TSTP Solution File: KRS272^7 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KRS272^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 03:16:18 EDT 2022
% Result : Theorem 76.40s 76.72s
% Output : CNFRefutation 76.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 95
% Syntax : Number of formulae : 277 ( 105 unt; 53 typ; 32 def)
% Number of atoms : 2693 ( 678 equ; 0 cnn)
% Maximal formula atoms : 18 ( 12 avg)
% Number of connectives : 7573 (1052 ~;1010 |; 31 &;5441 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 219 ( 219 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 6 con; 0-5 aty)
% Number of variables : 824 ( 66 ^ 750 !; 8 ?; 824 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_do,type,
do: mu > mu > mu > $i > $o ).
thf(tp_entry_box,type,
entry_box: mu > $i > $o ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_in,type,
in: mu > mu > mu > $i > $o ).
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_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_number,type,
number: mu > mu > $i > $o ).
thf(tp_one,type,
one: mu ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_SY259,type,
sK1_SY259: $i ).
thf(tp_sK2_SY467,type,
sK2_SY467: $i ).
thf(tp_sK3_SY480,type,
sK3_SY480: mu > mu > mu > mu > $i ).
thf(tp_sK4_SY482,type,
sK4_SY482: mu > mu > mu > mu > mu ).
thf(tp_sK5_SY479,type,
sK5_SY479: mu > mu > mu > mu > $i ).
thf(tp_sK6_SY367,type,
sK6_SY367: mu > mu > mu > $i > $i > mu ).
thf(tp_sK7_SY411,type,
sK7_SY411: $i > mu ).
thf(tp_sK8_SY442,type,
sK8_SY442: $i > $i > mu ).
thf(tp_sK9_X,type,
sK9_X: $i > mu ).
thf(tp_string,type,
string: mu > $i > $o ).
thf(tp_u,type,
u: mu ).
thf(tp_userid,type,
userid: mu > mu > $i > $o ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S: mu] :
( mforall_ind
@ ^ [I: mu] :
( mforall_ind
@ ^ [B: mu] :
( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
@ ( mexists_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [S2: mu] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(3,axiom,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [I: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(4,axiom,
! [V: $i] : ( exists_in_world @ u @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_u_ax) ).
thf(5,axiom,
! [V: $i] : ( exists_in_world @ one @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_one_ax) ).
thf(6,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax) ).
thf(7,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(8,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(9,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(10,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [I: mu] :
( mexists_ind
@ ^ [B: mu] :
( mexists_ind
@ ^ [A: mu] :
( mexists_ind
@ ^ [S: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S2: mu] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(11,negated_conjecture,
( ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [I: mu] :
( mexists_ind
@ ^ [B: mu] :
( mexists_ind
@ ^ [A: mu] :
( mexists_ind
@ ^ [S: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S2: mu] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [SY259: $i,SY260: $i] :
( ~ ( rel_s4 @ SY259 @ SY260 )
| ~ ! [SY252: mu] :
( ( exists_in_world @ SY252 @ SY260 )
=> ~ ~ ! [SY253: mu] :
( ( exists_in_world @ SY253 @ SY260 )
=> ~ ~ ! [SY254: mu] :
( ( exists_in_world @ SY254 @ SY260 )
=> ~ ~ ! [SY255: mu] :
( ( exists_in_world @ SY255 @ SY260 )
=> ~ ~ ( ~ ! [SY256: $i] :
( ~ ( rel_s4 @ SY260 @ SY256 )
| ~ ( ~ ( userid @ u @ SY252 @ SY256 )
| ~ ~ ( ~ ( entry_box @ SY253 @ SY256 )
| ~ ( number @ SY253 @ one @ SY256 ) ) ) )
| ~ ! [SY257: $i] :
( ~ ( rel_s4 @ SY260 @ SY257 )
| ! [SY235: mu] :
( ( exists_in_world @ SY235 @ SY257 )
=> ( ~ ( do @ SY255 @ SY254 @ SY235 @ SY257 )
| ( in @ SY252 @ SY253 @ SY235 @ SY257 ) ) ) ) ) ) ) ) ) ) )
= $false ),
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(13,plain,
( ( ! [SY370: $i,SY371: $i] :
( ~ ( rel_s4 @ SY370 @ SY371 )
| ! [SY364: mu] :
( ( exists_in_world @ SY364 @ SY371 )
=> ! [SY365: mu] :
( ( exists_in_world @ SY365 @ SY371 )
=> ! [SY366: mu] :
( ( exists_in_world @ SY366 @ SY371 )
=> ( ~ ~ ( ~ ( string @ SY365 @ SY371 )
| ~ ( entry_box @ SY366 @ SY371 ) )
| ~ ! [SY367: mu] :
( ( exists_in_world @ SY367 @ SY371 )
=> ~ ! [SY368: $i] :
( ~ ( rel_s4 @ SY371 @ SY368 )
| ! [SY356: mu] :
( ( exists_in_world @ SY356 @ SY368 )
=> ( ~ ( do @ SY364 @ SY367 @ SY356 @ SY368 )
| ( in @ SY365 @ SY366 @ SY356 @ SY368 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,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(14,plain,
( ( ! [SY410: $i] :
~ ! [SY411: mu] :
( ( exists_in_world @ SY411 @ SY410 )
=> ~ ! [SY412: $i] :
( ~ ( rel_s4 @ SY410 @ SY412 )
| ~ ( ~ ( entry_box @ SY411 @ SY412 )
| ~ ( number @ SY411 @ one @ SY412 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,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(15,plain,
( ( ! [SY444: $i,SY445: $i] :
( ~ ( rel_s4 @ SY444 @ SY445 )
| ~ ! [SY442: mu] :
( ( exists_in_world @ SY442 @ SY445 )
=> ~ ! [SY443: $i] :
( ~ ( rel_s4 @ SY445 @ SY443 )
| ~ ( ~ ( userid @ u @ SY442 @ SY443 )
| ~ ( string @ SY442 @ SY443 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,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(16,plain,
( ( ! [V: $i] : ( exists_in_world @ u @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[4,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(17,plain,
( ( ! [V: $i] : ( exists_in_world @ one @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[5,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(18,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ) )
= $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(19,plain,
( ( ! [SY457: $i,SY458: $i,SY459: $i] :
( ( ( rel_s4 @ SY457 @ SY458 )
& ( rel_s4 @ SY458 @ SY459 ) )
=> ( rel_s4 @ SY457 @ SY459 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,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(20,plain,
( ( ! [SY463: $i] : ( rel_s4 @ SY463 @ SY463 ) )
= $true ),
inference(unfold_def,[status(thm)],[8,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(21,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $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(22,plain,
( ( ! [SY467: $i] :
( ~ ( rel_s4 @ sK1_SY259 @ SY467 )
| ~ ! [SY252: mu] :
( ( exists_in_world @ SY252 @ SY467 )
=> ~ ~ ! [SY253: mu] :
( ( exists_in_world @ SY253 @ SY467 )
=> ~ ~ ! [SY254: mu] :
( ( exists_in_world @ SY254 @ SY467 )
=> ~ ~ ! [SY255: mu] :
( ( exists_in_world @ SY255 @ SY467 )
=> ~ ~ ( ~ ! [SY256: $i] :
( ~ ( rel_s4 @ SY467 @ SY256 )
| ~ ( ~ ( userid @ u @ SY252 @ SY256 )
| ~ ~ ( ~ ( entry_box @ SY253 @ SY256 )
| ~ ( number @ SY253 @ one @ SY256 ) ) ) )
| ~ ! [SY257: $i] :
( ~ ( rel_s4 @ SY467 @ SY257 )
| ! [SY235: mu] :
( ( exists_in_world @ SY235 @ SY257 )
=> ( ~ ( do @ SY255 @ SY254 @ SY235 @ SY257 )
| ( in @ SY252 @ SY253 @ SY235 @ SY257 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ~ ( rel_s4 @ sK1_SY259 @ sK2_SY467 )
| ~ ! [SY475: mu] :
( ( exists_in_world @ SY475 @ sK2_SY467 )
=> ~ ~ ! [SY476: mu] :
( ( exists_in_world @ SY476 @ sK2_SY467 )
=> ~ ~ ! [SY477: mu] :
( ( exists_in_world @ SY477 @ sK2_SY467 )
=> ~ ~ ! [SY478: mu] :
( ( exists_in_world @ SY478 @ sK2_SY467 )
=> ~ ~ ( ~ ! [SY479: $i] :
( ~ ( rel_s4 @ sK2_SY467 @ SY479 )
| ~ ( ~ ( userid @ u @ SY475 @ SY479 )
| ~ ~ ( ~ ( entry_box @ SY476 @ SY479 )
| ~ ( number @ SY476 @ one @ SY479 ) ) ) )
| ~ ! [SY480: $i] :
( ~ ( rel_s4 @ sK2_SY467 @ SY480 )
| ! [SY235: mu] :
( ( exists_in_world @ SY235 @ SY480 )
=> ( ~ ( do @ SY478 @ SY477 @ SY235 @ SY480 )
| ( in @ SY475 @ SY476 @ SY235 @ SY480 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY259 @ sK2_SY467 )
| ~ ! [SY475: mu] :
( ( exists_in_world @ SY475 @ sK2_SY467 )
=> ~ ~ ! [SY476: mu] :
( ( exists_in_world @ SY476 @ sK2_SY467 )
=> ~ ~ ! [SY477: mu] :
( ( exists_in_world @ SY477 @ sK2_SY467 )
=> ~ ~ ! [SY478: mu] :
( ( exists_in_world @ SY478 @ sK2_SY467 )
=> ~ ~ ( ~ ! [SY479: $i] :
( ~ ( rel_s4 @ sK2_SY467 @ SY479 )
| ~ ( ~ ( userid @ u @ SY475 @ SY479 )
| ~ ~ ( ~ ( entry_box @ SY476 @ SY479 )
| ~ ( number @ SY476 @ one @ SY479 ) ) ) )
| ~ ! [SY480: $i] :
( ~ ( rel_s4 @ sK2_SY467 @ SY480 )
| ! [SY235: mu] :
( ( exists_in_world @ SY235 @ SY480 )
=> ( ~ ( do @ SY478 @ SY477 @ SY235 @ SY480 )
| ( in @ SY475 @ SY476 @ SY235 @ SY480 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ( rel_s4 @ sK1_SY259 @ sK2_SY467 )
& ! [SY475: mu] :
( ~ ( exists_in_world @ SY475 @ sK2_SY467 )
| ! [SY476: mu] :
( ~ ( exists_in_world @ SY476 @ sK2_SY467 )
| ! [SY477: mu] :
( ~ ( exists_in_world @ SY477 @ sK2_SY467 )
| ! [SY478: mu] :
( ~ ( exists_in_world @ SY478 @ sK2_SY467 )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ( ~ ( userid @ u @ SY475 @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) )
| ~ ( entry_box @ SY476 @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) )
| ~ ( number @ SY476 @ one @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) ) ) )
| ( ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ( exists_in_world @ ( sK4_SY482 @ SY478 @ SY477 @ SY476 @ SY475 ) @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ( do @ SY478 @ SY477 @ ( sK4_SY482 @ SY478 @ SY477 @ SY476 @ SY475 ) @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ~ ( in @ SY475 @ SY476 @ ( sK4_SY482 @ SY478 @ SY477 @ SY476 @ SY475 ) @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(26,plain,
( ( ! [SY370: $i,SY371: $i] :
( ~ ( rel_s4 @ SY370 @ SY371 )
| ! [SY364: mu] :
( ~ ( exists_in_world @ SY364 @ SY371 )
| ! [SY365: mu] :
( ~ ( exists_in_world @ SY365 @ SY371 )
| ! [SY366: mu] :
( ~ ( exists_in_world @ SY366 @ SY371 )
| ~ ( string @ SY365 @ SY371 )
| ~ ( entry_box @ SY366 @ SY371 )
| ( ( exists_in_world @ ( sK6_SY367 @ SY366 @ SY365 @ SY364 @ SY371 @ SY370 ) @ SY371 )
& ! [SY483: $i] :
( ~ ( rel_s4 @ SY371 @ SY483 )
| ! [SY484: mu] :
( ~ ( exists_in_world @ SY484 @ SY483 )
| ~ ( do @ SY364 @ ( sK6_SY367 @ SY366 @ SY365 @ SY364 @ SY371 @ SY370 ) @ SY484 @ SY483 )
| ( in @ SY365 @ SY366 @ SY484 @ SY483 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(27,plain,
( ( ! [SY410: $i] :
( ( exists_in_world @ ( sK7_SY411 @ SY410 ) @ SY410 )
& ! [SY485: $i] :
( ~ ( rel_s4 @ SY410 @ SY485 )
| ( entry_box @ ( sK7_SY411 @ SY410 ) @ SY485 ) )
& ! [SY486: $i] :
( ~ ( rel_s4 @ SY410 @ SY486 )
| ( number @ ( sK7_SY411 @ SY410 ) @ one @ SY486 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(28,plain,
( ( ! [SY444: $i,SY445: $i] :
( ~ ( rel_s4 @ SY444 @ SY445 )
| ( ( exists_in_world @ ( sK8_SY442 @ SY445 @ SY444 ) @ SY445 )
& ! [SY487: $i] :
( ~ ( rel_s4 @ SY445 @ SY487 )
| ( userid @ u @ ( sK8_SY442 @ SY445 @ SY444 ) @ SY487 ) )
& ! [SY488: $i] :
( ~ ( rel_s4 @ SY445 @ SY488 )
| ( string @ ( sK8_SY442 @ SY445 @ SY444 ) @ SY488 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(29,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(30,plain,
( ( ! [SY457: $i,SY458: $i,SY459: $i] :
( ~ ( rel_s4 @ SY457 @ SY458 )
| ~ ( rel_s4 @ SY458 @ SY459 )
| ( rel_s4 @ SY457 @ SY459 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(31,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK9_X @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(32,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK9_X @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(33,plain,
( ( ! [SY463: $i] : ( rel_s4 @ SY463 @ SY463 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( ! [SY457: $i,SY458: $i,SY459: $i] :
( ~ ( rel_s4 @ SY457 @ SY458 )
| ~ ( rel_s4 @ SY458 @ SY459 )
| ( rel_s4 @ SY457 @ SY459 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(35,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(36,plain,
( ( ! [V: $i] : ( exists_in_world @ one @ V ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(37,plain,
( ( ! [V: $i] : ( exists_in_world @ u @ V ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [SY444: $i,SY445: $i] :
( ~ ( rel_s4 @ SY444 @ SY445 )
| ( ( exists_in_world @ ( sK8_SY442 @ SY445 @ SY444 ) @ SY445 )
& ! [SY487: $i] :
( ~ ( rel_s4 @ SY445 @ SY487 )
| ( userid @ u @ ( sK8_SY442 @ SY445 @ SY444 ) @ SY487 ) )
& ! [SY488: $i] :
( ~ ( rel_s4 @ SY445 @ SY488 )
| ( string @ ( sK8_SY442 @ SY445 @ SY444 ) @ SY488 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(39,plain,
( ( ! [SY410: $i] :
( ( exists_in_world @ ( sK7_SY411 @ SY410 ) @ SY410 )
& ! [SY485: $i] :
( ~ ( rel_s4 @ SY410 @ SY485 )
| ( entry_box @ ( sK7_SY411 @ SY410 ) @ SY485 ) )
& ! [SY486: $i] :
( ~ ( rel_s4 @ SY410 @ SY486 )
| ( number @ ( sK7_SY411 @ SY410 ) @ one @ SY486 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(40,plain,
( ( ! [SY370: $i,SY371: $i] :
( ~ ( rel_s4 @ SY370 @ SY371 )
| ! [SY364: mu] :
( ~ ( exists_in_world @ SY364 @ SY371 )
| ! [SY365: mu] :
( ~ ( exists_in_world @ SY365 @ SY371 )
| ! [SY366: mu] :
( ~ ( exists_in_world @ SY366 @ SY371 )
| ~ ( string @ SY365 @ SY371 )
| ~ ( entry_box @ SY366 @ SY371 )
| ( ( exists_in_world @ ( sK6_SY367 @ SY366 @ SY365 @ SY364 @ SY371 @ SY370 ) @ SY371 )
& ! [SY483: $i] :
( ~ ( rel_s4 @ SY371 @ SY483 )
| ! [SY484: mu] :
( ~ ( exists_in_world @ SY484 @ SY483 )
| ~ ( do @ SY364 @ ( sK6_SY367 @ SY366 @ SY365 @ SY364 @ SY371 @ SY370 ) @ SY484 @ SY483 )
| ( in @ SY365 @ SY366 @ SY484 @ SY483 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(41,plain,
( ( ( rel_s4 @ sK1_SY259 @ sK2_SY467 )
& ! [SY475: mu] :
( ~ ( exists_in_world @ SY475 @ sK2_SY467 )
| ! [SY476: mu] :
( ~ ( exists_in_world @ SY476 @ sK2_SY467 )
| ! [SY477: mu] :
( ~ ( exists_in_world @ SY477 @ sK2_SY467 )
| ! [SY478: mu] :
( ~ ( exists_in_world @ SY478 @ sK2_SY467 )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ( ~ ( userid @ u @ SY475 @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) )
| ~ ( entry_box @ SY476 @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) )
| ~ ( number @ SY476 @ one @ ( sK5_SY479 @ SY478 @ SY477 @ SY476 @ SY475 ) ) ) )
| ( ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ( exists_in_world @ ( sK4_SY482 @ SY478 @ SY477 @ SY476 @ SY475 ) @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ( do @ SY478 @ SY477 @ ( sK4_SY482 @ SY478 @ SY477 @ SY476 @ SY475 ) @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) )
& ~ ( in @ SY475 @ SY476 @ ( sK4_SY482 @ SY478 @ SY477 @ SY476 @ SY475 ) @ ( sK3_SY480 @ SY478 @ SY477 @ SY476 @ SY475 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(42,plain,
( ( ! [SX0: $i] :
~ ( ~ ( exists_in_world @ ( sK7_SY411 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ( entry_box @ ( sK7_SY411 @ SX0 ) @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ( number @ ( sK7_SY411 @ SX0 ) @ one @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39,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(43,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY259 @ sK2_SY467 )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY467 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY467 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY467 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41,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(44,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ( ~ ( exists_in_world @ ( sK8_SY442 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ( userid @ u @ ( sK8_SY442 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ( string @ ( sK8_SY442 @ SX1 @ SX0 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38,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(45,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX1 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX1 )
| ~ ( string @ SX3 @ SX1 )
| ~ ( entry_box @ SX4 @ SX1 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX1 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ~ ( do @ SX2 @ ( sK6_SY367 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 @ SX5 )
| ( in @ SX3 @ SX4 @ SX6 @ SX5 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40,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(46,plain,
! [SV1: $i] :
( ( exists_in_world @ ( sK9_X @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(47,plain,
! [SV2: $i] :
( ( rel_s4 @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(48,plain,
! [SV3: $i] :
( ( ! [SY489: $i,SY490: $i] :
( ~ ( rel_s4 @ SV3 @ SY489 )
| ~ ( rel_s4 @ SY489 @ SY490 )
| ( rel_s4 @ SV3 @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(49,plain,
! [SV4: mu] :
( ( ! [SY491: $i,SY492: $i] :
( ~ ( exists_in_world @ SV4 @ SY491 )
| ~ ( rel_s4 @ SY491 @ SY492 )
| ( exists_in_world @ SV4 @ SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(50,plain,
! [SV5: $i] :
( ( exists_in_world @ one @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV6: $i] :
( ( exists_in_world @ u @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV7: $i] :
( ( ~ ( ~ ( exists_in_world @ ( sK7_SY411 @ SV7 ) @ SV7 )
| ~ ~ ( ~ ! [SY493: $i] :
( ~ ( rel_s4 @ SV7 @ SY493 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SY493 ) )
| ~ ! [SY494: $i] :
( ~ ( rel_s4 @ SV7 @ SY494 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SY494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(53,plain,
( ( ~ ( rel_s4 @ sK1_SY259 @ sK2_SY467 )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY467 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY467 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY467 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(54,plain,
! [SV8: $i] :
( ( ! [SY495: $i] :
( ~ ( rel_s4 @ SV8 @ SY495 )
| ~ ( ~ ( exists_in_world @ ( sK8_SY442 @ SY495 @ SV8 ) @ SY495 )
| ~ ~ ( ~ ! [SY496: $i] :
( ~ ( rel_s4 @ SY495 @ SY496 )
| ( userid @ u @ ( sK8_SY442 @ SY495 @ SV8 ) @ SY496 ) )
| ~ ! [SY497: $i] :
( ~ ( rel_s4 @ SY495 @ SY497 )
| ( string @ ( sK8_SY442 @ SY495 @ SV8 ) @ SY497 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV9: $i] :
( ( ! [SY498: $i] :
( ~ ( rel_s4 @ SV9 @ SY498 )
| ! [SY499: mu] :
( ~ ( exists_in_world @ SY499 @ SY498 )
| ! [SY500: mu] :
( ~ ( exists_in_world @ SY500 @ SY498 )
| ! [SY501: mu] :
( ~ ( exists_in_world @ SY501 @ SY498 )
| ~ ( string @ SY500 @ SY498 )
| ~ ( entry_box @ SY501 @ SY498 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY501 @ SY500 @ SY499 @ SY498 @ SV9 ) @ SY498 )
| ~ ! [SY502: $i] :
( ~ ( rel_s4 @ SY498 @ SY502 )
| ! [SY503: mu] :
( ~ ( exists_in_world @ SY503 @ SY502 )
| ~ ( do @ SY499 @ ( sK6_SY367 @ SY501 @ SY500 @ SY499 @ SY498 @ SV9 ) @ SY503 @ SY502 )
| ( in @ SY500 @ SY501 @ SY503 @ SY502 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY504: $i] :
( ~ ( rel_s4 @ SV3 @ SV10 )
| ~ ( rel_s4 @ SV10 @ SY504 )
| ( rel_s4 @ SV3 @ SY504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV11: $i,SV4: mu] :
( ( ! [SY505: $i] :
( ~ ( exists_in_world @ SV4 @ SV11 )
| ~ ( rel_s4 @ SV11 @ SY505 )
| ( exists_in_world @ SV4 @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK7_SY411 @ SV7 ) @ SV7 )
| ~ ~ ( ~ ! [SY493: $i] :
( ~ ( rel_s4 @ SV7 @ SY493 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SY493 ) )
| ~ ! [SY494: $i] :
( ~ ( rel_s4 @ SV7 @ SY494 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SY494 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
( ( ~ ( rel_s4 @ sK1_SY259 @ sK2_SY467 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(60,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY467 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY467 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY467 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(61,plain,
! [SV12: $i,SV8: $i] :
( ( ~ ( rel_s4 @ SV8 @ SV12 )
| ~ ( ~ ( exists_in_world @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) )
| ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( rel_s4 @ SV9 @ SV13 )
| ! [SY508: mu] :
( ~ ( exists_in_world @ SY508 @ SV13 )
| ! [SY509: mu] :
( ~ ( exists_in_world @ SY509 @ SV13 )
| ! [SY510: mu] :
( ~ ( exists_in_world @ SY510 @ SV13 )
| ~ ( string @ SY509 @ SV13 )
| ~ ( entry_box @ SY510 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY510 @ SY509 @ SY508 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY511: $i] :
( ~ ( rel_s4 @ SV13 @ SY511 )
| ! [SY512: mu] :
( ~ ( exists_in_world @ SY512 @ SY511 )
| ~ ( do @ SY508 @ ( sK6_SY367 @ SY510 @ SY509 @ SY508 @ SV13 @ SV9 ) @ SY512 @ SY511 )
| ( in @ SY509 @ SY510 @ SY512 @ SY511 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV14: $i,SV10: $i,SV3: $i] :
( ( ~ ( rel_s4 @ SV3 @ SV10 )
| ~ ( rel_s4 @ SV10 @ SV14 )
| ( rel_s4 @ SV3 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV15: $i,SV11: $i,SV4: mu] :
( ( ~ ( exists_in_world @ SV4 @ SV11 )
| ~ ( rel_s4 @ SV11 @ SV15 )
| ( exists_in_world @ SV4 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK7_SY411 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ! [SY493: $i] :
( ~ ( rel_s4 @ SV7 @ SY493 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SY493 ) )
| ~ ! [SY494: $i] :
( ~ ( rel_s4 @ SV7 @ SY494 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SY494 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(67,plain,
( ( rel_s4 @ sK1_SY259 @ sK2_SY467 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(68,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY467 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY467 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY467 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY479 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY482 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY480 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(69,plain,
! [SV12: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( exists_in_world @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) )
| ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV13 ) )
= $true )
| ( ( ! [SY508: mu] :
( ~ ( exists_in_world @ SY508 @ SV13 )
| ! [SY509: mu] :
( ~ ( exists_in_world @ SY509 @ SV13 )
| ! [SY510: mu] :
( ~ ( exists_in_world @ SY510 @ SV13 )
| ~ ( string @ SY509 @ SV13 )
| ~ ( entry_box @ SY510 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY510 @ SY509 @ SY508 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY511: $i] :
( ~ ( rel_s4 @ SV13 @ SY511 )
| ! [SY512: mu] :
( ~ ( exists_in_world @ SY512 @ SY511 )
| ~ ( do @ SY508 @ ( sK6_SY367 @ SY510 @ SY509 @ SY508 @ SV13 @ SV9 ) @ SY512 @ SY511 )
| ( in @ SY509 @ SY510 @ SY512 @ SY511 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(71,plain,
! [SV14: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV10 )
| ~ ( rel_s4 @ SV10 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV15: $i,SV11: $i,SV4: mu] :
( ( ( ~ ( exists_in_world @ SV4 @ SV11 )
| ~ ( rel_s4 @ SV11 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV4 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV7: $i] :
( ( exists_in_world @ ( sK7_SY411 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY493: $i] :
( ~ ( rel_s4 @ SV7 @ SY493 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SY493 ) )
| ~ ! [SY494: $i] :
( ~ ( rel_s4 @ SV7 @ SY494 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SY494 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(75,plain,
! [SV16: mu] :
( ( ~ ( exists_in_world @ SV16 @ sK2_SY467 )
| ! [SY513: mu] :
( ~ ( exists_in_world @ SY513 @ sK2_SY467 )
| ! [SY514: mu] :
( ~ ( exists_in_world @ SY514 @ sK2_SY467 )
| ! [SY515: mu] :
( ~ ( exists_in_world @ SY515 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( entry_box @ SY513 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( number @ SY513 @ one @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY515 @ SY514 @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SY513 @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(76,plain,
! [SV12: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV12 )
= $false )
| ( ( ~ ( ~ ( exists_in_world @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) )
| ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(77,plain,
! [SV13: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( ! [SY508: mu] :
( ~ ( exists_in_world @ SY508 @ SV13 )
| ! [SY509: mu] :
( ~ ( exists_in_world @ SY509 @ SV13 )
| ! [SY510: mu] :
( ~ ( exists_in_world @ SY510 @ SV13 )
| ~ ( string @ SY509 @ SV13 )
| ~ ( entry_box @ SY510 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY510 @ SY509 @ SY508 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY511: $i] :
( ~ ( rel_s4 @ SV13 @ SY511 )
| ! [SY512: mu] :
( ~ ( exists_in_world @ SY512 @ SY511 )
| ~ ( do @ SY508 @ ( sK6_SY367 @ SY510 @ SY509 @ SY508 @ SV13 @ SV9 ) @ SY512 @ SY511 )
| ( in @ SY509 @ SY510 @ SY512 @ SY511 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(78,plain,
! [SV14: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV10 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV10 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(79,plain,
! [SV15: $i,SV11: $i,SV4: mu] :
( ( ( ~ ( exists_in_world @ SV4 @ SV11 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV11 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV4 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV7: $i] :
( ( ~ ! [SY493: $i] :
( ~ ( rel_s4 @ SV7 @ SY493 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SY493 ) )
| ~ ! [SY494: $i] :
( ~ ( rel_s4 @ SV7 @ SY494 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SY494 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ sK2_SY467 ) )
= $true )
| ( ( ! [SY513: mu] :
( ~ ( exists_in_world @ SY513 @ sK2_SY467 )
| ! [SY514: mu] :
( ~ ( exists_in_world @ SY514 @ sK2_SY467 )
| ! [SY515: mu] :
( ~ ( exists_in_world @ SY515 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( entry_box @ SY513 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( number @ SY513 @ one @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY515 @ SY514 @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SY513 @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) )
| ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV9: $i,SV13: $i,SV17: mu] :
( ( ( ~ ( exists_in_world @ SV17 @ SV13 )
| ! [SY516: mu] :
( ~ ( exists_in_world @ SY516 @ SV13 )
| ! [SY517: mu] :
( ~ ( exists_in_world @ SY517 @ SV13 )
| ~ ( string @ SY516 @ SV13 )
| ~ ( entry_box @ SY517 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY517 @ SY516 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY518: $i] :
( ~ ( rel_s4 @ SV13 @ SY518 )
| ! [SY519: mu] :
( ~ ( exists_in_world @ SY519 @ SY518 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SY517 @ SY516 @ SV17 @ SV13 @ SV9 ) @ SY519 @ SY518 )
| ( in @ SY516 @ SY517 @ SY519 @ SY518 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV14: $i,SV10: $i,SV3: $i] :
( ( ( rel_s4 @ SV3 @ SV10 )
= $false )
| ( ( ~ ( rel_s4 @ SV10 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV15: $i,SV11: $i,SV4: mu] :
( ( ( exists_in_world @ SV4 @ SV11 )
= $false )
| ( ( ~ ( rel_s4 @ SV11 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV4 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV7: $i] :
( ( ~ ! [SY493: $i] :
( ~ ( rel_s4 @ SV7 @ SY493 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SY493 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV7: $i] :
( ( ~ ! [SY494: $i] :
( ~ ( rel_s4 @ SV7 @ SY494 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SY494 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV16: mu] :
( ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false )
| ( ( ! [SY513: mu] :
( ~ ( exists_in_world @ SY513 @ sK2_SY467 )
| ! [SY514: mu] :
( ~ ( exists_in_world @ SY514 @ sK2_SY467 )
| ! [SY515: mu] :
( ~ ( exists_in_world @ SY515 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( entry_box @ SY513 @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ( number @ SY513 @ one @ ( sK5_SY479 @ SY515 @ SY514 @ SY513 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY515 @ SY514 @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SY513 @ ( sK4_SY482 @ SY515 @ SY514 @ SY513 @ SV16 ) @ ( sK3_SY480 @ SY515 @ SY514 @ SY513 @ SV16 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) )
| ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(91,plain,
! [SV9: $i,SV13: $i,SV17: mu] :
( ( ( ~ ( exists_in_world @ SV17 @ SV13 ) )
= $true )
| ( ( ! [SY516: mu] :
( ~ ( exists_in_world @ SY516 @ SV13 )
| ! [SY517: mu] :
( ~ ( exists_in_world @ SY517 @ SV13 )
| ~ ( string @ SY516 @ SV13 )
| ~ ( entry_box @ SY517 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY517 @ SY516 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY518: $i] :
( ~ ( rel_s4 @ SV13 @ SY518 )
| ! [SY519: mu] :
( ~ ( exists_in_world @ SY519 @ SY518 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SY517 @ SY516 @ SV17 @ SV13 @ SV9 ) @ SY519 @ SY518 )
| ( in @ SY516 @ SY517 @ SY519 @ SY518 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV3: $i,SV14: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV14 )
= $false )
| ( ( rel_s4 @ SV3 @ SV10 )
= $false )
| ( ( rel_s4 @ SV3 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV4: mu,SV15: $i,SV11: $i] :
( ( ( rel_s4 @ SV11 @ SV15 )
= $false )
| ( ( exists_in_world @ SV4 @ SV11 )
= $false )
| ( ( exists_in_world @ SV4 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV7: $i] :
( ( ! [SY493: $i] :
( ~ ( rel_s4 @ SV7 @ SY493 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SY493 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(95,plain,
! [SV7: $i] :
( ( ! [SY494: $i] :
( ~ ( rel_s4 @ SV7 @ SY494 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SY494 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(96,plain,
! [SV16: mu,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ sK2_SY467 )
| ! [SY520: mu] :
( ~ ( exists_in_world @ SY520 @ sK2_SY467 )
| ! [SY521: mu] :
( ~ ( exists_in_world @ SY521 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY521 @ SY520 @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV8: $i,SV12: $i] :
( ( ( exists_in_world @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV12 )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) )
| ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(99,plain,
! [SV9: $i,SV13: $i,SV17: mu] :
( ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( ! [SY516: mu] :
( ~ ( exists_in_world @ SY516 @ SV13 )
| ! [SY517: mu] :
( ~ ( exists_in_world @ SY517 @ SV13 )
| ~ ( string @ SY516 @ SV13 )
| ~ ( entry_box @ SY517 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY517 @ SY516 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY518: $i] :
( ~ ( rel_s4 @ SV13 @ SY518 )
| ! [SY519: mu] :
( ~ ( exists_in_world @ SY519 @ SY518 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SY517 @ SY516 @ SV17 @ SV13 @ SV9 ) @ SY519 @ SY518 )
| ( in @ SY516 @ SY517 @ SY519 @ SY518 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( rel_s4 @ SV7 @ SV19 )
| ( entry_box @ ( sK7_SY411 @ SV7 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV20: $i,SV7: $i] :
( ( ~ ( rel_s4 @ SV7 @ SV20 )
| ( number @ ( sK7_SY411 @ SV7 ) @ one @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV16: mu,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ sK2_SY467 ) )
= $true )
| ( ( ! [SY520: mu] :
( ~ ( exists_in_world @ SY520 @ sK2_SY467 )
| ! [SY521: mu] :
( ~ ( exists_in_world @ SY521 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY521 @ SY520 @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) )
| ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV9: $i,SV17: mu,SV13: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV13 )
| ! [SY522: mu] :
( ~ ( exists_in_world @ SY522 @ SV13 )
| ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SY522 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY522 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY523: $i] :
( ~ ( rel_s4 @ SV13 @ SY523 )
| ! [SY524: mu] :
( ~ ( exists_in_world @ SY524 @ SY523 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SY522 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY524 @ SY523 )
| ( in @ SV21 @ SY522 @ SY524 @ SY523 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV19 ) )
= $true )
| ( ( entry_box @ ( sK7_SY411 @ SV7 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV20: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV20 ) )
= $true )
| ( ( number @ ( sK7_SY411 @ SV7 ) @ one @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV16: mu,SV18: mu] :
( ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( ! [SY520: mu] :
( ~ ( exists_in_world @ SY520 @ sK2_SY467 )
| ! [SY521: mu] :
( ~ ( exists_in_world @ SY521 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SY521 @ SY520 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY521 @ SY520 @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SY521 @ SY520 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY521 @ SY520 @ SV18 @ SV16 ) ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV9: $i,SV17: mu,SV13: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV13 ) )
= $true )
| ( ( ! [SY522: mu] :
( ~ ( exists_in_world @ SY522 @ SV13 )
| ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SY522 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY522 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY523: $i] :
( ~ ( rel_s4 @ SV13 @ SY523 )
| ! [SY524: mu] :
( ~ ( exists_in_world @ SY524 @ SY523 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SY522 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY524 @ SY523 )
| ( in @ SV21 @ SY522 @ SY524 @ SY523 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV19: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV19 )
= $false )
| ( ( entry_box @ ( sK7_SY411 @ SV7 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV20: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV20 )
= $false )
| ( ( number @ ( sK7_SY411 @ SV7 ) @ one @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV16: mu,SV18: mu,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ sK2_SY467 )
| ! [SY525: mu] :
( ~ ( exists_in_world @ SY525 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY525 @ SV22 @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV8: $i,SV12: $i] :
( ( ( ! [SY506: $i] :
( ~ ( rel_s4 @ SV12 @ SY506 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY506 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(115,plain,
! [SV8: $i,SV12: $i] :
( ( ( ! [SY507: $i] :
( ~ ( rel_s4 @ SV12 @ SY507 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SY507 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(116,plain,
! [SV9: $i,SV17: mu,SV13: $i,SV21: mu] :
( ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( ! [SY522: mu] :
( ~ ( exists_in_world @ SY522 @ SV13 )
| ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SY522 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SY522 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY523: $i] :
( ~ ( rel_s4 @ SV13 @ SY523 )
| ! [SY524: mu] :
( ~ ( exists_in_world @ SY524 @ SY523 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SY522 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY524 @ SY523 )
| ( in @ SV21 @ SY522 @ SY524 @ SY523 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV16: mu,SV18: mu,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ sK2_SY467 ) )
= $true )
| ( ( ! [SY525: mu] :
( ~ ( exists_in_world @ SY525 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY525 @ SV22 @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV8: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV23 )
| ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV23 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV8: $i,SV24: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV24 )
| ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV24 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(120,plain,
! [SV9: $i,SV17: mu,SV21: mu,SV13: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV13 )
| ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SV25 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(121,plain,
! [SV16: mu,SV18: mu,SV22: mu] :
( ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( ! [SY525: mu] :
( ~ ( exists_in_world @ SY525 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SY525 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY525 @ SV22 @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SY525 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SY525 @ SV22 @ SV18 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(122,plain,
! [SV8: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV23 ) )
= $true )
| ( ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV23 )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV8: $i,SV24: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV24 ) )
= $true )
| ( ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV24 )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(124,plain,
! [SV9: $i,SV17: mu,SV21: mu,SV13: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV13 ) )
= $true )
| ( ( ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SV25 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ sK2_SY467 )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV8: $i,SV23: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV23 )
= $false )
| ( ( userid @ u @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV23 )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(127,plain,
! [SV8: $i,SV24: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV24 )
= $false )
| ( ( string @ ( sK8_SY442 @ SV12 @ SV8 ) @ SV24 )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV9: $i,SV17: mu,SV21: mu,SV13: $i,SV25: mu] :
( ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SV25 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ sK2_SY467 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV9: $i,SV17: mu,SV25: mu,SV13: $i,SV21: mu] :
( ( ( ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SV25 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(132,plain,
! [SV9: $i,SV17: mu,SV25: mu,SV13: $i,SV21: mu] :
( ( ( ~ ( string @ SV21 @ SV13 ) )
= $true )
| ( ( ~ ( entry_box @ SV25 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(133,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(134,plain,
! [SV9: $i,SV17: mu,SV25: mu,SV13: $i,SV21: mu] :
( ( ( string @ SV21 @ SV13 )
= $false )
| ( ( ~ ( entry_box @ SV25 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(135,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(136,plain,
! [SV9: $i,SV17: mu,SV21: mu,SV13: $i,SV25: mu] :
( ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( ~ ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(137,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(138,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(139,plain,
! [SV9: $i,SV13: $i,SV17: mu,SV21: mu,SV25: mu] :
( ( ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(141,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(142,plain,
! [SV9: $i,SV13: $i,SV17: mu,SV21: mu,SV25: mu] :
( ( ( ~ ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 ) )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(143,plain,
! [SV9: $i,SV21: mu,SV25: mu,SV17: mu,SV13: $i] :
( ( ( ~ ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(144,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( ~ ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV9: $i,SV13: $i,SV17: mu,SV21: mu,SV25: mu] :
( ( ( exists_in_world @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
= $true )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(147,plain,
! [SV9: $i,SV21: mu,SV25: mu,SV17: mu,SV13: $i] :
( ( ( ! [SY526: $i] :
( ~ ( rel_s4 @ SV13 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY527 @ SY526 )
| ( in @ SV21 @ SV25 @ SY527 @ SY526 ) ) ) )
= $true )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(148,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(150,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV9: $i,SV21: mu,SV25: mu,SV17: mu,SV27: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV27 )
| ! [SY528: mu] :
( ~ ( exists_in_world @ SY528 @ SV27 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY528 @ SV27 )
| ( in @ SV21 @ SV25 @ SY528 @ SV27 ) ) )
= $true )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(152,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(153,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(154,plain,
! [SV16: mu,SV22: mu,SV26: mu,SV18: mu] :
( ( ( ~ ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(155,plain,
! [SV9: $i,SV21: mu,SV25: mu,SV17: mu,SV27: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV27 ) )
= $true )
| ( ( ! [SY528: mu] :
( ~ ( exists_in_world @ SY528 @ SV27 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY528 @ SV27 )
| ( in @ SV21 @ SV25 @ SY528 @ SV27 ) ) )
= $true )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(156,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(157,plain,
! [SV16: mu,SV22: mu,SV26: mu,SV18: mu] :
( ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV9: $i,SV21: mu,SV25: mu,SV17: mu,SV27: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV27 )
= $false )
| ( ( ! [SY528: mu] :
( ~ ( exists_in_world @ SY528 @ SV27 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY528 @ SV27 )
| ( in @ SV21 @ SV25 @ SY528 @ SV27 ) ) )
= $true )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(160,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(161,plain,
! [SV16: mu,SV22: mu,SV26: mu,SV18: mu] :
( ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(162,plain,
! [SV9: $i,SV13: $i,SV21: mu,SV25: mu,SV17: mu,SV27: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV27 )
| ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV28 @ SV27 )
| ( in @ SV21 @ SV25 @ SV28 @ SV27 ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(163,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(165,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV9: $i,SV13: $i,SV21: mu,SV25: mu,SV17: mu,SV27: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV27 ) )
= $true )
| ( ( ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV28 @ SV27 )
| ( in @ SV21 @ SV25 @ SV28 @ SV27 ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(167,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(168,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(169,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(170,plain,
! [SV9: $i,SV13: $i,SV21: mu,SV25: mu,SV17: mu,SV27: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV27 )
= $false )
| ( ( ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV28 @ SV27 )
| ( in @ SV21 @ SV25 @ SV28 @ SV27 ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(172,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(173,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( rel_s4 @ sK2_SY467 @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(174,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(175,plain,
! [SV27: $i,SV28: mu,SV9: $i,SV13: $i,SV21: mu,SV25: mu,SV17: mu] :
( ( ( ~ ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV28 @ SV27 ) )
= $true )
| ( ( in @ SV21 @ SV25 @ SV28 @ SV27 )
= $true )
| ( ( exists_in_world @ SV28 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(176,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(177,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(178,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(179,plain,
! [SV27: $i,SV28: mu,SV9: $i,SV13: $i,SV21: mu,SV25: mu,SV17: mu] :
( ( ( do @ SV17 @ ( sK6_SY367 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV28 @ SV27 )
= $false )
| ( ( in @ SV21 @ SV25 @ SV28 @ SV27 )
= $true )
| ( ( exists_in_world @ SV28 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false )
| ( ( string @ SV21 @ SV13 )
= $false )
| ( ( entry_box @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV25 @ SV13 )
= $false )
| ( ( exists_in_world @ SV21 @ SV13 )
= $false )
| ( ( exists_in_world @ SV17 @ SV13 )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(180,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( rel_s4 @ sK2_SY467 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(182,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(183,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( exists_in_world @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(184,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(185,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(186,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(187,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(188,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( do @ SV26 @ SV22 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(189,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(190,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( in @ SV16 @ SV18 @ ( sK4_SY482 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY480 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY479 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY467 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(191,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[46,190,188,183,180,179,176,173,163,152,146,127,126,112,111,97,93,92,73,67,51,50,47]) ).
thf(192,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS272^7 : TPTP v8.1.0. Released v5.5.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 14:55:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.39
% 0.13/0.39 No.of.Axioms: 9
% 0.13/0.39
% 0.13/0.39 Length.of.Defs: 5540
% 0.13/0.39
% 0.13/0.39 Contains.Choice.Funs: false
% 0.20/0.43 (rf:0,axioms:9,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:11,loop_count:0,foatp_calls:0,translation:fof_full)................eprover: CPU time limit exceeded, terminating
% 25.46/25.64 ....eprover: CPU time limit exceeded, terminating
% 54.12/54.31 ........
% 75.25/75.50 (rf:0,axioms:9,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:11,loop_count:0,foatp_calls:0,translation:fof_full).........................
% 76.40/76.72
% 76.40/76.72 ********************************
% 76.40/76.72 * All subproblems solved! *
% 76.40/76.72 ********************************
% 76.40/76.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:191,loop_count:0,foatp_calls:1,translation:fof_full)
% 76.55/76.74
% 76.55/76.74 %**** Beginning of derivation protocol ****
% 76.55/76.74 % SZS output start CNFRefutation
% See solution above
% 76.55/76.74
% 76.55/76.74 %**** End of derivation protocol ****
% 76.55/76.74 %**** no. of clauses in derivation: 192 ****
% 76.55/76.74 %**** clause counter: 191 ****
% 76.55/76.74
% 76.55/76.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:3,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:191,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------