%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KRS272^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:26:46 AM UTC 2026
% Result : Theorem 45.45s 7.71s
% Output : CNFRefutation 45.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 42
% Syntax : Number of formulae : 224 ( 105 unt; 0 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 : 59 ( 59 >; 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_SY181,type,
sK1_SY181: $i ).
thf(tp_sK2_SY389,type,
sK2_SY389: $i ).
thf(tp_sK3_SY402,type,
sK3_SY402: mu > mu > mu > mu > $i ).
thf(tp_sK4_SY404,type,
sK4_SY404: mu > mu > mu > mu > mu ).
thf(tp_sK5_SY401,type,
sK5_SY401: mu > mu > mu > mu > $i ).
thf(tp_sK6_SY289,type,
sK6_SY289: mu > mu > mu > $i > $i > mu ).
thf(tp_sK7_SY333,type,
sK7_SY333: $i > mu ).
thf(tp_sK8_SY364,type,
sK8_SY364: $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/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(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/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(4,axiom,
! [V: $i] : ( exists_in_world @ u @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_u_ax) ).
thf(5,axiom,
! [V: $i] : ( exists_in_world @ one @ V ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cumulative_ax) ).
thf(7,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(8,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(9,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox/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/sandbox/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,
( ( ! [SY181: $i,SY182: $i] :
( ~ ( rel_s4 @ SY181 @ SY182 )
| ~ ! [SY174: mu] :
( ( exists_in_world @ SY174 @ SY182 )
=> ~ ~ ! [SY175: mu] :
( ( exists_in_world @ SY175 @ SY182 )
=> ~ ~ ! [SY176: mu] :
( ( exists_in_world @ SY176 @ SY182 )
=> ~ ~ ! [SY177: mu] :
( ( exists_in_world @ SY177 @ SY182 )
=> ~ ~ ( ~ ! [SY178: $i] :
( ~ ( rel_s4 @ SY182 @ SY178 )
| ~ ( ~ ( userid @ u @ SY174 @ SY178 )
| ~ ~ ( ~ ( entry_box @ SY175 @ SY178 )
| ~ ( number @ SY175 @ one @ SY178 ) ) ) )
| ~ ! [SY179: $i] :
( ~ ( rel_s4 @ SY182 @ SY179 )
| ! [SY157: mu] :
( ( exists_in_world @ SY157 @ SY179 )
=> ( ~ ( do @ SY177 @ SY176 @ SY157 @ SY179 )
| ( in @ SY174 @ SY175 @ SY157 @ SY179 ) ) ) ) ) ) ) ) ) ) )
= $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,
( ( ! [SY292: $i,SY293: $i] :
( ~ ( rel_s4 @ SY292 @ SY293 )
| ! [SY286: mu] :
( ( exists_in_world @ SY286 @ SY293 )
=> ! [SY287: mu] :
( ( exists_in_world @ SY287 @ SY293 )
=> ! [SY288: mu] :
( ( exists_in_world @ SY288 @ SY293 )
=> ( ~ ~ ( ~ ( string @ SY287 @ SY293 )
| ~ ( entry_box @ SY288 @ SY293 ) )
| ~ ! [SY289: mu] :
( ( exists_in_world @ SY289 @ SY293 )
=> ~ ! [SY290: $i] :
( ~ ( rel_s4 @ SY293 @ SY290 )
| ! [SY278: mu] :
( ( exists_in_world @ SY278 @ SY290 )
=> ( ~ ( do @ SY286 @ SY289 @ SY278 @ SY290 )
| ( in @ SY287 @ SY288 @ SY278 @ SY290 ) ) ) ) ) ) ) ) ) ) )
= $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,
( ( ! [SY332: $i] :
~ ! [SY333: mu] :
( ( exists_in_world @ SY333 @ SY332 )
=> ~ ! [SY334: $i] :
( ~ ( rel_s4 @ SY332 @ SY334 )
| ~ ( ~ ( entry_box @ SY333 @ SY334 )
| ~ ( number @ SY333 @ one @ SY334 ) ) ) ) )
= $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,
( ( ! [SY366: $i,SY367: $i] :
( ~ ( rel_s4 @ SY366 @ SY367 )
| ~ ! [SY364: mu] :
( ( exists_in_world @ SY364 @ SY367 )
=> ~ ! [SY365: $i] :
( ~ ( rel_s4 @ SY367 @ SY365 )
| ~ ( ~ ( userid @ u @ SY364 @ SY365 )
| ~ ( string @ SY364 @ SY365 ) ) ) ) ) )
= $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,
( ( ! [SY379: $i,SY380: $i,SY381: $i] :
( ( ( rel_s4 @ SY379 @ SY380 )
& ( rel_s4 @ SY380 @ SY381 ) )
=> ( rel_s4 @ SY379 @ SY381 ) ) )
= $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,
( ( ! [SY385: $i] : ( rel_s4 @ SY385 @ SY385 ) )
= $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,
( ( ! [SY389: $i] :
( ~ ( rel_s4 @ sK1_SY181 @ SY389 )
| ~ ! [SY174: mu] :
( ( exists_in_world @ SY174 @ SY389 )
=> ~ ~ ! [SY175: mu] :
( ( exists_in_world @ SY175 @ SY389 )
=> ~ ~ ! [SY176: mu] :
( ( exists_in_world @ SY176 @ SY389 )
=> ~ ~ ! [SY177: mu] :
( ( exists_in_world @ SY177 @ SY389 )
=> ~ ~ ( ~ ! [SY178: $i] :
( ~ ( rel_s4 @ SY389 @ SY178 )
| ~ ( ~ ( userid @ u @ SY174 @ SY178 )
| ~ ~ ( ~ ( entry_box @ SY175 @ SY178 )
| ~ ( number @ SY175 @ one @ SY178 ) ) ) )
| ~ ! [SY179: $i] :
( ~ ( rel_s4 @ SY389 @ SY179 )
| ! [SY157: mu] :
( ( exists_in_world @ SY157 @ SY179 )
=> ( ~ ( do @ SY177 @ SY176 @ SY157 @ SY179 )
| ( in @ SY174 @ SY175 @ SY157 @ SY179 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ~ ( rel_s4 @ sK1_SY181 @ sK2_SY389 )
| ~ ! [SY397: mu] :
( ( exists_in_world @ SY397 @ sK2_SY389 )
=> ~ ~ ! [SY398: mu] :
( ( exists_in_world @ SY398 @ sK2_SY389 )
=> ~ ~ ! [SY399: mu] :
( ( exists_in_world @ SY399 @ sK2_SY389 )
=> ~ ~ ! [SY400: mu] :
( ( exists_in_world @ SY400 @ sK2_SY389 )
=> ~ ~ ( ~ ! [SY401: $i] :
( ~ ( rel_s4 @ sK2_SY389 @ SY401 )
| ~ ( ~ ( userid @ u @ SY397 @ SY401 )
| ~ ~ ( ~ ( entry_box @ SY398 @ SY401 )
| ~ ( number @ SY398 @ one @ SY401 ) ) ) )
| ~ ! [SY402: $i] :
( ~ ( rel_s4 @ sK2_SY389 @ SY402 )
| ! [SY157: mu] :
( ( exists_in_world @ SY157 @ SY402 )
=> ( ~ ( do @ SY400 @ SY399 @ SY157 @ SY402 )
| ( in @ SY397 @ SY398 @ SY157 @ SY402 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY181 @ sK2_SY389 )
| ~ ! [SY397: mu] :
( ( exists_in_world @ SY397 @ sK2_SY389 )
=> ~ ~ ! [SY398: mu] :
( ( exists_in_world @ SY398 @ sK2_SY389 )
=> ~ ~ ! [SY399: mu] :
( ( exists_in_world @ SY399 @ sK2_SY389 )
=> ~ ~ ! [SY400: mu] :
( ( exists_in_world @ SY400 @ sK2_SY389 )
=> ~ ~ ( ~ ! [SY401: $i] :
( ~ ( rel_s4 @ sK2_SY389 @ SY401 )
| ~ ( ~ ( userid @ u @ SY397 @ SY401 )
| ~ ~ ( ~ ( entry_box @ SY398 @ SY401 )
| ~ ( number @ SY398 @ one @ SY401 ) ) ) )
| ~ ! [SY402: $i] :
( ~ ( rel_s4 @ sK2_SY389 @ SY402 )
| ! [SY157: mu] :
( ( exists_in_world @ SY157 @ SY402 )
=> ( ~ ( do @ SY400 @ SY399 @ SY157 @ SY402 )
| ( in @ SY397 @ SY398 @ SY157 @ SY402 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ( rel_s4 @ sK1_SY181 @ sK2_SY389 )
& ! [SY397: mu] :
( ~ ( exists_in_world @ SY397 @ sK2_SY389 )
| ! [SY398: mu] :
( ~ ( exists_in_world @ SY398 @ sK2_SY389 )
| ! [SY399: mu] :
( ~ ( exists_in_world @ SY399 @ sK2_SY389 )
| ! [SY400: mu] :
( ~ ( exists_in_world @ SY400 @ sK2_SY389 )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ( ~ ( userid @ u @ SY397 @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) )
| ~ ( entry_box @ SY398 @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) )
| ~ ( number @ SY398 @ one @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) ) ) )
| ( ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ( exists_in_world @ ( sK4_SY404 @ SY400 @ SY399 @ SY398 @ SY397 ) @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ( do @ SY400 @ SY399 @ ( sK4_SY404 @ SY400 @ SY399 @ SY398 @ SY397 ) @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ~ ( in @ SY397 @ SY398 @ ( sK4_SY404 @ SY400 @ SY399 @ SY398 @ SY397 ) @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(26,plain,
( ( ! [SY292: $i,SY293: $i] :
( ~ ( rel_s4 @ SY292 @ SY293 )
| ! [SY286: mu] :
( ~ ( exists_in_world @ SY286 @ SY293 )
| ! [SY287: mu] :
( ~ ( exists_in_world @ SY287 @ SY293 )
| ! [SY288: mu] :
( ~ ( exists_in_world @ SY288 @ SY293 )
| ~ ( string @ SY287 @ SY293 )
| ~ ( entry_box @ SY288 @ SY293 )
| ( ( exists_in_world @ ( sK6_SY289 @ SY288 @ SY287 @ SY286 @ SY293 @ SY292 ) @ SY293 )
& ! [SY405: $i] :
( ~ ( rel_s4 @ SY293 @ SY405 )
| ! [SY406: mu] :
( ~ ( exists_in_world @ SY406 @ SY405 )
| ~ ( do @ SY286 @ ( sK6_SY289 @ SY288 @ SY287 @ SY286 @ SY293 @ SY292 ) @ SY406 @ SY405 )
| ( in @ SY287 @ SY288 @ SY406 @ SY405 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(27,plain,
( ( ! [SY332: $i] :
( ( exists_in_world @ ( sK7_SY333 @ SY332 ) @ SY332 )
& ! [SY407: $i] :
( ~ ( rel_s4 @ SY332 @ SY407 )
| ( entry_box @ ( sK7_SY333 @ SY332 ) @ SY407 ) )
& ! [SY408: $i] :
( ~ ( rel_s4 @ SY332 @ SY408 )
| ( number @ ( sK7_SY333 @ SY332 ) @ one @ SY408 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(28,plain,
( ( ! [SY366: $i,SY367: $i] :
( ~ ( rel_s4 @ SY366 @ SY367 )
| ( ( exists_in_world @ ( sK8_SY364 @ SY367 @ SY366 ) @ SY367 )
& ! [SY409: $i] :
( ~ ( rel_s4 @ SY367 @ SY409 )
| ( userid @ u @ ( sK8_SY364 @ SY367 @ SY366 ) @ SY409 ) )
& ! [SY410: $i] :
( ~ ( rel_s4 @ SY367 @ SY410 )
| ( string @ ( sK8_SY364 @ SY367 @ SY366 ) @ SY410 ) ) ) ) )
= $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,
( ( ! [SY379: $i,SY380: $i,SY381: $i] :
( ~ ( rel_s4 @ SY379 @ SY380 )
| ~ ( rel_s4 @ SY380 @ SY381 )
| ( rel_s4 @ SY379 @ SY381 ) ) )
= $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,
( ( ! [SY385: $i] : ( rel_s4 @ SY385 @ SY385 ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(34,plain,
( ( ! [SY379: $i,SY380: $i,SY381: $i] :
( ~ ( rel_s4 @ SY379 @ SY380 )
| ~ ( rel_s4 @ SY380 @ SY381 )
| ( rel_s4 @ SY379 @ SY381 ) ) )
= $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,
( ( ! [SY366: $i,SY367: $i] :
( ~ ( rel_s4 @ SY366 @ SY367 )
| ( ( exists_in_world @ ( sK8_SY364 @ SY367 @ SY366 ) @ SY367 )
& ! [SY409: $i] :
( ~ ( rel_s4 @ SY367 @ SY409 )
| ( userid @ u @ ( sK8_SY364 @ SY367 @ SY366 ) @ SY409 ) )
& ! [SY410: $i] :
( ~ ( rel_s4 @ SY367 @ SY410 )
| ( string @ ( sK8_SY364 @ SY367 @ SY366 ) @ SY410 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(39,plain,
( ( ! [SY332: $i] :
( ( exists_in_world @ ( sK7_SY333 @ SY332 ) @ SY332 )
& ! [SY407: $i] :
( ~ ( rel_s4 @ SY332 @ SY407 )
| ( entry_box @ ( sK7_SY333 @ SY332 ) @ SY407 ) )
& ! [SY408: $i] :
( ~ ( rel_s4 @ SY332 @ SY408 )
| ( number @ ( sK7_SY333 @ SY332 ) @ one @ SY408 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(40,plain,
( ( ! [SY292: $i,SY293: $i] :
( ~ ( rel_s4 @ SY292 @ SY293 )
| ! [SY286: mu] :
( ~ ( exists_in_world @ SY286 @ SY293 )
| ! [SY287: mu] :
( ~ ( exists_in_world @ SY287 @ SY293 )
| ! [SY288: mu] :
( ~ ( exists_in_world @ SY288 @ SY293 )
| ~ ( string @ SY287 @ SY293 )
| ~ ( entry_box @ SY288 @ SY293 )
| ( ( exists_in_world @ ( sK6_SY289 @ SY288 @ SY287 @ SY286 @ SY293 @ SY292 ) @ SY293 )
& ! [SY405: $i] :
( ~ ( rel_s4 @ SY293 @ SY405 )
| ! [SY406: mu] :
( ~ ( exists_in_world @ SY406 @ SY405 )
| ~ ( do @ SY286 @ ( sK6_SY289 @ SY288 @ SY287 @ SY286 @ SY293 @ SY292 ) @ SY406 @ SY405 )
| ( in @ SY287 @ SY288 @ SY406 @ SY405 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(41,plain,
( ( ( rel_s4 @ sK1_SY181 @ sK2_SY389 )
& ! [SY397: mu] :
( ~ ( exists_in_world @ SY397 @ sK2_SY389 )
| ! [SY398: mu] :
( ~ ( exists_in_world @ SY398 @ sK2_SY389 )
| ! [SY399: mu] :
( ~ ( exists_in_world @ SY399 @ sK2_SY389 )
| ! [SY400: mu] :
( ~ ( exists_in_world @ SY400 @ sK2_SY389 )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ( ~ ( userid @ u @ SY397 @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) )
| ~ ( entry_box @ SY398 @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) )
| ~ ( number @ SY398 @ one @ ( sK5_SY401 @ SY400 @ SY399 @ SY398 @ SY397 ) ) ) )
| ( ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ( exists_in_world @ ( sK4_SY404 @ SY400 @ SY399 @ SY398 @ SY397 ) @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ( do @ SY400 @ SY399 @ ( sK4_SY404 @ SY400 @ SY399 @ SY398 @ SY397 ) @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) )
& ~ ( in @ SY397 @ SY398 @ ( sK4_SY404 @ SY400 @ SY399 @ SY398 @ SY397 ) @ ( sK3_SY402 @ SY400 @ SY399 @ SY398 @ SY397 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(42,plain,
( ( ! [SX0: $i] :
~ ( ~ ( exists_in_world @ ( sK7_SY333 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ( entry_box @ ( sK7_SY333 @ SX0 ) @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ( number @ ( sK7_SY333 @ 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_SY181 @ sK2_SY389 )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY389 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY389 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY389 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ 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_SY364 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ( userid @ u @ ( sK8_SY364 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ( string @ ( sK8_SY364 @ 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_SY289 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX1 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ~ ( do @ SX2 @ ( sK6_SY289 @ 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] :
( ( ! [SY411: $i,SY412: $i] :
( ~ ( rel_s4 @ SV3 @ SY411 )
| ~ ( rel_s4 @ SY411 @ SY412 )
| ( rel_s4 @ SV3 @ SY412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(49,plain,
! [SV4: mu] :
( ( ! [SY413: $i,SY414: $i] :
( ~ ( exists_in_world @ SV4 @ SY413 )
| ~ ( rel_s4 @ SY413 @ SY414 )
| ( exists_in_world @ SV4 @ SY414 ) ) )
= $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_SY333 @ SV7 ) @ SV7 )
| ~ ~ ( ~ ! [SY415: $i] :
( ~ ( rel_s4 @ SV7 @ SY415 )
| ( entry_box @ ( sK7_SY333 @ SV7 ) @ SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( rel_s4 @ SV7 @ SY416 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SY416 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(53,plain,
( ( ~ ( rel_s4 @ sK1_SY181 @ sK2_SY389 )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY389 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY389 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY389 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(54,plain,
! [SV8: $i] :
( ( ! [SY417: $i] :
( ~ ( rel_s4 @ SV8 @ SY417 )
| ~ ( ~ ( exists_in_world @ ( sK8_SY364 @ SY417 @ SV8 ) @ SY417 )
| ~ ~ ( ~ ! [SY418: $i] :
( ~ ( rel_s4 @ SY417 @ SY418 )
| ( userid @ u @ ( sK8_SY364 @ SY417 @ SV8 ) @ SY418 ) )
| ~ ! [SY419: $i] :
( ~ ( rel_s4 @ SY417 @ SY419 )
| ( string @ ( sK8_SY364 @ SY417 @ SV8 ) @ SY419 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV9: $i] :
( ( ! [SY420: $i] :
( ~ ( rel_s4 @ SV9 @ SY420 )
| ! [SY421: mu] :
( ~ ( exists_in_world @ SY421 @ SY420 )
| ! [SY422: mu] :
( ~ ( exists_in_world @ SY422 @ SY420 )
| ! [SY423: mu] :
( ~ ( exists_in_world @ SY423 @ SY420 )
| ~ ( string @ SY422 @ SY420 )
| ~ ( entry_box @ SY423 @ SY420 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY423 @ SY422 @ SY421 @ SY420 @ SV9 ) @ SY420 )
| ~ ! [SY424: $i] :
( ~ ( rel_s4 @ SY420 @ SY424 )
| ! [SY425: mu] :
( ~ ( exists_in_world @ SY425 @ SY424 )
| ~ ( do @ SY421 @ ( sK6_SY289 @ SY423 @ SY422 @ SY421 @ SY420 @ SV9 ) @ SY425 @ SY424 )
| ( in @ SY422 @ SY423 @ SY425 @ SY424 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY426: $i] :
( ~ ( rel_s4 @ SV3 @ SV10 )
| ~ ( rel_s4 @ SV10 @ SY426 )
| ( rel_s4 @ SV3 @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV11: $i,SV4: mu] :
( ( ! [SY427: $i] :
( ~ ( exists_in_world @ SV4 @ SV11 )
| ~ ( rel_s4 @ SV11 @ SY427 )
| ( exists_in_world @ SV4 @ SY427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK7_SY333 @ SV7 ) @ SV7 )
| ~ ~ ( ~ ! [SY415: $i] :
( ~ ( rel_s4 @ SV7 @ SY415 )
| ( entry_box @ ( sK7_SY333 @ SV7 ) @ SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( rel_s4 @ SV7 @ SY416 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SY416 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
( ( ~ ( rel_s4 @ sK1_SY181 @ sK2_SY389 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(60,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY389 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY389 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY389 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ 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_SY364 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) )
| ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( rel_s4 @ SV9 @ SV13 )
| ! [SY430: mu] :
( ~ ( exists_in_world @ SY430 @ SV13 )
| ! [SY431: mu] :
( ~ ( exists_in_world @ SY431 @ SV13 )
| ! [SY432: mu] :
( ~ ( exists_in_world @ SY432 @ SV13 )
| ~ ( string @ SY431 @ SV13 )
| ~ ( entry_box @ SY432 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY432 @ SY431 @ SY430 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY433: $i] :
( ~ ( rel_s4 @ SV13 @ SY433 )
| ! [SY434: mu] :
( ~ ( exists_in_world @ SY434 @ SY433 )
| ~ ( do @ SY430 @ ( sK6_SY289 @ SY432 @ SY431 @ SY430 @ SV13 @ SV9 ) @ SY434 @ SY433 )
| ( in @ SY431 @ SY432 @ SY434 @ SY433 ) ) ) ) ) ) ) )
= $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_SY333 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ! [SY415: $i] :
( ~ ( rel_s4 @ SV7 @ SY415 )
| ( entry_box @ ( sK7_SY333 @ SV7 ) @ SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( rel_s4 @ SV7 @ SY416 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SY416 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(67,plain,
( ( rel_s4 @ sK1_SY181 @ sK2_SY389 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(68,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY389 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY389 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ sK2_SY389 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ( userid @ u @ SX0 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( entry_box @ SX1 @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( number @ SX1 @ one @ ( sK5_SY401 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( do @ SX3 @ SX2 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX0 @ SX1 @ ( sK4_SY404 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK3_SY402 @ 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_SY364 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) )
| ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV13 ) )
= $true )
| ( ( ! [SY430: mu] :
( ~ ( exists_in_world @ SY430 @ SV13 )
| ! [SY431: mu] :
( ~ ( exists_in_world @ SY431 @ SV13 )
| ! [SY432: mu] :
( ~ ( exists_in_world @ SY432 @ SV13 )
| ~ ( string @ SY431 @ SV13 )
| ~ ( entry_box @ SY432 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY432 @ SY431 @ SY430 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY433: $i] :
( ~ ( rel_s4 @ SV13 @ SY433 )
| ! [SY434: mu] :
( ~ ( exists_in_world @ SY434 @ SY433 )
| ~ ( do @ SY430 @ ( sK6_SY289 @ SY432 @ SY431 @ SY430 @ SV13 @ SV9 ) @ SY434 @ SY433 )
| ( in @ SY431 @ SY432 @ SY434 @ SY433 ) ) ) ) ) ) ) )
= $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_SY333 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY415: $i] :
( ~ ( rel_s4 @ SV7 @ SY415 )
| ( entry_box @ ( sK7_SY333 @ SV7 ) @ SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( rel_s4 @ SV7 @ SY416 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SY416 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(75,plain,
! [SV16: mu] :
( ( ~ ( exists_in_world @ SV16 @ sK2_SY389 )
| ! [SY435: mu] :
( ~ ( exists_in_world @ SY435 @ sK2_SY389 )
| ! [SY436: mu] :
( ~ ( exists_in_world @ SY436 @ sK2_SY389 )
| ! [SY437: mu] :
( ~ ( exists_in_world @ SY437 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( entry_box @ SY435 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( number @ SY435 @ one @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY437 @ SY436 @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SY435 @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ 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_SY364 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) )
| ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(77,plain,
! [SV13: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( ! [SY430: mu] :
( ~ ( exists_in_world @ SY430 @ SV13 )
| ! [SY431: mu] :
( ~ ( exists_in_world @ SY431 @ SV13 )
| ! [SY432: mu] :
( ~ ( exists_in_world @ SY432 @ SV13 )
| ~ ( string @ SY431 @ SV13 )
| ~ ( entry_box @ SY432 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY432 @ SY431 @ SY430 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY433: $i] :
( ~ ( rel_s4 @ SV13 @ SY433 )
| ! [SY434: mu] :
( ~ ( exists_in_world @ SY434 @ SY433 )
| ~ ( do @ SY430 @ ( sK6_SY289 @ SY432 @ SY431 @ SY430 @ SV13 @ SV9 ) @ SY434 @ SY433 )
| ( in @ SY431 @ SY432 @ SY434 @ SY433 ) ) ) ) ) ) ) )
= $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] :
( ( ~ ! [SY415: $i] :
( ~ ( rel_s4 @ SV7 @ SY415 )
| ( entry_box @ ( sK7_SY333 @ SV7 ) @ SY415 ) )
| ~ ! [SY416: $i] :
( ~ ( rel_s4 @ SV7 @ SY416 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SY416 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ sK2_SY389 ) )
= $true )
| ( ( ! [SY435: mu] :
( ~ ( exists_in_world @ SY435 @ sK2_SY389 )
| ! [SY436: mu] :
( ~ ( exists_in_world @ SY436 @ sK2_SY389 )
| ! [SY437: mu] :
( ~ ( exists_in_world @ SY437 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( entry_box @ SY435 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( number @ SY435 @ one @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY437 @ SY436 @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SY435 @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK8_SY364 @ SV12 @ SV8 ) @ SV12 )
| ~ ~ ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) )
| ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) ) )
= $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 )
| ! [SY438: mu] :
( ~ ( exists_in_world @ SY438 @ SV13 )
| ! [SY439: mu] :
( ~ ( exists_in_world @ SY439 @ SV13 )
| ~ ( string @ SY438 @ SV13 )
| ~ ( entry_box @ SY439 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY439 @ SY438 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY440: $i] :
( ~ ( rel_s4 @ SV13 @ SY440 )
| ! [SY441: mu] :
( ~ ( exists_in_world @ SY441 @ SY440 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SY439 @ SY438 @ SV17 @ SV13 @ SV9 ) @ SY441 @ SY440 )
| ( in @ SY438 @ SY439 @ SY441 @ SY440 ) ) ) ) ) ) )
= $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] :
( ( ~ ! [SY415: $i] :
( ~ ( rel_s4 @ SV7 @ SY415 )
| ( entry_box @ ( sK7_SY333 @ SV7 ) @ SY415 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(87,plain,
! [SV7: $i] :
( ( ~ ! [SY416: $i] :
( ~ ( rel_s4 @ SV7 @ SY416 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SY416 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(88,plain,
! [SV16: mu] :
( ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false )
| ( ( ! [SY435: mu] :
( ~ ( exists_in_world @ SY435 @ sK2_SY389 )
| ! [SY436: mu] :
( ~ ( exists_in_world @ SY436 @ sK2_SY389 )
| ! [SY437: mu] :
( ~ ( exists_in_world @ SY437 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( entry_box @ SY435 @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ( number @ SY435 @ one @ ( sK5_SY401 @ SY437 @ SY436 @ SY435 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY437 @ SY436 @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SY435 @ ( sK4_SY404 @ SY437 @ SY436 @ SY435 @ SV16 ) @ ( sK3_SY402 @ SY437 @ SY436 @ SY435 @ SV16 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK8_SY364 @ SV12 @ SV8 ) @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(90,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) )
| ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) ) )
= $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 )
| ( ( ! [SY438: mu] :
( ~ ( exists_in_world @ SY438 @ SV13 )
| ! [SY439: mu] :
( ~ ( exists_in_world @ SY439 @ SV13 )
| ~ ( string @ SY438 @ SV13 )
| ~ ( entry_box @ SY439 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY439 @ SY438 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY440: $i] :
( ~ ( rel_s4 @ SV13 @ SY440 )
| ! [SY441: mu] :
( ~ ( exists_in_world @ SY441 @ SY440 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SY439 @ SY438 @ SV17 @ SV13 @ SV9 ) @ SY441 @ SY440 )
| ( in @ SY438 @ SY439 @ SY441 @ SY440 ) ) ) ) ) ) )
= $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] :
( ( ! [SY415: $i] :
( ~ ( rel_s4 @ SV7 @ SY415 )
| ( entry_box @ ( sK7_SY333 @ SV7 ) @ SY415 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(95,plain,
! [SV7: $i] :
( ( ! [SY416: $i] :
( ~ ( rel_s4 @ SV7 @ SY416 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SY416 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(96,plain,
! [SV16: mu,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ sK2_SY389 )
| ! [SY442: mu] :
( ~ ( exists_in_world @ SY442 @ sK2_SY389 )
| ! [SY443: mu] :
( ~ ( exists_in_world @ SY443 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY443 @ SY442 @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV8: $i,SV12: $i] :
( ( ( exists_in_world @ ( sK8_SY364 @ SV12 @ SV8 ) @ SV12 )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) )
| ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) ) )
= $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 )
| ( ( ! [SY438: mu] :
( ~ ( exists_in_world @ SY438 @ SV13 )
| ! [SY439: mu] :
( ~ ( exists_in_world @ SY439 @ SV13 )
| ~ ( string @ SY438 @ SV13 )
| ~ ( entry_box @ SY439 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY439 @ SY438 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY440: $i] :
( ~ ( rel_s4 @ SV13 @ SY440 )
| ! [SY441: mu] :
( ~ ( exists_in_world @ SY441 @ SY440 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SY439 @ SY438 @ SV17 @ SV13 @ SV9 ) @ SY441 @ SY440 )
| ( in @ SY438 @ SY439 @ SY441 @ SY440 ) ) ) ) ) ) )
= $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_SY333 @ SV7 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV20: $i,SV7: $i] :
( ( ~ ( rel_s4 @ SV7 @ SV20 )
| ( number @ ( sK7_SY333 @ SV7 ) @ one @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV16: mu,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ sK2_SY389 ) )
= $true )
| ( ( ! [SY442: mu] :
( ~ ( exists_in_world @ SY442 @ sK2_SY389 )
| ! [SY443: mu] :
( ~ ( exists_in_world @ SY443 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY443 @ SY442 @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) )
| ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) )
= $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 )
| ! [SY444: mu] :
( ~ ( exists_in_world @ SY444 @ SV13 )
| ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SY444 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY444 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY445: $i] :
( ~ ( rel_s4 @ SV13 @ SY445 )
| ! [SY446: mu] :
( ~ ( exists_in_world @ SY446 @ SY445 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SY444 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY446 @ SY445 )
| ( in @ SV21 @ SY444 @ SY446 @ SY445 ) ) ) ) ) )
= $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_SY333 @ SV7 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV20: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV20 ) )
= $true )
| ( ( number @ ( sK7_SY333 @ SV7 ) @ one @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV16: mu,SV18: mu] :
( ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( ! [SY442: mu] :
( ~ ( exists_in_world @ SY442 @ sK2_SY389 )
| ! [SY443: mu] :
( ~ ( exists_in_world @ SY443 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SY443 @ SY442 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY443 @ SY442 @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SY443 @ SY442 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY443 @ SY442 @ SV18 @ SV16 ) ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV8: $i,SV12: $i] :
( ( ( ~ ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) )
= $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 )
| ( ( ! [SY444: mu] :
( ~ ( exists_in_world @ SY444 @ SV13 )
| ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SY444 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY444 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY445: $i] :
( ~ ( rel_s4 @ SV13 @ SY445 )
| ! [SY446: mu] :
( ~ ( exists_in_world @ SY446 @ SY445 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SY444 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY446 @ SY445 )
| ( in @ SV21 @ SY444 @ SY446 @ SY445 ) ) ) ) ) )
= $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_SY333 @ SV7 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV20: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV20 )
= $false )
| ( ( number @ ( sK7_SY333 @ 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_SY389 )
| ! [SY447: mu] :
( ~ ( exists_in_world @ SY447 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY447 @ SV22 @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV8: $i,SV12: $i] :
( ( ( ! [SY428: $i] :
( ~ ( rel_s4 @ SV12 @ SY428 )
| ( userid @ u @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY428 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(115,plain,
! [SV8: $i,SV12: $i] :
( ( ( ! [SY429: $i] :
( ~ ( rel_s4 @ SV12 @ SY429 )
| ( string @ ( sK8_SY364 @ SV12 @ SV8 ) @ SY429 ) ) )
= $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 )
| ( ( ! [SY444: mu] :
( ~ ( exists_in_world @ SY444 @ SV13 )
| ~ ( string @ SV21 @ SV13 )
| ~ ( entry_box @ SY444 @ SV13 )
| ~ ( ~ ( exists_in_world @ ( sK6_SY289 @ SY444 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY445: $i] :
( ~ ( rel_s4 @ SV13 @ SY445 )
| ! [SY446: mu] :
( ~ ( exists_in_world @ SY446 @ SY445 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SY444 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY446 @ SY445 )
| ( in @ SV21 @ SY444 @ SY446 @ SY445 ) ) ) ) ) )
= $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_SY389 ) )
= $true )
| ( ( ! [SY447: mu] :
( ~ ( exists_in_world @ SY447 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY447 @ SV22 @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV8: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV23 )
| ( userid @ u @ ( sK8_SY364 @ 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_SY364 @ 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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) ) )
= $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_SY389 )
= $false )
| ( ( ! [SY447: mu] :
( ~ ( exists_in_world @ SY447 @ sK2_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SY447 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SY447 @ SV22 @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SY447 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SY447 @ SV22 @ SV18 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY364 @ 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_SY364 @ 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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) ) )
= $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_SY389 )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY364 @ 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_SY364 @ 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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) ) )
= $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_SY389 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) ) )
= $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_SY389 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
| ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) ) )
= $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_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) ) )
= $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_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) ) )
= $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_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(138,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( ~ ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SV13 )
| ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) )
= $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_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(141,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ 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] :
( ( ( ~ ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) )
= $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_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(145,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( ~ ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ 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] :
( ( ( ! [SY448: $i] :
( ~ ( rel_s4 @ SV13 @ SY448 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SY448 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY449 @ SY448 )
| ( in @ SV21 @ SV25 @ SY449 @ SY448 ) ) ) )
= $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_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(150,plain,
! [SV18: mu,SV22: mu,SV26: mu,SV16: mu] :
( ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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 )
| ! [SY450: mu] :
( ~ ( exists_in_world @ SY450 @ SV27 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY450 @ SV27 )
| ( in @ SV21 @ SV25 @ SY450 @ 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_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(153,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(154,plain,
! [SV16: mu,SV22: mu,SV26: mu,SV18: mu] :
( ( ( ~ ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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 )
| ( ( ! [SY450: mu] :
( ~ ( exists_in_world @ SY450 @ SV27 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY450 @ SV27 )
| ( in @ SV21 @ SV25 @ SY450 @ 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_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(157,plain,
! [SV16: mu,SV22: mu,SV26: mu,SV18: mu] :
( ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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 )
| ( ( ! [SY450: mu] :
( ~ ( exists_in_world @ SY450 @ SV27 )
| ~ ( do @ SV17 @ ( sK6_SY289 @ SV25 @ SV21 @ SV17 @ SV13 @ SV9 ) @ SY450 @ SV27 )
| ( in @ SV21 @ SV25 @ SY450 @ 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_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(160,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(161,plain,
! [SV16: mu,SV22: mu,SV26: mu,SV18: mu] :
( ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ 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_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(165,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ 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_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(168,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(169,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ 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_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(172,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(173,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( rel_s4 @ sK2_SY389 @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(174,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ 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_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(177,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(178,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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_SY289 @ 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_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( rel_s4 @ sK2_SY389 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(182,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(183,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( exists_in_world @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(184,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(185,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
| ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(186,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( ~ ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(187,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(188,plain,
! [SV16: mu,SV18: mu,SV22: mu,SV26: mu] :
( ( ( do @ SV26 @ SV22 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(189,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( ~ ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) ) )
= $true )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(190,plain,
! [SV22: mu,SV26: mu,SV18: mu,SV16: mu] :
( ( ( in @ SV16 @ SV18 @ ( sK4_SY404 @ SV26 @ SV22 @ SV18 @ SV16 ) @ ( sK3_SY402 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( userid @ u @ SV16 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( entry_box @ SV18 @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( number @ SV18 @ one @ ( sK5_SY401 @ SV26 @ SV22 @ SV18 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV22 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV18 @ sK2_SY389 )
= $false )
| ( ( exists_in_world @ SV16 @ sK2_SY389 )
= $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
% 0.00/0.01 % Problem : KRS272^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 11:43:46 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.45/7.71
% 45.45/7.71 No.of.Axioms: 9
% 45.45/7.71
% 45.45/7.71 Length.of.Defs: 5508
% 45.45/7.71
% 45.45/7.71 Contains.Choice.Funs: false
% 45.45/7.71 .................
% 45.45/7.71
% 45.45/7.71 ********************************
% 45.45/7.71 * All subproblems solved! *
% 45.45/7.71 ********************************
% 45.45/7.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:191,loop_count:0,foatp_calls:1,translation:fof_full)
% 45.45/7.71
% 45.45/7.71 %**** Beginning of derivation protocol ****
% 45.45/7.71 % SZS output start CNFRefutation
% See solution above
% 45.45/7.71
% 45.45/7.71 %**** End of derivation protocol ****
% 45.45/7.71 %**** no. of clauses in derivation: 192 ****
% 45.45/7.71 %**** clause counter: 191 ****
% 45.45/7.71
% 45.45/7.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:191,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------