 @ SV17 )
= $false )
| ( ( ~ ( qmltpeq @ SV38 @ SV57 @ SV17 )
| ( qmltpeq @ SV57 @ SV38 @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(260,plain,
! [SV39: mu,SV18: $i,SV58: mu] :
( ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( ~ ( ~ ( ~ ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
| ( subset @ SV39 @ SV58 @ SV18 ) )
| ~ ( ~ ( subset @ SV39 @ SV58 @ SV18 )
| ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 ) ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(261,plain,
! [SV40: mu,SV19: $i,SV59: mu] :
( ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( ! [SY751: mu] :
( ~ ( exists_in_world @ SY751 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SY751 @ SV19 ) )
| ( qmltpeq @ SV40 @ SY751 @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(262,plain,
! [SV41: mu,SV20: $i,SV60: mu] :
( ( ( exists_in_world @ SV60 @ SV20 )
= $false )
| ( ( ! [SY752: mu] :
( ~ ( exists_in_world @ SY752 @ SV20 )
| ~ ( qmltpeq @ SV41 @ SV60 @ SV20 )
| ( qmltpeq @ ( union @ SY752 @ SV41 ) @ ( union @ SY752 @ SV60 ) @ SV20 ) ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(263,plain,
! [SV42: mu,SV21: $i,SV61: mu] :
( ( ( exists_in_world @ SV61 @ SV21 )
= $false )
| ( ( ! [SY753: mu] :
( ~ ( exists_in_world @ SY753 @ SV21 )
| ~ ( qmltpeq @ SV42 @ SV61 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SY753 ) @ ( intersection @ SV61 @ SY753 ) @ SV21 ) ) )
= $true )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(264,plain,
! [SV43: mu,SV22: $i,SV62: mu] :
( ( ( exists_in_world @ SV62 @ SV22 )
= $false )
| ( ( ! [SY754: mu] :
( ~ ( exists_in_world @ SY754 @ SV22 )
| ~ ( qmltpeq @ SV43 @ SV62 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SY754 ) @ ( difference @ SV62 @ SY754 ) @ SV22 ) ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(265,plain,
! [SV2: $i,SV44: mu,SV23: mu] :
( ( ( ~ ( qmltpeq @ SV23 @ SV44 @ SV2 ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SV44 ) @ SV2 )
= $true )
| ( ( exists_in_world @ SV44 @ SV2 )
= $false )
| ( ( exists_in_world @ SV23 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(266,plain,
! [SV45: mu,SV24: mu,SV3: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV3 )
| ~ ( qmltpeq @ SV24 @ SV45 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SV63 ) @ ( union @ SV45 @ SV63 ) @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV3 )
= $false )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(267,plain,
! [SV46: mu,SV25: mu,SV4: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV4 )
| ~ ( qmltpeq @ SV25 @ SV46 @ SV4 )
| ( qmltpeq @ ( intersection @ SV64 @ SV25 ) @ ( intersection @ SV64 @ SV46 ) @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV4 )
= $false )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(268,plain,
! [SV47: mu,SV26: mu,SV5: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV5 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SV65 @ SV5 ) )
| ( subset @ SV47 @ SV65 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(269,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( ~ ( equal_set @ SV27 @ SV48 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SV48 @ SV6 ) ) )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(270,plain,
! [SV49: mu,SV28: mu,SV7: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV7 )
| ~ ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SV66 @ SV28 @ SV7 ) )
| ( subset @ SV66 @ SV49 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(271,plain,
! [SV50: mu,SV30: mu,SV9: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV9 )
| ~ ( qmltpeq @ SV30 @ SV50 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SV67 @ SV30 ) @ ( unordered_pair @ SV67 @ SV50 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV9 )
= $false )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(272,plain,
! [SV10: $i,SV51: mu,SV31: mu] :
( ( ( ~ ( qmltpeq @ SV31 @ SV51 @ SV10 ) )
= $true )
| ( ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SV51 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV51 @ SV10 )
= $false )
| ( ( exists_in_world @ SV31 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(273,plain,
! [SV11: $i,SV52: mu,SV32: mu] :
( ( ( ~ ( qmltpeq @ SV32 @ SV52 @ SV11 ) )
= $true )
| ( ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SV52 ) @ SV11 )
= $true )
| ( ( exists_in_world @ SV52 @ SV11 )
= $false )
| ( ( exists_in_world @ SV32 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(274,plain,
! [SV53: mu,SV33: mu,SV12: $i,SV68: mu] :
( ( ( ~ ( exists_in_world @ SV68 @ SV12 )
| ~ ( qmltpeq @ SV33 @ SV53 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SV68 ) @ ( unordered_pair @ SV53 @ SV68 ) @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV12 )
= $false )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(275,plain,
! [SV13: $i,SV54: mu,SV34: mu] :
( ( ( ~ ( qmltpeq @ SV34 @ SV54 @ SV13 ) )
= $true )
| ( ( qmltpeq @ ( product @ SV34 ) @ ( product @ SV54 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV54 @ SV13 )
= $false )
| ( ( exists_in_world @ SV34 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(276,plain,
! [SV14: $i,SV55: mu,SV35: mu] :
( ( ( ~ ( ~ ( subset @ SV35 @ SV55 @ SV14 )
| ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) )
| ~ ( ~ ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) )
| ( subset @ SV35 @ SV55 @ SV14 ) ) )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(277,plain,
! [SV56: mu,SV37: mu,SV16: $i,SV69: mu] :
( ( ( ~ ( exists_in_world @ SV69 @ SV16 )
| ~ ( qmltpeq @ SV37 @ SV56 @ SV16 )
| ( qmltpeq @ ( difference @ SV69 @ SV37 ) @ ( difference @ SV69 @ SV56 ) @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV16 )
= $false )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(278,plain,
! [SV17: $i,SV57: mu,SV38: mu] :
( ( ( ~ ( qmltpeq @ SV38 @ SV57 @ SV17 ) )
= $true )
| ( ( qmltpeq @ SV57 @ SV38 @ SV17 )
= $true )
| ( ( exists_in_world @ SV57 @ SV17 )
= $false )
| ( ( exists_in_world @ SV38 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(279,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( ~ ( ~ ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
| ( subset @ SV39 @ SV58 @ SV18 ) )
| ~ ( ~ ( subset @ SV39 @ SV58 @ SV18 )
| ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 ) ) )
= $false )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(280,plain,
! [SV59: mu,SV40: mu,SV19: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV19 )
| ~ ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) )
| ( qmltpeq @ SV40 @ SV70 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(281,plain,
! [SV60: mu,SV41: mu,SV20: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV20 )
| ~ ( qmltpeq @ SV41 @ SV60 @ SV20 )
| ( qmltpeq @ ( union @ SV71 @ SV41 ) @ ( union @ SV71 @ SV60 ) @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV20 )
= $false )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(282,plain,
! [SV61: mu,SV42: mu,SV21: $i,SV72: mu] :
( ( ( ~ ( exists_in_world @ SV72 @ SV21 )
| ~ ( qmltpeq @ SV42 @ SV61 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SV72 ) @ ( intersection @ SV61 @ SV72 ) @ SV21 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV21 )
= $false )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(283,plain,
! [SV62: mu,SV43: mu,SV22: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV22 )
| ~ ( qmltpeq @ SV43 @ SV62 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SV73 ) @ ( difference @ SV62 @ SV73 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV22 )
= $false )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(284,plain,
! [SV2: $i,SV44: mu,SV23: mu] :
( ( ( qmltpeq @ SV23 @ SV44 @ SV2 )
= $false )
| ( ( qmltpeq @ ( singleton @ SV23 ) @ ( singleton @ SV44 ) @ SV2 )
= $true )
| ( ( exists_in_world @ SV44 @ SV2 )
= $false )
| ( ( exists_in_world @ SV23 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(285,plain,
! [SV45: mu,SV24: mu,SV3: $i,SV63: mu] :
( ( ( ~ ( exists_in_world @ SV63 @ SV3 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV24 @ SV45 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SV63 ) @ ( union @ SV45 @ SV63 ) @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV3 )
= $false )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(286,plain,
! [SV46: mu,SV25: mu,SV4: $i,SV64: mu] :
( ( ( ~ ( exists_in_world @ SV64 @ SV4 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV25 @ SV46 @ SV4 )
| ( qmltpeq @ ( intersection @ SV64 @ SV25 ) @ ( intersection @ SV64 @ SV46 ) @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV4 )
= $false )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(287,plain,
! [SV47: mu,SV26: mu,SV5: $i,SV65: mu] :
( ( ( ~ ( exists_in_world @ SV65 @ SV5 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SV65 @ SV5 ) )
| ( subset @ SV47 @ SV65 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(288,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( ~ ( equal_set @ SV27 @ SV48 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) ) )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(289,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SV48 @ SV6 ) ) )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(290,plain,
! [SV49: mu,SV28: mu,SV7: $i,SV66: mu] :
( ( ( ~ ( exists_in_world @ SV66 @ SV7 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SV66 @ SV28 @ SV7 ) )
| ( subset @ SV66 @ SV49 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(291,plain,
! [SV50: mu,SV30: mu,SV9: $i,SV67: mu] :
( ( ( ~ ( exists_in_world @ SV67 @ SV9 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV30 @ SV50 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SV67 @ SV30 ) @ ( unordered_pair @ SV67 @ SV50 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV9 )
= $false )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(292,plain,
! [SV10: $i,SV51: mu,SV31: mu] :
( ( ( qmltpeq @ SV31 @ SV51 @ SV10 )
= $false )
| ( ( qmltpeq @ ( power_set @ SV31 ) @ ( power_set @ SV51 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV51 @ SV10 )
= $false )
| ( ( exists_in_world @ SV31 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(293,plain,
! [SV11: $i,SV52: mu,SV32: mu] :
( ( ( qmltpeq @ SV32 @ SV52 @ SV11 )
= $false )
| ( ( qmltpeq @ ( sum @ SV32 ) @ ( sum @ SV52 ) @ SV11 )
= $true )
| ( ( exists_in_world @ SV52 @ SV11 )
= $false )
| ( ( exists_in_world @ SV32 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(294,plain,
! [SV53: mu,SV33: mu,SV12: $i,SV68: mu] :
( ( ( ~ ( exists_in_world @ SV68 @ SV12 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV33 @ SV53 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SV68 ) @ ( unordered_pair @ SV53 @ SV68 ) @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV12 )
= $false )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(295,plain,
! [SV13: $i,SV54: mu,SV34: mu] :
( ( ( qmltpeq @ SV34 @ SV54 @ SV13 )
= $false )
| ( ( qmltpeq @ ( product @ SV34 ) @ ( product @ SV54 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV54 @ SV13 )
= $false )
| ( ( exists_in_world @ SV34 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(296,plain,
! [SV14: $i,SV55: mu,SV35: mu] :
( ( ( ~ ( ~ ( subset @ SV35 @ SV55 @ SV14 )
| ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) ) )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(297,plain,
! [SV55: mu,SV35: mu,SV14: $i] :
( ( ( ~ ( ~ ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) )
| ( subset @ SV35 @ SV55 @ SV14 ) ) )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(298,plain,
! [SV56: mu,SV37: mu,SV16: $i,SV69: mu] :
( ( ( ~ ( exists_in_world @ SV69 @ SV16 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV37 @ SV56 @ SV16 )
| ( qmltpeq @ ( difference @ SV69 @ SV37 ) @ ( difference @ SV69 @ SV56 ) @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV16 )
= $false )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(299,plain,
! [SV17: $i,SV57: mu,SV38: mu] :
( ( ( qmltpeq @ SV38 @ SV57 @ SV17 )
= $false )
| ( ( qmltpeq @ SV57 @ SV38 @ SV17 )
= $true )
| ( ( exists_in_world @ SV57 @ SV17 )
= $false )
| ( ( exists_in_world @ SV38 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(300,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( ~ ( ~ ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
| ( subset @ SV39 @ SV58 @ SV18 ) ) )
= $false )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(301,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( ~ ( ~ ( subset @ SV39 @ SV58 @ SV18 )
| ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 ) ) )
= $false )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(302,plain,
! [SV59: mu,SV40: mu,SV19: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV19 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) )
| ( qmltpeq @ SV40 @ SV70 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(303,plain,
! [SV60: mu,SV41: mu,SV20: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV20 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV41 @ SV60 @ SV20 )
| ( qmltpeq @ ( union @ SV71 @ SV41 ) @ ( union @ SV71 @ SV60 ) @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV20 )
= $false )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(304,plain,
! [SV61: mu,SV42: mu,SV21: $i,SV72: mu] :
( ( ( ~ ( exists_in_world @ SV72 @ SV21 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV42 @ SV61 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SV72 ) @ ( intersection @ SV61 @ SV72 ) @ SV21 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV21 )
= $false )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(305,plain,
! [SV62: mu,SV43: mu,SV22: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV22 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV43 @ SV62 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SV73 ) @ ( difference @ SV62 @ SV73 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV22 )
= $false )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(306,plain,
! [SV45: mu,SV24: mu,SV3: $i,SV63: mu] :
( ( ( exists_in_world @ SV63 @ SV3 )
= $false )
| ( ( ~ ( qmltpeq @ SV24 @ SV45 @ SV3 )
| ( qmltpeq @ ( union @ SV24 @ SV63 ) @ ( union @ SV45 @ SV63 ) @ SV3 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV3 )
= $false )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(307,plain,
! [SV46: mu,SV25: mu,SV4: $i,SV64: mu] :
( ( ( exists_in_world @ SV64 @ SV4 )
= $false )
| ( ( ~ ( qmltpeq @ SV25 @ SV46 @ SV4 )
| ( qmltpeq @ ( intersection @ SV64 @ SV25 ) @ ( intersection @ SV64 @ SV46 ) @ SV4 ) )
= $true )
| ( ( exists_in_world @ SV46 @ SV4 )
= $false )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(308,plain,
! [SV47: mu,SV26: mu,SV5: $i,SV65: mu] :
( ( ( exists_in_world @ SV65 @ SV5 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SV65 @ SV5 ) )
| ( subset @ SV47 @ SV65 @ SV5 ) )
= $true )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(309,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( equal_set @ SV27 @ SV48 @ SV6 )
| ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(310,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
| ( equal_set @ SV27 @ SV48 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(311,plain,
! [SV49: mu,SV28: mu,SV7: $i,SV66: mu] :
( ( ( exists_in_world @ SV66 @ SV7 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SV66 @ SV28 @ SV7 ) )
| ( subset @ SV66 @ SV49 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(312,plain,
! [SV50: mu,SV30: mu,SV9: $i,SV67: mu] :
( ( ( exists_in_world @ SV67 @ SV9 )
= $false )
| ( ( ~ ( qmltpeq @ SV30 @ SV50 @ SV9 )
| ( qmltpeq @ ( unordered_pair @ SV67 @ SV30 ) @ ( unordered_pair @ SV67 @ SV50 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV9 )
= $false )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(313,plain,
! [SV53: mu,SV33: mu,SV12: $i,SV68: mu] :
( ( ( exists_in_world @ SV68 @ SV12 )
= $false )
| ( ( ~ ( qmltpeq @ SV33 @ SV53 @ SV12 )
| ( qmltpeq @ ( unordered_pair @ SV33 @ SV68 ) @ ( unordered_pair @ SV53 @ SV68 ) @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV12 )
= $false )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(314,plain,
! [SV14: $i,SV55: mu,SV35: mu] :
( ( ( ~ ( subset @ SV35 @ SV55 @ SV14 )
| ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(315,plain,
! [SV55: mu,SV35: mu,SV14: $i] :
( ( ( ~ ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) )
| ( subset @ SV35 @ SV55 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(316,plain,
! [SV56: mu,SV37: mu,SV16: $i,SV69: mu] :
( ( ( exists_in_world @ SV69 @ SV16 )
= $false )
| ( ( ~ ( qmltpeq @ SV37 @ SV56 @ SV16 )
| ( qmltpeq @ ( difference @ SV69 @ SV37 ) @ ( difference @ SV69 @ SV56 ) @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV16 )
= $false )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(317,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( ~ ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
| ( subset @ SV39 @ SV58 @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(318,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( ~ ( subset @ SV39 @ SV58 @ SV18 )
| ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(319,plain,
! [SV59: mu,SV40: mu,SV19: $i,SV70: mu] :
( ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) )
| ( qmltpeq @ SV40 @ SV70 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(320,plain,
! [SV60: mu,SV41: mu,SV20: $i,SV71: mu] :
( ( ( exists_in_world @ SV71 @ SV20 )
= $false )
| ( ( ~ ( qmltpeq @ SV41 @ SV60 @ SV20 )
| ( qmltpeq @ ( union @ SV71 @ SV41 ) @ ( union @ SV71 @ SV60 ) @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV20 )
= $false )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(321,plain,
! [SV61: mu,SV42: mu,SV21: $i,SV72: mu] :
( ( ( exists_in_world @ SV72 @ SV21 )
= $false )
| ( ( ~ ( qmltpeq @ SV42 @ SV61 @ SV21 )
| ( qmltpeq @ ( intersection @ SV42 @ SV72 ) @ ( intersection @ SV61 @ SV72 ) @ SV21 ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV21 )
= $false )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(322,plain,
! [SV62: mu,SV43: mu,SV22: $i,SV73: mu] :
( ( ( exists_in_world @ SV73 @ SV22 )
= $false )
| ( ( ~ ( qmltpeq @ SV43 @ SV62 @ SV22 )
| ( qmltpeq @ ( difference @ SV43 @ SV73 ) @ ( difference @ SV62 @ SV73 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV62 @ SV22 )
= $false )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(323,plain,
! [SV63: mu,SV3: $i,SV45: mu,SV24: mu] :
( ( ( ~ ( qmltpeq @ SV24 @ SV45 @ SV3 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV24 @ SV63 ) @ ( union @ SV45 @ SV63 ) @ SV3 )
= $true )
| ( ( exists_in_world @ SV63 @ SV3 )
= $false )
| ( ( exists_in_world @ SV45 @ SV3 )
= $false )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(324,plain,
! [SV64: mu,SV4: $i,SV46: mu,SV25: mu] :
( ( ( ~ ( qmltpeq @ SV25 @ SV46 @ SV4 ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV64 @ SV25 ) @ ( intersection @ SV64 @ SV46 ) @ SV4 )
= $true )
| ( ( exists_in_world @ SV64 @ SV4 )
= $false )
| ( ( exists_in_world @ SV46 @ SV4 )
= $false )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(325,plain,
! [SV65: mu,SV5: $i,SV47: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SV65 @ SV5 ) ) )
= $true )
| ( ( subset @ SV47 @ SV65 @ SV5 )
= $true )
| ( ( exists_in_world @ SV65 @ SV5 )
= $false )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(326,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( equal_set @ SV27 @ SV48 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(327,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
= $true )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(328,plain,
! [SV66: mu,SV7: $i,SV49: mu,SV28: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SV66 @ SV28 @ SV7 ) ) )
= $true )
| ( ( subset @ SV66 @ SV49 @ SV7 )
= $true )
| ( ( exists_in_world @ SV66 @ SV7 )
= $false )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(329,plain,
! [SV67: mu,SV9: $i,SV50: mu,SV30: mu] :
( ( ( ~ ( qmltpeq @ SV30 @ SV50 @ SV9 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV67 @ SV30 ) @ ( unordered_pair @ SV67 @ SV50 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV67 @ SV9 )
= $false )
| ( ( exists_in_world @ SV50 @ SV9 )
= $false )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(330,plain,
! [SV68: mu,SV12: $i,SV53: mu,SV33: mu] :
( ( ( ~ ( qmltpeq @ SV33 @ SV53 @ SV12 ) )
= $true )
| ( ( qmltpeq @ ( unordered_pair @ SV33 @ SV68 ) @ ( unordered_pair @ SV53 @ SV68 ) @ SV12 )
= $true )
| ( ( exists_in_world @ SV68 @ SV12 )
= $false )
| ( ( exists_in_world @ SV53 @ SV12 )
= $false )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(331,plain,
! [SV14: $i,SV55: mu,SV35: mu] :
( ( ( ~ ( subset @ SV35 @ SV55 @ SV14 ) )
= $true )
| ( ( ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(332,plain,
! [SV55: mu,SV35: mu,SV14: $i] :
( ( ( ~ ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) ) )
= $true )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(333,plain,
! [SV69: mu,SV16: $i,SV56: mu,SV37: mu] :
( ( ( ~ ( qmltpeq @ SV37 @ SV56 @ SV16 ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV69 @ SV37 ) @ ( difference @ SV69 @ SV56 ) @ SV16 )
= $true )
| ( ( exists_in_world @ SV69 @ SV16 )
= $false )
| ( ( exists_in_world @ SV56 @ SV16 )
= $false )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(334,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( ~ ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 ) )
= $true )
| ( ( subset @ SV39 @ SV58 @ SV18 )
= $true )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(335,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( ~ ( subset @ SV39 @ SV58 @ SV18 ) )
= $true )
| ( ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
= $true )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(336,plain,
! [SV70: mu,SV19: $i,SV59: mu,SV40: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) ) )
= $true )
| ( ( qmltpeq @ SV40 @ SV70 @ SV19 )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(337,plain,
! [SV71: mu,SV20: $i,SV60: mu,SV41: mu] :
( ( ( ~ ( qmltpeq @ SV41 @ SV60 @ SV20 ) )
= $true )
| ( ( qmltpeq @ ( union @ SV71 @ SV41 ) @ ( union @ SV71 @ SV60 ) @ SV20 )
= $true )
| ( ( exists_in_world @ SV71 @ SV20 )
= $false )
| ( ( exists_in_world @ SV60 @ SV20 )
= $false )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(338,plain,
! [SV72: mu,SV21: $i,SV61: mu,SV42: mu] :
( ( ( ~ ( qmltpeq @ SV42 @ SV61 @ SV21 ) )
= $true )
| ( ( qmltpeq @ ( intersection @ SV42 @ SV72 ) @ ( intersection @ SV61 @ SV72 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV72 @ SV21 )
= $false )
| ( ( exists_in_world @ SV61 @ SV21 )
= $false )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(339,plain,
! [SV73: mu,SV22: $i,SV62: mu,SV43: mu] :
( ( ( ~ ( qmltpeq @ SV43 @ SV62 @ SV22 ) )
= $true )
| ( ( qmltpeq @ ( difference @ SV43 @ SV73 ) @ ( difference @ SV62 @ SV73 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV73 @ SV22 )
= $false )
| ( ( exists_in_world @ SV62 @ SV22 )
= $false )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(340,plain,
! [SV63: mu,SV3: $i,SV45: mu,SV24: mu] :
( ( ( qmltpeq @ SV24 @ SV45 @ SV3 )
= $false )
| ( ( qmltpeq @ ( union @ SV24 @ SV63 ) @ ( union @ SV45 @ SV63 ) @ SV3 )
= $true )
| ( ( exists_in_world @ SV63 @ SV3 )
= $false )
| ( ( exists_in_world @ SV45 @ SV3 )
= $false )
| ( ( exists_in_world @ SV24 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(341,plain,
! [SV64: mu,SV4: $i,SV46: mu,SV25: mu] :
( ( ( qmltpeq @ SV25 @ SV46 @ SV4 )
= $false )
| ( ( qmltpeq @ ( intersection @ SV64 @ SV25 ) @ ( intersection @ SV64 @ SV46 ) @ SV4 )
= $true )
| ( ( exists_in_world @ SV64 @ SV4 )
= $false )
| ( ( exists_in_world @ SV46 @ SV4 )
= $false )
| ( ( exists_in_world @ SV25 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(342,plain,
! [SV65: mu,SV5: $i,SV47: mu,SV26: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SV65 @ SV5 ) ) )
= $false )
| ( ( subset @ SV47 @ SV65 @ SV5 )
= $true )
| ( ( exists_in_world @ SV65 @ SV5 )
= $false )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(343,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(344,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) ) )
= $false )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(345,plain,
! [SV66: mu,SV7: $i,SV49: mu,SV28: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SV66 @ SV28 @ SV7 ) ) )
= $false )
| ( ( subset @ SV66 @ SV49 @ SV7 )
= $true )
| ( ( exists_in_world @ SV66 @ SV7 )
= $false )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(346,plain,
! [SV67: mu,SV9: $i,SV50: mu,SV30: mu] :
( ( ( qmltpeq @ SV30 @ SV50 @ SV9 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV67 @ SV30 ) @ ( unordered_pair @ SV67 @ SV50 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV67 @ SV9 )
= $false )
| ( ( exists_in_world @ SV50 @ SV9 )
= $false )
| ( ( exists_in_world @ SV30 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(347,plain,
! [SV68: mu,SV12: $i,SV53: mu,SV33: mu] :
( ( ( qmltpeq @ SV33 @ SV53 @ SV12 )
= $false )
| ( ( qmltpeq @ ( unordered_pair @ SV33 @ SV68 ) @ ( unordered_pair @ SV53 @ SV68 ) @ SV12 )
= $true )
| ( ( exists_in_world @ SV68 @ SV12 )
= $false )
| ( ( exists_in_world @ SV53 @ SV12 )
= $false )
| ( ( exists_in_world @ SV33 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(348,plain,
! [SV14: $i,SV55: mu,SV35: mu] :
( ( ( subset @ SV35 @ SV55 @ SV14 )
= $false )
| ( ( ! [SY748: mu] :
( ~ ( exists_in_world @ SY748 @ SV14 )
| ~ ( member @ SY748 @ SV35 @ SV14 )
| ( member @ SY748 @ SV55 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(349,plain,
! [SV55: mu,SV35: mu,SV14: $i] :
( ( ( ! [SY749: mu] :
( ~ ( exists_in_world @ SY749 @ SV14 )
| ~ ( member @ SY749 @ SV35 @ SV14 )
| ( member @ SY749 @ SV55 @ SV14 ) ) )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(350,plain,
! [SV69: mu,SV16: $i,SV56: mu,SV37: mu] :
( ( ( qmltpeq @ SV37 @ SV56 @ SV16 )
= $false )
| ( ( qmltpeq @ ( difference @ SV69 @ SV37 ) @ ( difference @ SV69 @ SV56 ) @ SV16 )
= $true )
| ( ( exists_in_world @ SV69 @ SV16 )
= $false )
| ( ( exists_in_world @ SV56 @ SV16 )
= $false )
| ( ( exists_in_world @ SV37 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(351,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
= $false )
| ( ( subset @ SV39 @ SV58 @ SV18 )
= $true )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(352,plain,
! [SV18: $i,SV58: mu,SV39: mu] :
( ( ( subset @ SV39 @ SV58 @ SV18 )
= $false )
| ( ( member @ SV39 @ ( power_set @ SV58 ) @ SV18 )
= $true )
| ( ( exists_in_world @ SV58 @ SV18 )
= $false )
| ( ( exists_in_world @ SV39 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(353,plain,
! [SV70: mu,SV19: $i,SV59: mu,SV40: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) ) )
= $false )
| ( ( qmltpeq @ SV40 @ SV70 @ SV19 )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(354,plain,
! [SV71: mu,SV20: $i,SV60: mu,SV41: mu] :
( ( ( qmltpeq @ SV41 @ SV60 @ SV20 )
= $false )
| ( ( qmltpeq @ ( union @ SV71 @ SV41 ) @ ( union @ SV71 @ SV60 ) @ SV20 )
= $true )
| ( ( exists_in_world @ SV71 @ SV20 )
= $false )
| ( ( exists_in_world @ SV60 @ SV20 )
= $false )
| ( ( exists_in_world @ SV41 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(355,plain,
! [SV72: mu,SV21: $i,SV61: mu,SV42: mu] :
( ( ( qmltpeq @ SV42 @ SV61 @ SV21 )
= $false )
| ( ( qmltpeq @ ( intersection @ SV42 @ SV72 ) @ ( intersection @ SV61 @ SV72 ) @ SV21 )
= $true )
| ( ( exists_in_world @ SV72 @ SV21 )
= $false )
| ( ( exists_in_world @ SV61 @ SV21 )
= $false )
| ( ( exists_in_world @ SV42 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(356,plain,
! [SV73: mu,SV22: $i,SV62: mu,SV43: mu] :
( ( ( qmltpeq @ SV43 @ SV62 @ SV22 )
= $false )
| ( ( qmltpeq @ ( difference @ SV43 @ SV73 ) @ ( difference @ SV62 @ SV73 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV73 @ SV22 )
= $false )
| ( ( exists_in_world @ SV62 @ SV22 )
= $false )
| ( ( exists_in_world @ SV43 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(357,plain,
! [SV65: mu,SV5: $i,SV47: mu,SV26: mu] :
( ( ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 )
| ~ ( subset @ SV26 @ SV65 @ SV5 ) )
= $true )
| ( ( subset @ SV47 @ SV65 @ SV5 )
= $true )
| ( ( exists_in_world @ SV65 @ SV5 )
= $false )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(358,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
= $false )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(359,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( subset @ SV27 @ SV48 @ SV6 )
| ~ ( subset @ SV48 @ SV27 @ SV6 ) )
= $true )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(360,plain,
! [SV66: mu,SV7: $i,SV49: mu,SV28: mu] :
( ( ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 )
| ~ ( subset @ SV66 @ SV28 @ SV7 ) )
= $true )
| ( ( subset @ SV66 @ SV49 @ SV7 )
= $true )
| ( ( exists_in_world @ SV66 @ SV7 )
= $false )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(361,plain,
! [SV55: mu,SV35: mu,SV14: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV14 )
| ~ ( member @ SV74 @ SV35 @ SV14 )
| ( member @ SV74 @ SV55 @ SV14 ) )
= $true )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(362,plain,
! [SV14: $i,SV35: mu,SV55: mu] :
( ( ( ~ ( exists_in_world @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV14 )
| ~ ( member @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV35 @ SV14 )
| ( member @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV55 @ SV14 ) )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[349]) ).
thf(363,plain,
! [SV70: mu,SV19: $i,SV59: mu,SV40: mu] :
( ( ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 )
| ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) )
= $true )
| ( ( qmltpeq @ SV40 @ SV70 @ SV19 )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(364,plain,
! [SV65: mu,SV5: $i,SV47: mu,SV26: mu] :
( ( ( ~ ( qmltpeq @ SV26 @ SV47 @ SV5 ) )
= $true )
| ( ( ~ ( subset @ SV26 @ SV65 @ SV5 ) )
= $true )
| ( ( subset @ SV47 @ SV65 @ SV5 )
= $true )
| ( ( exists_in_world @ SV65 @ SV5 )
= $false )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(365,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( subset @ SV27 @ SV48 @ SV6 ) )
= $false )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(366,plain,
! [SV6: $i,SV27: mu,SV48: mu] :
( ( ( ~ ( subset @ SV48 @ SV27 @ SV6 ) )
= $false )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(367,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( ~ ( subset @ SV27 @ SV48 @ SV6 ) )
= $true )
| ( ( ~ ( subset @ SV48 @ SV27 @ SV6 ) )
= $true )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(368,plain,
! [SV66: mu,SV7: $i,SV49: mu,SV28: mu] :
( ( ( ~ ( qmltpeq @ SV28 @ SV49 @ SV7 ) )
= $true )
| ( ( ~ ( subset @ SV66 @ SV28 @ SV7 ) )
= $true )
| ( ( subset @ SV66 @ SV49 @ SV7 )
= $true )
| ( ( exists_in_world @ SV66 @ SV7 )
= $false )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(369,plain,
! [SV55: mu,SV35: mu,SV14: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV14 ) )
= $true )
| ( ( ~ ( member @ SV74 @ SV35 @ SV14 )
| ( member @ SV74 @ SV55 @ SV14 ) )
= $true )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(370,plain,
! [SV14: $i,SV35: mu,SV55: mu] :
( ( ( ~ ( exists_in_world @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV14 ) )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(371,plain,
! [SV14: $i,SV35: mu,SV55: mu] :
( ( ( ~ ( member @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV35 @ SV14 )
| ( member @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV55 @ SV14 ) )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(372,plain,
! [SV70: mu,SV19: $i,SV59: mu,SV40: mu] :
( ( ( ~ ( qmltpeq @ SV40 @ SV59 @ SV19 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) )
= $true )
| ( ( qmltpeq @ SV40 @ SV70 @ SV19 )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(373,plain,
! [SV65: mu,SV5: $i,SV47: mu,SV26: mu] :
( ( ( qmltpeq @ SV26 @ SV47 @ SV5 )
= $false )
| ( ( ~ ( subset @ SV26 @ SV65 @ SV5 ) )
= $true )
| ( ( subset @ SV47 @ SV65 @ SV5 )
= $true )
| ( ( exists_in_world @ SV65 @ SV5 )
= $false )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(374,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( subset @ SV27 @ SV48 @ SV6 )
= $true )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(375,plain,
! [SV6: $i,SV27: mu,SV48: mu] :
( ( ( subset @ SV48 @ SV27 @ SV6 )
= $true )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(376,plain,
! [SV6: $i,SV48: mu,SV27: mu] :
( ( ( subset @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( ~ ( subset @ SV48 @ SV27 @ SV6 ) )
= $true )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(377,plain,
! [SV66: mu,SV7: $i,SV49: mu,SV28: mu] :
( ( ( qmltpeq @ SV28 @ SV49 @ SV7 )
= $false )
| ( ( ~ ( subset @ SV66 @ SV28 @ SV7 ) )
= $true )
| ( ( subset @ SV66 @ SV49 @ SV7 )
= $true )
| ( ( exists_in_world @ SV66 @ SV7 )
= $false )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(378,plain,
! [SV55: mu,SV35: mu,SV14: $i,SV74: mu] :
( ( ( exists_in_world @ SV74 @ SV14 )
= $false )
| ( ( ~ ( member @ SV74 @ SV35 @ SV14 )
| ( member @ SV74 @ SV55 @ SV14 ) )
= $true )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(379,plain,
! [SV14: $i,SV35: mu,SV55: mu] :
( ( ( exists_in_world @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV14 )
= $true )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(380,plain,
! [SV14: $i,SV35: mu,SV55: mu] :
( ( ( ~ ( member @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV35 @ SV14 ) )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(381,plain,
! [SV14: $i,SV35: mu,SV55: mu] :
( ( ( member @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV55 @ SV14 )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(382,plain,
! [SV70: mu,SV19: $i,SV59: mu,SV40: mu] :
( ( ( qmltpeq @ SV40 @ SV59 @ SV19 )
= $false )
| ( ( ~ ( qmltpeq @ SV59 @ SV70 @ SV19 ) )
= $true )
| ( ( qmltpeq @ SV40 @ SV70 @ SV19 )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(383,plain,
! [SV47: mu,SV5: $i,SV65: mu,SV26: mu] :
( ( ( subset @ SV26 @ SV65 @ SV5 )
= $false )
| ( ( qmltpeq @ SV26 @ SV47 @ SV5 )
= $false )
| ( ( subset @ SV47 @ SV65 @ SV5 )
= $true )
| ( ( exists_in_world @ SV65 @ SV5 )
= $false )
| ( ( exists_in_world @ SV47 @ SV5 )
= $false )
| ( ( exists_in_world @ SV26 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(384,plain,
! [SV6: $i,SV27: mu,SV48: mu] :
( ( ( subset @ SV48 @ SV27 @ SV6 )
= $false )
| ( ( subset @ SV27 @ SV48 @ SV6 )
= $false )
| ( ( equal_set @ SV27 @ SV48 @ SV6 )
= $true )
| ( ( exists_in_world @ SV48 @ SV6 )
= $false )
| ( ( exists_in_world @ SV27 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(385,plain,
! [SV49: mu,SV7: $i,SV28: mu,SV66: mu] :
( ( ( subset @ SV66 @ SV28 @ SV7 )
= $false )
| ( ( qmltpeq @ SV28 @ SV49 @ SV7 )
= $false )
| ( ( subset @ SV66 @ SV49 @ SV7 )
= $true )
| ( ( exists_in_world @ SV66 @ SV7 )
= $false )
| ( ( exists_in_world @ SV49 @ SV7 )
= $false )
| ( ( exists_in_world @ SV28 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(386,plain,
! [SV55: mu,SV14: $i,SV35: mu,SV74: mu] :
( ( ( ~ ( member @ SV74 @ SV35 @ SV14 ) )
= $true )
| ( ( member @ SV74 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV74 @ SV14 )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(387,plain,
! [SV14: $i,SV35: mu,SV55: mu] :
( ( ( member @ ( sK3_SY749 @ SV55 @ SV35 @ SV14 ) @ SV35 @ SV14 )
= $true )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(388,plain,
! [SV40: mu,SV19: $i,SV70: mu,SV59: mu] :
( ( ( qmltpeq @ SV59 @ SV70 @ SV19 )
= $false )
| ( ( qmltpeq @ SV40 @ SV59 @ SV19 )
= $false )
| ( ( qmltpeq @ SV40 @ SV70 @ SV19 )
= $true )
| ( ( exists_in_world @ SV70 @ SV19 )
= $false )
| ( ( exists_in_world @ SV59 @ SV19 )
= $false )
| ( ( exists_in_world @ SV40 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(389,plain,
! [SV55: mu,SV14: $i,SV35: mu,SV74: mu] :
( ( ( member @ SV74 @ SV35 @ SV14 )
= $false )
| ( ( member @ SV74 @ SV55 @ SV14 )
= $true )
| ( ( exists_in_world @ SV74 @ SV14 )
= $false )
| ( ( subset @ SV35 @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV55 @ SV14 )
= $false )
| ( ( exists_in_world @ SV35 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(390,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[98,389,388,387,385,384,383,381,379,375,374,356,355,354,352,351,350,347,346,341,340,299,295,293,292,284,213,199,122,121]) ).
thf(391,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET062^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n020.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 14:30:21 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.39/0.61
% 1.39/0.61 No.of.Axioms: 22
% 1.39/0.61
% 1.39/0.61 Length.of.Defs: 5508
% 1.39/0.61
% 1.39/0.61 Contains.Choice.Funs: false
% 1.39/0.61 ..........................
% 1.39/0.61
% 1.39/0.61 ********************************
% 1.39/0.61 * All subproblems solved! *
% 1.39/0.61 ********************************
% 1.39/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:390,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.39/0.61
% 1.39/0.61 %**** Beginning of derivation protocol ****
% 1.39/0.61 % SZS output start CNFRefutation
% See solution above
% 0.50/0.61
% 0.50/0.61 %**** End of derivation protocol ****
% 0.50/0.61 %**** no. of clauses in derivation: 368 ****
% 0.50/0.61 %**** clause counter: 390 ****
% 0.50/0.61
% 0.50/0.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:23,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:390,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------