%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PLA033^7 : 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 : n019.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 10:36:22 AM UTC 2026
% Result : Theorem 0.44s 0.32s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 45
% Syntax : Number of formulae : 225 ( 111 unt; 0 typ; 32 def)
% Number of atoms : 2255 ( 554 equ; 0 cnn)
% Maximal formula atoms : 25 ( 10 avg)
% Number of connectives : 4472 (1045 ~; 841 |; 13 &;2539 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 7 con; 0-4 aty)
% Number of variables : 804 ( 58 ^; 737 !; 9 ?; 804 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_closed,type,
closed: mu > $i > $o ).
thf(tp_combo,type,
combo: mu > mu > $i > $o ).
thf(tp_d,type,
d: mu ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_h,type,
h: 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_n,type,
n: mu ).
thf(tp_o,type,
o: mu ).
thf(tp_open,type,
open: mu > $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_SY72,type,
sK1_SY72: $i ).
thf(tp_sK2_SY323,type,
sK2_SY323: $i ).
thf(tp_sK3_SY334,type,
sK3_SY334: $i > mu ).
thf(tp_sK4_SY342,type,
sK4_SY342: $i > mu ).
thf(tp_sK5_SY371,type,
sK5_SY371: $i > mu > mu > $i > mu ).
thf(tp_sK6_SX2,type,
sK6_SX2: mu > mu > $i ).
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
@ ( mexists_ind
@ ^ [V: mu] : ( mbox_s4 @ ( combo @ d @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(2,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S: mu] : ( mnot @ ( mand @ ( open @ S ) @ ( closed @ S ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(3,axiom,
mvalid @ ( mbox_s4 @ ( mor @ ( combo @ d @ n ) @ ( mnot @ ( combo @ d @ n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(4,axiom,
mvalid @ ( mbox_s4 @ ( closed @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(5,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S: mu] :
( mforall_ind
@ ^ [V: mu] :
( mexists_ind
@ ^ [O: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( combo @ S @ V ) @ ( h @ O ) ) ) @ ( mbox_s4 @ ( open @ S ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( mnot @ ( combo @ S @ V ) ) @ ( h @ o ) ) ) @ ( mbox_s4 @ ( closed @ S ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(6,axiom,
! [V: $i] : ( exists_in_world @ d @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_d_ax) ).
thf(7,axiom,
! [V: $i] : ( exists_in_world @ n @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_n_ax) ).
thf(8,axiom,
! [V: $i] : ( exists_in_world @ o @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_o_ax) ).
thf(9,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(10,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(11,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(12,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(13,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [V: mu] :
( mexists_ind
@ ^ [O: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(14,negated_conjecture,
( ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [V: mu] :
( mexists_ind
@ ^ [O: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,plain,
( ( ! [SY72: $i,SY73: $i] :
( ~ ( rel_s4 @ SY72 @ SY73 )
| ~ ! [SY68: mu] :
( ( exists_in_world @ SY68 @ SY73 )
=> ~ ~ ! [SY69: mu] :
( ( exists_in_world @ SY69 @ SY73 )
=> ~ ( ~ ! [SY70: $i] :
( ~ ( rel_s4 @ SY73 @ SY70 )
| ~ ( ~ ( combo @ d @ SY68 @ SY70 )
| ~ ( h @ SY69 @ SY70 ) ) )
| ! [SY71: $i] :
( ~ ( rel_s4 @ SY73 @ SY71 )
| ( open @ d @ SY71 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[14,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,
( ( ! [SY100: $i] :
~ ! [SY101: mu] :
( ( exists_in_world @ SY101 @ SY100 )
=> ~ ! [SY102: $i] :
( ~ ( rel_s4 @ SY100 @ SY102 )
| ( combo @ d @ SY101 @ SY102 ) ) ) )
= $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(17,plain,
( ( ! [SY122: $i,SY123: $i] :
( ~ ( rel_s4 @ SY122 @ SY123 )
| ! [SY121: mu] :
( ( exists_in_world @ SY121 @ SY123 )
=> ~ ~ ( ~ ( open @ SY121 @ SY123 )
| ~ ( closed @ SY121 @ SY123 ) ) ) ) )
= $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(18,plain,
( ( ! [SY134: $i,SY135: $i] :
( ~ ( rel_s4 @ SY134 @ SY135 )
| ( combo @ d @ n @ SY135 )
| ~ ( combo @ d @ n @ SY135 ) ) )
= $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(19,plain,
( ( ! [SY140: $i,SY141: $i] :
( ~ ( rel_s4 @ SY140 @ SY141 )
| ( closed @ d @ SY141 ) ) )
= $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(20,plain,
( ( ! [SY289: $i,SY290: $i] :
( ~ ( rel_s4 @ SY289 @ SY290 )
| ! [SY282: mu] :
( ( exists_in_world @ SY282 @ SY290 )
=> ! [SY283: mu] :
( ( exists_in_world @ SY283 @ SY290 )
=> ~ ! [SY284: mu] :
( ( exists_in_world @ SY284 @ SY290 )
=> ~ ~ ( ~ ! [SY285: $i] :
( ~ ( rel_s4 @ SY290 @ SY285 )
| ~ ~ ( ~ ( closed @ SY282 @ SY285 )
| ~ ~ ( ~ ( combo @ SY282 @ SY283 @ SY285 )
| ~ ( h @ SY284 @ SY285 ) ) )
| ! [SY271: $i] :
( ~ ( rel_s4 @ SY285 @ SY271 )
| ( open @ SY282 @ SY271 ) ) )
| ~ ! [SY287: $i] :
( ~ ( rel_s4 @ SY290 @ SY287 )
| ~ ~ ( ~ ( closed @ SY282 @ SY287 )
| ~ ~ ( ~ ~ ( combo @ SY282 @ SY283 @ SY287 )
| ~ ( h @ o @ SY287 ) ) )
| ! [SY273: $i] :
( ~ ( rel_s4 @ SY287 @ SY273 )
| ( closed @ SY282 @ SY273 ) ) ) ) ) ) ) ) )
= $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(21,plain,
( ( ! [V: $i] : ( exists_in_world @ d @ V ) )
= $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(22,plain,
( ( ! [V: $i] : ( exists_in_world @ n @ V ) )
= $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(23,plain,
( ( ! [V: $i] : ( exists_in_world @ o @ V ) )
= $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(24,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)],[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(25,plain,
( ( ! [SY313: $i,SY314: $i,SY315: $i] :
( ( ( rel_s4 @ SY313 @ SY314 )
& ( rel_s4 @ SY314 @ SY315 ) )
=> ( rel_s4 @ SY313 @ SY315 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(26,plain,
( ( ! [SY319: $i] : ( rel_s4 @ SY319 @ SY319 ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(27,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(28,plain,
( ( ! [SY323: $i] :
( ~ ( rel_s4 @ sK1_SY72 @ SY323 )
| ~ ! [SY68: mu] :
( ( exists_in_world @ SY68 @ SY323 )
=> ~ ~ ! [SY69: mu] :
( ( exists_in_world @ SY69 @ SY323 )
=> ~ ( ~ ! [SY70: $i] :
( ~ ( rel_s4 @ SY323 @ SY70 )
| ~ ( ~ ( combo @ d @ SY68 @ SY70 )
| ~ ( h @ SY69 @ SY70 ) ) )
| ! [SY71: $i] :
( ~ ( rel_s4 @ SY323 @ SY71 )
| ( open @ d @ SY71 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(29,plain,
( ( ~ ( rel_s4 @ sK1_SY72 @ sK2_SY323 )
| ~ ! [SY328: mu] :
( ( exists_in_world @ SY328 @ sK2_SY323 )
=> ~ ~ ! [SY329: mu] :
( ( exists_in_world @ SY329 @ sK2_SY323 )
=> ~ ( ~ ! [SY330: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY330 )
| ~ ( ~ ( combo @ d @ SY328 @ SY330 )
| ~ ( h @ SY329 @ SY330 ) ) )
| ! [SY331: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY331 )
| ( open @ d @ SY331 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY72 @ sK2_SY323 )
| ~ ! [SY328: mu] :
( ( exists_in_world @ SY328 @ sK2_SY323 )
=> ~ ~ ! [SY329: mu] :
( ( exists_in_world @ SY329 @ sK2_SY323 )
=> ~ ( ~ ! [SY330: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY330 )
| ~ ( ~ ( combo @ d @ SY328 @ SY330 )
| ~ ( h @ SY329 @ SY330 ) ) )
| ! [SY331: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY331 )
| ( open @ d @ SY331 ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(31,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(32,plain,
( ( ! [SY319: $i] : ( rel_s4 @ SY319 @ SY319 ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(33,plain,
( ( ! [SY313: $i,SY314: $i,SY315: $i] :
( ( ( rel_s4 @ SY313 @ SY314 )
& ( rel_s4 @ SY314 @ SY315 ) )
=> ( rel_s4 @ SY313 @ SY315 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(34,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)],[24]) ).
thf(35,plain,
( ( ! [V: $i] : ( exists_in_world @ o @ V ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(36,plain,
( ( ! [V: $i] : ( exists_in_world @ n @ V ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
( ( ! [V: $i] : ( exists_in_world @ d @ V ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(38,plain,
( ( ! [SY289: $i,SY290: $i] :
( ~ ( rel_s4 @ SY289 @ SY290 )
| ! [SY282: mu] :
( ( exists_in_world @ SY282 @ SY290 )
=> ! [SY283: mu] :
( ( exists_in_world @ SY283 @ SY290 )
=> ~ ! [SY284: mu] :
( ( exists_in_world @ SY284 @ SY290 )
=> ~ ~ ( ~ ! [SY285: $i] :
( ~ ( rel_s4 @ SY290 @ SY285 )
| ~ ~ ( ~ ( closed @ SY282 @ SY285 )
| ~ ~ ( ~ ( combo @ SY282 @ SY283 @ SY285 )
| ~ ( h @ SY284 @ SY285 ) ) )
| ! [SY271: $i] :
( ~ ( rel_s4 @ SY285 @ SY271 )
| ( open @ SY282 @ SY271 ) ) )
| ~ ! [SY287: $i] :
( ~ ( rel_s4 @ SY290 @ SY287 )
| ~ ~ ( ~ ( closed @ SY282 @ SY287 )
| ~ ~ ( ~ ~ ( combo @ SY282 @ SY283 @ SY287 )
| ~ ( h @ o @ SY287 ) ) )
| ! [SY273: $i] :
( ~ ( rel_s4 @ SY287 @ SY273 )
| ( closed @ SY282 @ SY273 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(39,plain,
( ( ! [SY140: $i,SY141: $i] :
( ~ ( rel_s4 @ SY140 @ SY141 )
| ( closed @ d @ SY141 ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(40,plain,
( ( ! [SY134: $i,SY135: $i] :
( ~ ( rel_s4 @ SY134 @ SY135 )
| ( combo @ d @ n @ SY135 )
| ~ ( combo @ d @ n @ SY135 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(41,plain,
( ( ! [SY122: $i,SY123: $i] :
( ~ ( rel_s4 @ SY122 @ SY123 )
| ! [SY121: mu] :
( ( exists_in_world @ SY121 @ SY123 )
=> ~ ~ ( ~ ( open @ SY121 @ SY123 )
| ~ ( closed @ SY121 @ SY123 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [SY100: $i] :
~ ! [SY101: mu] :
( ( exists_in_world @ SY101 @ SY100 )
=> ~ ! [SY102: $i] :
( ~ ( rel_s4 @ SY100 @ SY102 )
| ( combo @ d @ SY101 @ SY102 ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(43,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY72 @ sK2_SY323 )
| ~ ! [SY328: mu] :
( ( exists_in_world @ SY328 @ sK2_SY323 )
=> ~ ~ ! [SY329: mu] :
( ( exists_in_world @ SY329 @ sK2_SY323 )
=> ~ ( ~ ! [SY330: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY330 )
| ~ ( ~ ( combo @ d @ SY328 @ SY330 )
| ~ ( h @ SY329 @ SY330 ) ) )
| ! [SY331: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY331 )
| ( open @ d @ SY331 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY72 @ sK2_SY323 )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY323 )
| ~ ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY323 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ~ ( ~ ( combo @ d @ SX0 @ SX2 )
| ~ ( h @ SX1 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43,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: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( combo @ d @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42,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,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ~ ~ ( ~ ( open @ SX2 @ SX1 )
| ~ ( closed @ SX2 @ SX1 ) ) ) ) )
= $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(47,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( rel_s4 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(48,plain,
( ( ! [SX0: mu,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( exists_in_world @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( exists_in_world @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(49,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
~ ( exists_in_world @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[31,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(50,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 )
| ~ ~ ( ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX1 @ SX5 )
| ~ ~ ( ~ ( closed @ SX2 @ SX5 )
| ~ ~ ( ~ ( combo @ SX2 @ SX3 @ SX5 )
| ~ ( h @ SX4 @ SX5 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( open @ SX2 @ SX6 ) ) )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX1 @ SX5 )
| ~ ~ ( ~ ( closed @ SX2 @ SX5 )
| ~ ~ ( ~ ~ ( combo @ SX2 @ SX3 @ SX5 )
| ~ ( h @ o @ SX5 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( closed @ SX2 @ SX6 ) ) ) ) ) ) ) ) )
= $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(51,plain,
! [SV1: $i] :
( ( rel_s4 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(52,plain,
! [SV2: $i] :
( ( exists_in_world @ o @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(53,plain,
! [SV3: $i] :
( ( exists_in_world @ n @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(54,plain,
! [SV4: $i] :
( ( exists_in_world @ d @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(55,plain,
! [SV5: $i] :
( ( ! [SY332: $i] :
( ~ ( rel_s4 @ SV5 @ SY332 )
| ( closed @ d @ SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(56,plain,
! [SV6: $i] :
( ( ! [SY333: $i] :
( ~ ( rel_s4 @ SV6 @ SY333 )
| ( combo @ d @ n @ SY333 )
| ~ ( combo @ d @ n @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(57,plain,
( ( ~ ( rel_s4 @ sK1_SY72 @ sK2_SY323 )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY323 )
| ~ ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY323 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ~ ( ~ ( combo @ d @ SX0 @ SX2 )
| ~ ( h @ SX1 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV7: $i] :
( ( ~ ! [SY334: mu] :
( ~ ( exists_in_world @ SY334 @ SV7 )
| ~ ! [SY335: $i] :
( ~ ( rel_s4 @ SV7 @ SY335 )
| ( combo @ d @ SY334 @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
! [SV8: $i] :
( ( ! [SY336: $i] :
( ~ ( rel_s4 @ SV8 @ SY336 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SY336 )
| ~ ~ ( ~ ( open @ SX2 @ SY336 )
| ~ ( closed @ SX2 @ SY336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV9: $i] :
( ( ! [SY338: $i,SY339: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV9 @ SY338 )
| ~ ( rel_s4 @ SY338 @ SY339 ) )
| ( rel_s4 @ SV9 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
! [SV10: mu] :
( ( ! [SY340: $i,SY341: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV10 @ SY340 )
| ~ ( rel_s4 @ SY340 @ SY341 ) )
| ( exists_in_world @ SV10 @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(62,plain,
! [SV11: $i] :
( ( ~ ! [SY342: mu] :
~ ( exists_in_world @ SY342 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(63,plain,
! [SV12: $i] :
( ( ! [SY343: $i] :
( ~ ( rel_s4 @ SV12 @ SY343 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SY343 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY343 )
| ~ ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY343 )
| ~ ~ ( ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY343 @ SX5 )
| ~ ~ ( ~ ( closed @ SX2 @ SX5 )
| ~ ~ ( ~ ( combo @ SX2 @ SX3 @ SX5 )
| ~ ( h @ SX4 @ SX5 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( open @ SX2 @ SX6 ) ) )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY343 @ SX5 )
| ~ ~ ( ~ ( closed @ SX2 @ SX5 )
| ~ ~ ( ~ ~ ( combo @ SX2 @ SX3 @ SX5 )
| ~ ( h @ o @ SX5 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( closed @ SX2 @ SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(64,plain,
! [SV13: $i,SV5: $i] :
( ( ~ ( rel_s4 @ SV5 @ SV13 )
| ( closed @ d @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV14: $i,SV6: $i] :
( ( ~ ( rel_s4 @ SV6 @ SV14 )
| ( combo @ d @ n @ SV14 )
| ~ ( combo @ d @ n @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(66,plain,
( ( ~ ( rel_s4 @ sK1_SY72 @ sK2_SY323 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(67,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY323 )
| ~ ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY323 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ~ ( ~ ( combo @ d @ SX0 @ SX2 )
| ~ ( h @ SX1 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(68,plain,
! [SV7: $i] :
( ( ! [SY334: mu] :
( ~ ( exists_in_world @ SY334 @ SV7 )
| ~ ! [SY335: $i] :
( ~ ( rel_s4 @ SV7 @ SY335 )
| ( combo @ d @ SY334 @ SY335 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV15: $i,SV8: $i] :
( ( ~ ( rel_s4 @ SV8 @ SV15 )
| ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV15 )
| ~ ~ ( ~ ( open @ SY351 @ SV15 )
| ~ ( closed @ SY351 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY352: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV9 @ SV16 )
| ~ ( rel_s4 @ SV16 @ SY352 ) )
| ( rel_s4 @ SV9 @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV17: $i,SV10: mu] :
( ( ! [SY353: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV10 @ SV17 )
| ~ ( rel_s4 @ SV17 @ SY353 ) )
| ( exists_in_world @ SV10 @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV11: $i] :
( ( ! [SY342: mu] :
~ ( exists_in_world @ SY342 @ SV11 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV18: $i,SV12: $i] :
( ( ~ ( rel_s4 @ SV12 @ SV18 )
| ! [SY354: mu] :
( ~ ( exists_in_world @ SY354 @ SV18 )
| ! [SY355: mu] :
( ~ ( exists_in_world @ SY355 @ SV18 )
| ~ ! [SY356: mu] :
( ~ ( exists_in_world @ SY356 @ SV18 )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( rel_s4 @ SV18 @ SY357 )
| ~ ~ ( ~ ( closed @ SY354 @ SY357 )
| ~ ~ ( ~ ( combo @ SY354 @ SY355 @ SY357 )
| ~ ( h @ SY356 @ SY357 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY357 @ SX6 )
| ( open @ SY354 @ SX6 ) ) )
| ~ ! [SY359: $i] :
( ~ ( rel_s4 @ SV18 @ SY359 )
| ~ ~ ( ~ ( closed @ SY354 @ SY359 )
| ~ ~ ( ~ ~ ( combo @ SY354 @ SY355 @ SY359 )
| ~ ( h @ o @ SY359 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY359 @ SX6 )
| ( closed @ SY354 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV13: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV13 ) )
= $true )
| ( ( closed @ d @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV14: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV14 ) )
= $true )
| ( ( ( combo @ d @ n @ SV14 )
| ~ ( combo @ d @ n @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(76,plain,
( ( rel_s4 @ sK1_SY72 @ sK2_SY323 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(77,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK2_SY323 )
| ~ ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ sK2_SY323 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ~ ( ~ ( combo @ d @ SX0 @ SX2 )
| ~ ( h @ SX1 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(78,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK3_SY334 @ SV7 ) @ SV7 )
| ~ ! [SY361: $i] :
( ~ ( rel_s4 @ SV7 @ SY361 )
| ( combo @ d @ ( sK3_SY334 @ SV7 ) @ SY361 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[68]) ).
thf(79,plain,
! [SV15: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV15 ) )
= $true )
| ( ( ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV15 )
| ~ ~ ( ~ ( open @ SY351 @ SV15 )
| ~ ( closed @ SY351 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV9 @ SV16 )
| ~ ( rel_s4 @ SV16 @ SV19 ) )
| ( rel_s4 @ SV9 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV20: $i,SV17: $i,SV10: mu] :
( ( ~ ~ ( ~ ( exists_in_world @ SV10 @ SV17 )
| ~ ( rel_s4 @ SV17 @ SV20 ) )
| ( exists_in_world @ SV10 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV11: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY342 @ SV11 ) @ SV11 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(83,plain,
! [SV18: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV18 ) )
= $true )
| ( ( ! [SY354: mu] :
( ~ ( exists_in_world @ SY354 @ SV18 )
| ! [SY355: mu] :
( ~ ( exists_in_world @ SY355 @ SV18 )
| ~ ! [SY356: mu] :
( ~ ( exists_in_world @ SY356 @ SV18 )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( rel_s4 @ SV18 @ SY357 )
| ~ ~ ( ~ ( closed @ SY354 @ SY357 )
| ~ ~ ( ~ ( combo @ SY354 @ SY355 @ SY357 )
| ~ ( h @ SY356 @ SY357 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY357 @ SX6 )
| ( open @ SY354 @ SX6 ) ) )
| ~ ! [SY359: $i] :
( ~ ( rel_s4 @ SV18 @ SY359 )
| ~ ~ ( ~ ( closed @ SY354 @ SY359 )
| ~ ~ ( ~ ~ ( combo @ SY354 @ SY355 @ SY359 )
| ~ ( h @ o @ SY359 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY359 @ SX6 )
| ( closed @ SY354 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV13: $i,SV5: $i] :
( ( ( rel_s4 @ SV5 @ SV13 )
= $false )
| ( ( closed @ d @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV14: $i,SV6: $i] :
( ( ( rel_s4 @ SV6 @ SV14 )
= $false )
| ( ( ( combo @ d @ n @ SV14 )
| ~ ( combo @ d @ n @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV21: mu] :
( ( ~ ( exists_in_world @ SV21 @ sK2_SY323 )
| ~ ~ ! [SY362: mu] :
( ~ ( exists_in_world @ SY362 @ sK2_SY323 )
| ~ ( ~ ! [SY363: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY363 )
| ~ ( ~ ( combo @ d @ SV21 @ SY363 )
| ~ ( h @ SY362 @ SY363 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK3_SY334 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(88,plain,
! [SV7: $i] :
( ( ~ ! [SY361: $i] :
( ~ ( rel_s4 @ SV7 @ SY361 )
| ( combo @ d @ ( sK3_SY334 @ SV7 ) @ SY361 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(89,plain,
! [SV15: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV15 )
= $false )
| ( ( ! [SY351: mu] :
( ~ ( exists_in_world @ SY351 @ SV15 )
| ~ ~ ( ~ ( open @ SY351 @ SV15 )
| ~ ( closed @ SY351 @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV9 @ SV16 )
| ~ ( rel_s4 @ SV16 @ SV19 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV20: $i,SV17: $i,SV10: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ SV10 @ SV17 )
| ~ ( rel_s4 @ SV17 @ SV20 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV11: $i] :
( ( exists_in_world @ ( sK4_SY342 @ SV11 ) @ SV11 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(93,plain,
! [SV18: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV18 )
= $false )
| ( ( ! [SY354: mu] :
( ~ ( exists_in_world @ SY354 @ SV18 )
| ! [SY355: mu] :
( ~ ( exists_in_world @ SY355 @ SV18 )
| ~ ! [SY356: mu] :
( ~ ( exists_in_world @ SY356 @ SV18 )
| ~ ~ ( ~ ! [SY357: $i] :
( ~ ( rel_s4 @ SV18 @ SY357 )
| ~ ~ ( ~ ( closed @ SY354 @ SY357 )
| ~ ~ ( ~ ( combo @ SY354 @ SY355 @ SY357 )
| ~ ( h @ SY356 @ SY357 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY357 @ SX6 )
| ( open @ SY354 @ SX6 ) ) )
| ~ ! [SY359: $i] :
( ~ ( rel_s4 @ SV18 @ SY359 )
| ~ ~ ( ~ ( closed @ SY354 @ SY359 )
| ~ ~ ( ~ ~ ( combo @ SY354 @ SY355 @ SY359 )
| ~ ( h @ o @ SY359 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY359 @ SX6 )
| ( closed @ SY354 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(94,plain,
! [SV6: $i,SV14: $i] :
( ( ( combo @ d @ n @ SV14 )
= $true )
| ( ( ~ ( combo @ d @ n @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ sK2_SY323 ) )
= $true )
| ( ( ~ ~ ! [SY362: mu] :
( ~ ( exists_in_world @ SY362 @ sK2_SY323 )
| ~ ( ~ ! [SY363: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY363 )
| ~ ( ~ ( combo @ d @ SV21 @ SY363 )
| ~ ( h @ SY362 @ SY363 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV7: $i] :
( ( exists_in_world @ ( sK3_SY334 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV7: $i] :
( ( ! [SY361: $i] :
( ~ ( rel_s4 @ SV7 @ SY361 )
| ( combo @ d @ ( sK3_SY334 @ SV7 ) @ SY361 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(98,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV15 )
| ~ ~ ( ~ ( open @ SV22 @ SV15 )
| ~ ( closed @ SV22 @ SV15 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV9 @ SV16 )
| ~ ( rel_s4 @ SV16 @ SV19 ) ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV20: $i,SV17: $i,SV10: mu] :
( ( ( ~ ( ~ ( exists_in_world @ SV10 @ SV17 )
| ~ ( rel_s4 @ SV17 @ SV20 ) ) )
= $false )
| ( ( exists_in_world @ SV10 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(101,plain,
! [SV12: $i,SV18: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV18 )
| ! [SY365: mu] :
( ~ ( exists_in_world @ SY365 @ SV18 )
| ~ ! [SY366: mu] :
( ~ ( exists_in_world @ SY366 @ SV18 )
| ~ ~ ( ~ ! [SY367: $i] :
( ~ ( rel_s4 @ SV18 @ SY367 )
| ~ ~ ( ~ ( closed @ SV23 @ SY367 )
| ~ ~ ( ~ ( combo @ SV23 @ SY365 @ SY367 )
| ~ ( h @ SY366 @ SY367 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY367 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY369: $i] :
( ~ ( rel_s4 @ SV18 @ SY369 )
| ~ ~ ( ~ ( closed @ SV23 @ SY369 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SY365 @ SY369 )
| ~ ( h @ o @ SY369 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY369 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV6: $i,SV14: $i] :
( ( ( combo @ d @ n @ SV14 )
= $false )
| ( ( combo @ d @ n @ SV14 )
= $true )
| ( ( rel_s4 @ SV6 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV21: mu] :
( ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false )
| ( ( ~ ~ ! [SY362: mu] :
( ~ ( exists_in_world @ SY362 @ sK2_SY323 )
| ~ ( ~ ! [SY363: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY363 )
| ~ ( ~ ( combo @ d @ SV21 @ SY363 )
| ~ ( h @ SY362 @ SY363 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV24: $i,SV7: $i] :
( ( ~ ( rel_s4 @ SV7 @ SV24 )
| ( combo @ d @ ( sK3_SY334 @ SV7 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV15 ) )
= $true )
| ( ( ~ ~ ( ~ ( open @ SV22 @ SV15 )
| ~ ( closed @ SV22 @ SV15 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV16 )
| ~ ( rel_s4 @ SV16 @ SV19 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(107,plain,
! [SV20: $i,SV17: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV17 )
| ~ ( rel_s4 @ SV17 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV12: $i,SV18: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV18 ) )
= $true )
| ( ( ! [SY365: mu] :
( ~ ( exists_in_world @ SY365 @ SV18 )
| ~ ! [SY366: mu] :
( ~ ( exists_in_world @ SY366 @ SV18 )
| ~ ~ ( ~ ! [SY367: $i] :
( ~ ( rel_s4 @ SV18 @ SY367 )
| ~ ~ ( ~ ( closed @ SV23 @ SY367 )
| ~ ~ ( ~ ( combo @ SV23 @ SY365 @ SY367 )
| ~ ( h @ SY366 @ SY367 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY367 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY369: $i] :
( ~ ( rel_s4 @ SV18 @ SY369 )
| ~ ~ ( ~ ( closed @ SV23 @ SY369 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SY365 @ SY369 )
| ~ ( h @ o @ SY369 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY369 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV21: mu] :
( ( ( ~ ! [SY362: mu] :
( ~ ( exists_in_world @ SY362 @ sK2_SY323 )
| ~ ( ~ ! [SY363: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY363 )
| ~ ( ~ ( combo @ d @ SV21 @ SY363 )
| ~ ( h @ SY362 @ SY363 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV24: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV24 ) )
= $true )
| ( ( combo @ d @ ( sK3_SY334 @ SV7 ) @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( exists_in_world @ SV22 @ SV15 )
= $false )
| ( ( ~ ~ ( ~ ( open @ SV22 @ SV15 )
| ~ ( closed @ SV22 @ SV15 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV16 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV16 @ SV19 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV20: $i,SV17: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV17 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV17 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV12: $i,SV18: $i,SV23: mu] :
( ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( ! [SY365: mu] :
( ~ ( exists_in_world @ SY365 @ SV18 )
| ~ ! [SY366: mu] :
( ~ ( exists_in_world @ SY366 @ SV18 )
| ~ ~ ( ~ ! [SY367: $i] :
( ~ ( rel_s4 @ SV18 @ SY367 )
| ~ ~ ( ~ ( closed @ SV23 @ SY367 )
| ~ ~ ( ~ ( combo @ SV23 @ SY365 @ SY367 )
| ~ ( h @ SY366 @ SY367 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY367 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY369: $i] :
( ~ ( rel_s4 @ SV18 @ SY369 )
| ~ ~ ( ~ ( closed @ SV23 @ SY369 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SY365 @ SY369 )
| ~ ( h @ o @ SY369 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY369 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(115,plain,
! [SV21: mu] :
( ( ( ! [SY362: mu] :
( ~ ( exists_in_world @ SY362 @ sK2_SY323 )
| ~ ( ~ ! [SY363: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY363 )
| ~ ( ~ ( combo @ d @ SV21 @ SY363 )
| ~ ( h @ SY362 @ SY363 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(116,plain,
! [SV24: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV24 )
= $false )
| ( ( combo @ d @ ( sK3_SY334 @ SV7 ) @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( ~ ( ~ ( open @ SV22 @ SV15 )
| ~ ( closed @ SV22 @ SV15 ) ) )
= $false )
| ( ( exists_in_world @ SV22 @ SV15 )
= $false )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(118,plain,
! [SV19: $i,SV16: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV16 )
= $false )
| ( ( ~ ( rel_s4 @ SV16 @ SV19 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(119,plain,
! [SV20: $i,SV17: $i,SV10: mu] :
( ( ( exists_in_world @ SV10 @ SV17 )
= $false )
| ( ( ~ ( rel_s4 @ SV17 @ SV20 ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV12: $i,SV23: mu,SV18: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV18 )
| ~ ! [SY371: mu] :
( ~ ( exists_in_world @ SY371 @ SV18 )
| ~ ~ ( ~ ! [SY372: $i] :
( ~ ( rel_s4 @ SV18 @ SY372 )
| ~ ~ ( ~ ( closed @ SV23 @ SY372 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY372 )
| ~ ( h @ SY371 @ SY372 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY372 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV21: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ sK2_SY323 )
| ~ ( ~ ! [SY376: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY376 )
| ~ ( ~ ( combo @ d @ SV21 @ SY376 )
| ~ ( h @ SV26 @ SY376 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(122,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( ~ ( open @ SV22 @ SV15 )
| ~ ( closed @ SV22 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV15 )
= $false )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV9: $i,SV19: $i,SV16: $i] :
( ( ( rel_s4 @ SV16 @ SV19 )
= $false )
| ( ( rel_s4 @ SV9 @ SV16 )
= $false )
| ( ( rel_s4 @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV10: mu,SV20: $i,SV17: $i] :
( ( ( rel_s4 @ SV17 @ SV20 )
= $false )
| ( ( exists_in_world @ SV10 @ SV17 )
= $false )
| ( ( exists_in_world @ SV10 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV12: $i,SV23: mu,SV18: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV18 ) )
= $true )
| ( ( ~ ! [SY371: mu] :
( ~ ( exists_in_world @ SY371 @ SV18 )
| ~ ~ ( ~ ! [SY372: $i] :
( ~ ( rel_s4 @ SV18 @ SY372 )
| ~ ~ ( ~ ( closed @ SV23 @ SY372 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY372 )
| ~ ( h @ SY371 @ SY372 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY372 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV21: mu,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ sK2_SY323 ) )
= $true )
| ( ( ~ ( ~ ! [SY376: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY376 )
| ~ ( ~ ( combo @ d @ SV21 @ SY376 )
| ~ ( h @ SV26 @ SY376 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(127,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( ~ ( open @ SV22 @ SV15 ) )
= $true )
| ( ( ~ ( closed @ SV22 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV15 )
= $false )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(128,plain,
! [SV12: $i,SV23: mu,SV18: $i,SV25: mu] :
( ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( ~ ! [SY371: mu] :
( ~ ( exists_in_world @ SY371 @ SV18 )
| ~ ~ ( ~ ! [SY372: $i] :
( ~ ( rel_s4 @ SV18 @ SY372 )
| ~ ~ ( ~ ( closed @ SV23 @ SY372 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY372 )
| ~ ( h @ SY371 @ SY372 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY372 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV21: mu,SV26: mu] :
( ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( ~ ( ~ ! [SY376: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY376 )
| ~ ( ~ ( combo @ d @ SV21 @ SY376 )
| ~ ( h @ SV26 @ SY376 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( open @ SV22 @ SV15 )
= $false )
| ( ( ~ ( closed @ SV22 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV15 )
= $false )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ! [SY371: mu] :
( ~ ( exists_in_world @ SY371 @ SV18 )
| ~ ~ ( ~ ! [SY372: $i] :
( ~ ( rel_s4 @ SV18 @ SY372 )
| ~ ~ ( ~ ( closed @ SV23 @ SY372 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY372 )
| ~ ( h @ SY371 @ SY372 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY372 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV26: mu,SV21: mu] :
( ( ( ~ ! [SY376: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY376 )
| ~ ( ~ ( combo @ d @ SV21 @ SY376 )
| ~ ( h @ SV26 @ SY376 ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(133,plain,
! [SV8: $i,SV15: $i,SV22: mu] :
( ( ( closed @ SV22 @ SV15 )
= $false )
| ( ( open @ SV22 @ SV15 )
= $false )
| ( ( exists_in_world @ SV22 @ SV15 )
= $false )
| ( ( rel_s4 @ SV8 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(134,plain,
! [SV18: $i,SV23: mu,SV25: mu,SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV18 )
| ~ ~ ( ~ ! [SY378: $i] :
( ~ ( rel_s4 @ SV18 @ SY378 )
| ~ ~ ( ~ ( closed @ SV23 @ SY378 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY378 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SY378 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY378 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[131]) ).
thf(135,plain,
! [SV26: mu,SV21: mu] :
( ( ( ~ ! [SY376: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY376 )
| ~ ( ~ ( combo @ d @ SV21 @ SY376 )
| ~ ( h @ SV26 @ SY376 ) ) ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(136,plain,
! [SV21: mu,SV26: mu] :
( ( ( ! [SX2: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SX2 )
| ( open @ d @ SX2 ) ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(137,plain,
! [SV18: $i,SV23: mu,SV25: mu,SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV18 ) )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(138,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ~ ~ ( ~ ! [SY378: $i] :
( ~ ( rel_s4 @ SV18 @ SY378 )
| ~ ~ ( ~ ( closed @ SV23 @ SY378 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY378 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SY378 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY378 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(139,plain,
! [SV26: mu,SV21: mu] :
( ( ( ! [SY376: $i] :
( ~ ( rel_s4 @ sK2_SY323 @ SY376 )
| ~ ( ~ ( combo @ d @ SV21 @ SY376 )
| ~ ( h @ SV26 @ SY376 ) ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(140,plain,
! [SV26: mu,SV21: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY323 @ ( sK6_SX2 @ SV21 @ SV26 ) )
| ( open @ d @ ( sK6_SX2 @ SV21 @ SV26 ) ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[136]) ).
thf(141,plain,
! [SV18: $i,SV23: mu,SV25: mu,SV12: $i] :
( ( ( exists_in_world @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV18 )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(142,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ~ ( ~ ! [SY378: $i] :
( ~ ( rel_s4 @ SV18 @ SY378 )
| ~ ~ ( ~ ( closed @ SV23 @ SY378 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY378 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SY378 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY378 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(143,plain,
! [SV26: mu,SV21: mu,SV27: $i] :
( ( ( ~ ( rel_s4 @ sK2_SY323 @ SV27 )
| ~ ( ~ ( combo @ d @ SV21 @ SV27 )
| ~ ( h @ SV26 @ SV27 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV26: mu,SV21: mu] :
( ( ( ~ ( rel_s4 @ sK2_SY323 @ ( sK6_SX2 @ SV21 @ SV26 ) ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(145,plain,
! [SV26: mu,SV21: mu] :
( ( ( open @ d @ ( sK6_SX2 @ SV21 @ SV26 ) )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(146,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ~ ! [SY378: $i] :
( ~ ( rel_s4 @ SV18 @ SY378 )
| ~ ~ ( ~ ( closed @ SV23 @ SY378 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY378 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SY378 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY378 @ SY368 )
| ( open @ SV23 @ SY368 ) ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV26: mu,SV21: mu,SV27: $i] :
( ( ( ~ ( rel_s4 @ sK2_SY323 @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( combo @ d @ SV21 @ SV27 )
| ~ ( h @ SV26 @ SV27 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(148,plain,
! [SV26: mu,SV21: mu] :
( ( ( rel_s4 @ sK2_SY323 @ ( sK6_SX2 @ SV21 @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ~ ! [SY378: $i] :
( ~ ( rel_s4 @ SV18 @ SY378 )
| ~ ~ ( ~ ( closed @ SV23 @ SY378 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY378 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SY378 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY378 @ SY368 )
| ( open @ SV23 @ SY368 ) ) ) )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(150,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(151,plain,
! [SV26: mu,SV21: mu,SV27: $i] :
( ( ( rel_s4 @ sK2_SY323 @ SV27 )
= $false )
| ( ( ~ ( ~ ( combo @ d @ SV21 @ SV27 )
| ~ ( h @ SV26 @ SV27 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(152,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ! [SY378: $i] :
( ~ ( rel_s4 @ SV18 @ SY378 )
| ~ ~ ( ~ ( closed @ SV23 @ SY378 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SY378 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SY378 ) ) )
| ! [SY368: $i] :
( ~ ( rel_s4 @ SY378 @ SY368 )
| ( open @ SV23 @ SY368 ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(153,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV18: $i] :
( ( ( ! [SY374: $i] :
( ~ ( rel_s4 @ SV18 @ SY374 )
| ~ ~ ( ~ ( closed @ SV23 @ SY374 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SY374 )
| ~ ( h @ o @ SY374 ) ) )
| ! [SY370: $i] :
( ~ ( rel_s4 @ SY374 @ SY370 )
| ( closed @ SV23 @ SY370 ) ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(154,plain,
! [SV26: mu,SV27: $i,SV21: mu] :
( ( ( ~ ( combo @ d @ SV21 @ SV27 )
| ~ ( h @ SV26 @ SV27 ) )
= $false )
| ( ( rel_s4 @ sK2_SY323 @ SV27 )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(155,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV28: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV28 )
| ~ ~ ( ~ ( closed @ SV23 @ SV28 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) )
| ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(156,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV29: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV29 )
| ~ ~ ( ~ ( closed @ SV23 @ SV29 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) )
| ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(157,plain,
! [SV26: mu,SV27: $i,SV21: mu] :
( ( ( ~ ( combo @ d @ SV21 @ SV27 ) )
= $false )
| ( ( rel_s4 @ sK2_SY323 @ SV27 )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(158,plain,
! [SV21: mu,SV27: $i,SV26: mu] :
( ( ( ~ ( h @ SV26 @ SV27 ) )
= $false )
| ( ( rel_s4 @ sK2_SY323 @ SV27 )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(159,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV28: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV28 ) )
= $true )
| ( ( ~ ~ ( ~ ( closed @ SV23 @ SV28 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) )
| ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(160,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV29: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV29 ) )
= $true )
| ( ( ~ ~ ( ~ ( closed @ SV23 @ SV29 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) )
| ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(161,plain,
! [SV26: mu,SV27: $i,SV21: mu] :
( ( ( combo @ d @ SV21 @ SV27 )
= $true )
| ( ( rel_s4 @ sK2_SY323 @ SV27 )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(162,plain,
! [SV21: mu,SV27: $i,SV26: mu] :
( ( ( h @ SV26 @ SV27 )
= $true )
| ( ( rel_s4 @ sK2_SY323 @ SV27 )
= $false )
| ( ( exists_in_world @ SV26 @ sK2_SY323 )
= $false )
| ( ( exists_in_world @ SV21 @ sK2_SY323 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(163,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV28: $i,SV18: $i] :
( ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( ~ ~ ( ~ ( closed @ SV23 @ SV28 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) )
| ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(164,plain,
! [SV12: $i,SV25: mu,SV23: mu,SV29: $i,SV18: $i] :
( ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( ~ ~ ( ~ ( closed @ SV23 @ SV29 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) )
| ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV28: $i,SV23: mu] :
( ( ( ~ ~ ( ~ ( closed @ SV23 @ SV28 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(166,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV29: $i,SV23: mu] :
( ( ( ~ ~ ( ~ ( closed @ SV23 @ SV29 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) ) )
= $true )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(167,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV28: $i,SV23: mu] :
( ( ( ~ ( ~ ( closed @ SV23 @ SV28 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) ) )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(168,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV29: $i,SV23: mu] :
( ( ( ~ ( ~ ( closed @ SV23 @ SV29 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) ) )
= $false )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(169,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV28: $i,SV23: mu] :
( ( ( ~ ( closed @ SV23 @ SV28 )
| ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(170,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV29: $i,SV23: mu] :
( ( ( ~ ( closed @ SV23 @ SV29 )
| ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) )
= $true )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(171,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV28: $i,SV23: mu] :
( ( ( ~ ( closed @ SV23 @ SV28 ) )
= $true )
| ( ( ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(172,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV29: $i,SV23: mu] :
( ( ( ~ ( closed @ SV23 @ SV29 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) )
= $true )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(173,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV28: $i,SV23: mu] :
( ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( ~ ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(174,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV29: $i,SV23: mu] :
( ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( ~ ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) )
= $true )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(175,plain,
! [SV18: $i,SV12: $i,SV28: $i,SV25: mu,SV23: mu] :
( ( ( ~ ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) ) )
= $false )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(176,plain,
! [SV12: $i,SV18: $i,SV29: $i,SV25: mu,SV23: mu] :
( ( ( ~ ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) ) )
= $false )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(177,plain,
! [SV18: $i,SV12: $i,SV28: $i,SV25: mu,SV23: mu] :
( ( ( ~ ( combo @ SV23 @ SV25 @ SV28 )
| ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) )
= $true )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(178,plain,
! [SV12: $i,SV18: $i,SV29: $i,SV25: mu,SV23: mu] :
( ( ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 )
| ~ ( h @ o @ SV29 ) )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(179,plain,
! [SV18: $i,SV12: $i,SV28: $i,SV25: mu,SV23: mu] :
( ( ( ~ ( combo @ SV23 @ SV25 @ SV28 ) )
= $true )
| ( ( ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) )
= $true )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(180,plain,
! [SV12: $i,SV18: $i,SV29: $i,SV25: mu,SV23: mu] :
( ( ( ~ ~ ( combo @ SV23 @ SV25 @ SV29 ) )
= $true )
| ( ( ~ ( h @ o @ SV29 ) )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(181,plain,
! [SV18: $i,SV12: $i,SV28: $i,SV25: mu,SV23: mu] :
( ( ( combo @ SV23 @ SV25 @ SV28 )
= $false )
| ( ( ~ ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 ) )
= $true )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(182,plain,
! [SV12: $i,SV18: $i,SV29: $i,SV25: mu,SV23: mu] :
( ( ( ~ ( combo @ SV23 @ SV25 @ SV29 ) )
= $false )
| ( ( ~ ( h @ o @ SV29 ) )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(183,plain,
! [SV28: $i,SV18: $i,SV23: mu,SV25: mu,SV12: $i] :
( ( ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV28 )
= $false )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV28 @ SY382 )
| ( open @ SV23 @ SY382 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(184,plain,
! [SV12: $i,SV18: $i,SV29: $i,SV25: mu,SV23: mu] :
( ( ( combo @ SV23 @ SV25 @ SV29 )
= $true )
| ( ( ~ ( h @ o @ SV29 ) )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(185,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV23: mu,SV30: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV30 )
| ( open @ SV23 @ SV30 ) )
= $true )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV28 )
= $false )
| ( ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 )
= $false )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(186,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV23: mu,SV29: $i] :
( ( ( h @ o @ SV29 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV29 )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( ! [SY383: $i] :
( ~ ( rel_s4 @ SV29 @ SY383 )
| ( closed @ SV23 @ SY383 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(187,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV23: mu,SV30: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV30 ) )
= $true )
| ( ( open @ SV23 @ SV30 )
= $true )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV28 )
= $false )
| ( ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 )
= $false )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(188,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV23: mu,SV31: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV31 )
| ( closed @ SV23 @ SV31 ) )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV29 )
= $true )
| ( ( h @ o @ SV29 )
= $false )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(189,plain,
! [SV18: $i,SV12: $i,SV25: mu,SV23: mu,SV30: $i,SV28: $i] :
( ( ( rel_s4 @ SV28 @ SV30 )
= $false )
| ( ( open @ SV23 @ SV30 )
= $true )
| ( ( closed @ SV23 @ SV28 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV28 )
= $false )
| ( ( h @ ( sK5_SY371 @ SV12 @ SV25 @ SV23 @ SV18 ) @ SV28 )
= $false )
| ( ( rel_s4 @ SV18 @ SV28 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(190,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV23: mu,SV31: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV31 ) )
= $true )
| ( ( closed @ SV23 @ SV31 )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV29 )
= $true )
| ( ( h @ o @ SV29 )
= $false )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(191,plain,
! [SV12: $i,SV18: $i,SV25: mu,SV23: mu,SV31: $i,SV29: $i] :
( ( ( rel_s4 @ SV29 @ SV31 )
= $false )
| ( ( closed @ SV23 @ SV31 )
= $true )
| ( ( closed @ SV23 @ SV29 )
= $false )
| ( ( combo @ SV23 @ SV25 @ SV29 )
= $true )
| ( ( h @ o @ SV29 )
= $false )
| ( ( rel_s4 @ SV18 @ SV29 )
= $false )
| ( ( exists_in_world @ SV25 @ SV18 )
= $false )
| ( ( exists_in_world @ SV23 @ SV18 )
= $false )
| ( ( rel_s4 @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(192,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,191,189,162,161,148,145,141,133,124,123,116,102,96,92,84,76,54,53,52]) ).
thf(193,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA033^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 13:52:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.32
% 0.44/0.32 No.of.Axioms: 12
% 0.44/0.32
% 0.44/0.32 Length.of.Defs: 5508
% 0.44/0.32
% 0.44/0.32 Contains.Choice.Funs: false
% 0.44/0.32 .............
% 0.44/0.32
% 0.44/0.32 ********************************
% 0.44/0.32 * All subproblems solved! *
% 0.44/0.32 ********************************
% 0.44/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:192,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.44/0.32
% 0.44/0.32 %**** Beginning of derivation protocol ****
% 0.44/0.32 % SZS output start CNFRefutation
% See solution above
% 0.44/0.32
% 0.44/0.32 %**** End of derivation protocol ****
% 0.44/0.32 %**** no. of clauses in derivation: 193 ****
% 0.44/0.32 %**** clause counter: 192 ****
% 0.44/0.32
% 0.44/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:192,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------