%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET575^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:40:22 AM UTC 2026
% Result : Theorem 1.13s 0.42s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 35
% Syntax : Number of formulae : 238 ( 86 unt; 0 typ; 32 def)
% Number of atoms : 3961 (1006 equ; 0 cnn)
% Maximal formula atoms : 26 ( 16 avg)
% Number of connectives : 10589 (1560 ~;1611 |; 38 &;7353 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 50 usr; 8 con; 0-7 aty)
% Number of variables : 1306 ( 61 ^;1239 !; 6 ?;1306 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_intersect,type,
intersect: 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_member,type,
member: mu > mu > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK10_SY374,type,
sK10_SY374: mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK11_SY411,type,
sK11_SY411: mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK12_SY406,type,
sK12_SY406: $i > mu > $i > mu > $i > $i > mu ).
thf(tp_sK13_SY405,type,
sK13_SY405: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK1_SY108,type,
sK1_SY108: $i ).
thf(tp_sK2_SY471,type,
sK2_SY471: $i ).
thf(tp_sK3_SY480,type,
sK3_SY480: mu ).
thf(tp_sK4_SY488,type,
sK4_SY488: $i ).
thf(tp_sK5_SY495,type,
sK5_SY495: mu ).
thf(tp_sK6_SY501,type,
sK6_SY501: $i ).
thf(tp_sK7_SY509,type,
sK7_SY509: mu > $i ).
thf(tp_sK8_SY508,type,
sK8_SY508: mu > $i ).
thf(tp_sK9_SY170,type,
sK9_SY170: $i > mu > $i > mu > $i > $i > $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
@ ( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( intersect @ B @ C ) ) @ ( mbox_s4 @ ( intersect @ C @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(2,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] :
( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ B @ C ) )
@ ( mexists_ind
@ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( member @ D @ B ) ) @ ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( member @ D @ B ) ) @ ( mbox_s4 @ ( member @ D @ C ) ) ) )
@ ( mbox_s4 @ ( intersect @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
thf(7,conjecture,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ B @ C ) )
@ ( mexists_ind
@ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( member @ D @ B ) ) @ ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th15) ).
thf(8,negated_conjecture,
( ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ B @ C ) )
@ ( mexists_ind
@ ^ [D: mu] : ( mand @ ( mbox_s4 @ ( member @ D @ B ) ) @ ( mbox_s4 @ ( member @ D @ C ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [SY108: $i,SY109: $i] :
( ~ ( rel_s4 @ SY108 @ SY109 )
| ! [SY100: mu] :
( ( exists_in_world @ SY100 @ SY109 )
=> ! [SY101: $i] :
( ~ ( rel_s4 @ SY109 @ SY101 )
| ! [SY85: mu] :
( ( exists_in_world @ SY85 @ SY101 )
=> ! [SY86: $i] :
( ~ ( rel_s4 @ SY101 @ SY86 )
| ~ ! [SY87: $i] :
( ~ ( rel_s4 @ SY86 @ SY87 )
| ( intersect @ SY100 @ SY85 @ SY87 ) )
| ~ ! [SY88: mu] :
( ( exists_in_world @ SY88 @ SY86 )
=> ~ ~ ( ~ ! [SY89: $i] :
( ~ ( rel_s4 @ SY86 @ SY89 )
| ( member @ SY88 @ SY100 @ SY89 ) )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SY86 @ SY67 )
| ( member @ SY88 @ SY85 @ SY67 ) ) ) ) ) ) ) ) ) )
= $false ),
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(10,plain,
( ( ! [SY185: $i,SY186: $i] :
( ~ ( rel_s4 @ SY185 @ SY186 )
| ! [SY179: mu] :
( ( exists_in_world @ SY179 @ SY186 )
=> ! [SY180: $i] :
( ~ ( rel_s4 @ SY186 @ SY180 )
| ! [SY168: mu] :
( ( exists_in_world @ SY168 @ SY180 )
=> ! [SY169: $i] :
( ~ ( rel_s4 @ SY180 @ SY169 )
| ~ ! [SY170: $i] :
( ~ ( rel_s4 @ SY169 @ SY170 )
| ( intersect @ SY179 @ SY168 @ SY170 ) )
| ! [SY171: $i] :
( ~ ( rel_s4 @ SY169 @ SY171 )
| ( intersect @ SY168 @ SY179 @ SY171 ) ) ) ) ) ) ) )
= $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(11,plain,
( ( ! [SY441: $i,SY442: $i] :
( ~ ( rel_s4 @ SY441 @ SY442 )
| ! [SY428: mu] :
( ( exists_in_world @ SY428 @ SY442 )
=> ! [SY429: $i] :
( ~ ( rel_s4 @ SY442 @ SY429 )
| ! [SY403: mu] :
( ( exists_in_world @ SY403 @ SY429 )
=> ~ ( ~ ! [SY404: $i] :
( ~ ( rel_s4 @ SY429 @ SY404 )
| ~ ! [SY405: $i] :
( ~ ( rel_s4 @ SY404 @ SY405 )
| ( intersect @ SY428 @ SY403 @ SY405 ) )
| ~ ! [SY406: mu] :
( ( exists_in_world @ SY406 @ SY404 )
=> ~ ~ ( ~ ! [SY407: $i] :
( ~ ( rel_s4 @ SY404 @ SY407 )
| ( member @ SY406 @ SY428 @ SY407 ) )
| ~ ! [SY370: $i] :
( ~ ( rel_s4 @ SY404 @ SY370 )
| ( member @ SY406 @ SY403 @ SY370 ) ) ) ) )
| ~ ! [SY409: $i] :
( ~ ( rel_s4 @ SY429 @ SY409 )
| ~ ~ ! [SY410: mu] :
( ( exists_in_world @ SY410 @ SY409 )
=> ~ ~ ( ~ ! [SY411: $i] :
( ~ ( rel_s4 @ SY409 @ SY411 )
| ( member @ SY410 @ SY428 @ SY411 ) )
| ~ ! [SY374: $i] :
( ~ ( rel_s4 @ SY409 @ SY374 )
| ( member @ SY410 @ SY403 @ SY374 ) ) ) )
| ! [SY413: $i] :
( ~ ( rel_s4 @ SY409 @ SY413 )
| ( intersect @ SY428 @ SY403 @ SY413 ) ) ) ) ) ) ) ) )
= $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(12,plain,
( ( ! [SY471: $i] :
( ~ ( rel_s4 @ sK1_SY108 @ SY471 )
| ! [SY100: mu] :
( ( exists_in_world @ SY100 @ SY471 )
=> ! [SY101: $i] :
( ~ ( rel_s4 @ SY471 @ SY101 )
| ! [SY85: mu] :
( ( exists_in_world @ SY85 @ SY101 )
=> ! [SY86: $i] :
( ~ ( rel_s4 @ SY101 @ SY86 )
| ~ ! [SY87: $i] :
( ~ ( rel_s4 @ SY86 @ SY87 )
| ( intersect @ SY100 @ SY85 @ SY87 ) )
| ~ ! [SY88: mu] :
( ( exists_in_world @ SY88 @ SY86 )
=> ~ ~ ( ~ ! [SY89: $i] :
( ~ ( rel_s4 @ SY86 @ SY89 )
| ( member @ SY88 @ SY100 @ SY89 ) )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SY86 @ SY67 )
| ( member @ SY88 @ SY85 @ SY67 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(13,plain,
( ( ~ ( rel_s4 @ sK1_SY108 @ sK2_SY471 )
| ! [SY480: mu] :
( ( exists_in_world @ SY480 @ sK2_SY471 )
=> ! [SY481: $i] :
( ~ ( rel_s4 @ sK2_SY471 @ SY481 )
| ! [SY85: mu] :
( ( exists_in_world @ SY85 @ SY481 )
=> ! [SY86: $i] :
( ~ ( rel_s4 @ SY481 @ SY86 )
| ~ ! [SY87: $i] :
( ~ ( rel_s4 @ SY86 @ SY87 )
| ( intersect @ SY480 @ SY85 @ SY87 ) )
| ~ ! [SY88: mu] :
( ( exists_in_world @ SY88 @ SY86 )
=> ~ ~ ( ~ ! [SY89: $i] :
( ~ ( rel_s4 @ SY86 @ SY89 )
| ( member @ SY88 @ SY480 @ SY89 ) )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SY86 @ SY67 )
| ( member @ SY88 @ SY85 @ SY67 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY108 @ sK2_SY471 )
| ! [SY480: mu] :
( ( exists_in_world @ SY480 @ sK2_SY471 )
=> ! [SY481: $i] :
( ~ ( rel_s4 @ sK2_SY471 @ SY481 )
| ! [SY85: mu] :
( ( exists_in_world @ SY85 @ SY481 )
=> ! [SY86: $i] :
( ~ ( rel_s4 @ SY481 @ SY86 )
| ~ ! [SY87: $i] :
( ~ ( rel_s4 @ SY86 @ SY87 )
| ( intersect @ SY480 @ SY85 @ SY87 ) )
| ~ ! [SY88: mu] :
( ( exists_in_world @ SY88 @ SY86 )
=> ~ ~ ( ~ ! [SY89: $i] :
( ~ ( rel_s4 @ SY86 @ SY89 )
| ( member @ SY88 @ SY480 @ SY89 ) )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SY86 @ SY67 )
| ( member @ SY88 @ SY85 @ SY67 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ( rel_s4 @ sK1_SY108 @ sK2_SY471 )
& ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
& ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
& ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
& ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
& ! [SY506: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SY506 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SY506 ) )
& ! [SY507: mu] :
( ~ ( exists_in_world @ SY507 @ sK6_SY501 )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SY507 ) )
& ~ ( member @ SY507 @ sK3_SY480 @ ( sK8_SY508 @ SY507 ) ) )
| ( ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SY507 ) )
& ~ ( member @ SY507 @ sK5_SY495 @ ( sK7_SY509 @ SY507 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [SY185: $i,SY186: $i] :
( ~ ( rel_s4 @ SY185 @ SY186 )
| ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SY186 )
| ! [SY180: $i] :
( ~ ( rel_s4 @ SY186 @ SY180 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SY180 )
| ! [SY169: $i] :
( ~ ( rel_s4 @ SY180 @ SY169 )
| ( ( rel_s4 @ SY169 @ ( sK9_SY170 @ SY169 @ SY168 @ SY180 @ SY179 @ SY186 @ SY185 ) )
& ~ ( intersect @ SY179 @ SY168 @ ( sK9_SY170 @ SY169 @ SY168 @ SY180 @ SY179 @ SY186 @ SY185 ) ) )
| ! [SY171: $i] :
( ~ ( rel_s4 @ SY169 @ SY171 )
| ( intersect @ SY168 @ SY179 @ SY171 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(17,plain,
( ( ! [SY441: $i,SY442: $i] :
( ~ ( rel_s4 @ SY441 @ SY442 )
| ! [SY428: mu] :
( ~ ( exists_in_world @ SY428 @ SY442 )
| ! [SY429: $i] :
( ~ ( rel_s4 @ SY442 @ SY429 )
| ( ! [SY403: mu] :
( ~ ( exists_in_world @ SY403 @ SY429 )
| ! [SY404: $i] :
( ~ ( rel_s4 @ SY429 @ SY404 )
| ( ( rel_s4 @ SY404 @ ( sK13_SY405 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) )
& ~ ( intersect @ SY428 @ SY403 @ ( sK13_SY405 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) ) )
| ( ( exists_in_world @ ( sK12_SY406 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) @ SY404 )
& ! [SY510: $i] :
( ~ ( rel_s4 @ SY404 @ SY510 )
| ( member @ ( sK12_SY406 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) @ SY428 @ SY510 ) )
& ! [SY511: $i] :
( ~ ( rel_s4 @ SY404 @ SY511 )
| ( member @ ( sK12_SY406 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) @ SY403 @ SY511 ) ) ) ) )
& ! [SY403: mu] :
( ~ ( exists_in_world @ SY403 @ SY429 )
| ! [SY409: $i] :
( ~ ( rel_s4 @ SY429 @ SY409 )
| ! [SY410: mu] :
( ~ ( exists_in_world @ SY410 @ SY409 )
| ( ( rel_s4 @ SY409 @ ( sK11_SY411 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) )
& ~ ( member @ SY410 @ SY428 @ ( sK11_SY411 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) ) )
| ( ( rel_s4 @ SY409 @ ( sK10_SY374 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) )
& ~ ( member @ SY410 @ SY403 @ ( sK10_SY374 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) ) ) )
| ! [SY413: $i] :
( ~ ( rel_s4 @ SY409 @ SY413 )
| ( intersect @ SY428 @ SY403 @ SY413 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(18,plain,
( ( ! [SY441: $i,SY442: $i] :
( ~ ( rel_s4 @ SY441 @ SY442 )
| ! [SY428: mu] :
( ~ ( exists_in_world @ SY428 @ SY442 )
| ! [SY429: $i] :
( ~ ( rel_s4 @ SY442 @ SY429 )
| ( ! [SY403: mu] :
( ~ ( exists_in_world @ SY403 @ SY429 )
| ! [SY404: $i] :
( ~ ( rel_s4 @ SY429 @ SY404 )
| ( ( rel_s4 @ SY404 @ ( sK13_SY405 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) )
& ~ ( intersect @ SY428 @ SY403 @ ( sK13_SY405 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) ) )
| ( ( exists_in_world @ ( sK12_SY406 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) @ SY404 )
& ! [SY510: $i] :
( ~ ( rel_s4 @ SY404 @ SY510 )
| ( member @ ( sK12_SY406 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) @ SY428 @ SY510 ) )
& ! [SY511: $i] :
( ~ ( rel_s4 @ SY404 @ SY511 )
| ( member @ ( sK12_SY406 @ SY404 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) @ SY403 @ SY511 ) ) ) ) )
& ! [SY403: mu] :
( ~ ( exists_in_world @ SY403 @ SY429 )
| ! [SY409: $i] :
( ~ ( rel_s4 @ SY429 @ SY409 )
| ! [SY410: mu] :
( ~ ( exists_in_world @ SY410 @ SY409 )
| ( ( rel_s4 @ SY409 @ ( sK11_SY411 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) )
& ~ ( member @ SY410 @ SY428 @ ( sK11_SY411 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) ) )
| ( ( rel_s4 @ SY409 @ ( sK10_SY374 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) )
& ~ ( member @ SY410 @ SY403 @ ( sK10_SY374 @ SY410 @ SY409 @ SY403 @ SY429 @ SY428 @ SY442 @ SY441 ) ) ) )
| ! [SY413: $i] :
( ~ ( rel_s4 @ SY409 @ SY413 )
| ( intersect @ SY428 @ SY403 @ SY413 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [SY185: $i,SY186: $i] :
( ~ ( rel_s4 @ SY185 @ SY186 )
| ! [SY179: mu] :
( ~ ( exists_in_world @ SY179 @ SY186 )
| ! [SY180: $i] :
( ~ ( rel_s4 @ SY186 @ SY180 )
| ! [SY168: mu] :
( ~ ( exists_in_world @ SY168 @ SY180 )
| ! [SY169: $i] :
( ~ ( rel_s4 @ SY180 @ SY169 )
| ( ( rel_s4 @ SY169 @ ( sK9_SY170 @ SY169 @ SY168 @ SY180 @ SY179 @ SY186 @ SY185 ) )
& ~ ( intersect @ SY179 @ SY168 @ ( sK9_SY170 @ SY169 @ SY168 @ SY180 @ SY179 @ SY186 @ SY185 ) ) )
| ! [SY171: $i] :
( ~ ( rel_s4 @ SY169 @ SY171 )
| ( intersect @ SY168 @ SY179 @ SY171 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(20,plain,
( ( ( rel_s4 @ sK1_SY108 @ sK2_SY471 )
& ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
& ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
& ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
& ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
& ! [SY506: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SY506 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SY506 ) )
& ! [SY507: mu] :
( ~ ( exists_in_world @ SY507 @ sK6_SY501 )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SY507 ) )
& ~ ( member @ SY507 @ sK3_SY480 @ ( sK8_SY508 @ SY507 ) ) )
| ( ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SY507 ) )
& ~ ( member @ SY507 @ sK5_SY495 @ ( sK7_SY509 @ SY507 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(21,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY108 @ sK2_SY471 )
| ~ ~ ( ~ ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(22,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK9_SY170 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( intersect @ SX2 @ SX4 @ ( sK9_SY170 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( intersect @ SX4 @ SX2 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ~ ( ~ ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK13_SY405 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( intersect @ SX2 @ SX4 @ ( sK13_SY405 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX5 )
| ~ ~ ( ~ ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( member @ ( sK12_SY406 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX2 @ SX6 ) )
| ~ ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( member @ ( sK12_SY406 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 @ SX6 ) ) ) ) ) )
| ~ ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK11_SY411 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( member @ SX6 @ SX2 @ ( sK11_SY411 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK10_SY374 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( member @ SX6 @ SX4 @ ( sK10_SY374 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( intersect @ SX2 @ SX4 @ SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(24,plain,
( ( ~ ( rel_s4 @ sK1_SY108 @ sK2_SY471 )
| ~ ~ ( ~ ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY512: $i] :
( ~ ( rel_s4 @ SV1 @ SY512 )
| ! [SY513: mu] :
( ~ ( exists_in_world @ SY513 @ SY512 )
| ! [SY514: $i] :
( ~ ( rel_s4 @ SY512 @ SY514 )
| ! [SY515: mu] :
( ~ ( exists_in_world @ SY515 @ SY514 )
| ! [SY516: $i] :
( ~ ( rel_s4 @ SY514 @ SY516 )
| ~ ( ~ ( rel_s4 @ SY516 @ ( sK9_SY170 @ SY516 @ SY515 @ SY514 @ SY513 @ SY512 @ SV1 ) )
| ~ ~ ( intersect @ SY513 @ SY515 @ ( sK9_SY170 @ SY516 @ SY515 @ SY514 @ SY513 @ SY512 @ SV1 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY516 @ SX6 )
| ( intersect @ SY515 @ SY513 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY518: $i] :
( ~ ( rel_s4 @ SV2 @ SY518 )
| ! [SY519: mu] :
( ~ ( exists_in_world @ SY519 @ SY518 )
| ! [SY520: $i] :
( ~ ( rel_s4 @ SY518 @ SY520 )
| ~ ( ~ ! [SY521: mu] :
( ~ ( exists_in_world @ SY521 @ SY520 )
| ! [SY522: $i] :
( ~ ( rel_s4 @ SY520 @ SY522 )
| ~ ( ~ ( rel_s4 @ SY522 @ ( sK13_SY405 @ SY522 @ SY521 @ SY520 @ SY519 @ SY518 @ SV2 ) )
| ~ ~ ( intersect @ SY519 @ SY521 @ ( sK13_SY405 @ SY522 @ SY521 @ SY520 @ SY519 @ SY518 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY522 @ SY521 @ SY520 @ SY519 @ SY518 @ SV2 ) @ SY522 )
| ~ ~ ( ~ ! [SY523: $i] :
( ~ ( rel_s4 @ SY522 @ SY523 )
| ( member @ ( sK12_SY406 @ SY522 @ SY521 @ SY520 @ SY519 @ SY518 @ SV2 ) @ SY519 @ SY523 ) )
| ~ ! [SY524: $i] :
( ~ ( rel_s4 @ SY522 @ SY524 )
| ( member @ ( sK12_SY406 @ SY522 @ SY521 @ SY520 @ SY519 @ SY518 @ SV2 ) @ SY521 @ SY524 ) ) ) ) ) )
| ~ ! [SY525: mu] :
( ~ ( exists_in_world @ SY525 @ SY520 )
| ! [SY526: $i] :
( ~ ( rel_s4 @ SY520 @ SY526 )
| ! [SY527: mu] :
( ~ ( exists_in_world @ SY527 @ SY526 )
| ~ ( ~ ( rel_s4 @ SY526 @ ( sK11_SY411 @ SY527 @ SY526 @ SY525 @ SY520 @ SY519 @ SY518 @ SV2 ) )
| ~ ~ ( member @ SY527 @ SY519 @ ( sK11_SY411 @ SY527 @ SY526 @ SY525 @ SY520 @ SY519 @ SY518 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY526 @ ( sK10_SY374 @ SY527 @ SY526 @ SY525 @ SY520 @ SY519 @ SY518 @ SV2 ) )
| ~ ~ ( member @ SY527 @ SY525 @ ( sK10_SY374 @ SY527 @ SY526 @ SY525 @ SY520 @ SY519 @ SY518 @ SV2 ) ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY526 @ SX6 )
| ( intersect @ SY519 @ SY525 @ SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( rel_s4 @ sK1_SY108 @ sK2_SY471 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
( ( ~ ~ ( ~ ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
! [SV3: $i,SV1: $i] :
( ( ~ ( rel_s4 @ SV1 @ SV3 )
| ! [SY529: mu] :
( ~ ( exists_in_world @ SY529 @ SV3 )
| ! [SY530: $i] :
( ~ ( rel_s4 @ SV3 @ SY530 )
| ! [SY531: mu] :
( ~ ( exists_in_world @ SY531 @ SY530 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY530 @ SY532 )
| ~ ( ~ ( rel_s4 @ SY532 @ ( sK9_SY170 @ SY532 @ SY531 @ SY530 @ SY529 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SY529 @ SY531 @ ( sK9_SY170 @ SY532 @ SY531 @ SY530 @ SY529 @ SV3 @ SV1 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY532 @ SX6 )
| ( intersect @ SY531 @ SY529 @ SX6 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( rel_s4 @ SV2 @ SV4 )
| ! [SY534: mu] :
( ~ ( exists_in_world @ SY534 @ SV4 )
| ! [SY535: $i] :
( ~ ( rel_s4 @ SV4 @ SY535 )
| ~ ( ~ ! [SY536: mu] :
( ~ ( exists_in_world @ SY536 @ SY535 )
| ! [SY537: $i] :
( ~ ( rel_s4 @ SY535 @ SY537 )
| ~ ( ~ ( rel_s4 @ SY537 @ ( sK13_SY405 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SY534 @ SY536 @ ( sK13_SY405 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY537 )
| ~ ~ ( ~ ! [SY538: $i] :
( ~ ( rel_s4 @ SY537 @ SY538 )
| ( member @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY534 @ SY538 ) )
| ~ ! [SY539: $i] :
( ~ ( rel_s4 @ SY537 @ SY539 )
| ( member @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY536 @ SY539 ) ) ) ) ) )
| ~ ! [SY540: mu] :
( ~ ( exists_in_world @ SY540 @ SY535 )
| ! [SY541: $i] :
( ~ ( rel_s4 @ SY535 @ SY541 )
| ! [SY542: mu] :
( ~ ( exists_in_world @ SY542 @ SY541 )
| ~ ( ~ ( rel_s4 @ SY541 @ ( sK11_SY411 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY542 @ SY534 @ ( sK11_SY411 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY541 @ ( sK10_SY374 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY542 @ SY540 @ ( sK10_SY374 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY541 @ SX6 )
| ( intersect @ SY534 @ SY540 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( rel_s4 @ sK1_SY108 @ sK2_SY471 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( ~ ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i,SV1: $i] :
( ( ( ~ ( rel_s4 @ SV1 @ SV3 ) )
= $true )
| ( ( ! [SY529: mu] :
( ~ ( exists_in_world @ SY529 @ SV3 )
| ! [SY530: $i] :
( ~ ( rel_s4 @ SV3 @ SY530 )
| ! [SY531: mu] :
( ~ ( exists_in_world @ SY531 @ SY530 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY530 @ SY532 )
| ~ ( ~ ( rel_s4 @ SY532 @ ( sK9_SY170 @ SY532 @ SY531 @ SY530 @ SY529 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SY529 @ SY531 @ ( sK9_SY170 @ SY532 @ SY531 @ SY530 @ SY529 @ SV3 @ SV1 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY532 @ SX6 )
| ( intersect @ SY531 @ SY529 @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( rel_s4 @ SV2 @ SV4 ) )
= $true )
| ( ( ! [SY534: mu] :
( ~ ( exists_in_world @ SY534 @ SV4 )
| ! [SY535: $i] :
( ~ ( rel_s4 @ SV4 @ SY535 )
| ~ ( ~ ! [SY536: mu] :
( ~ ( exists_in_world @ SY536 @ SY535 )
| ! [SY537: $i] :
( ~ ( rel_s4 @ SY535 @ SY537 )
| ~ ( ~ ( rel_s4 @ SY537 @ ( sK13_SY405 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SY534 @ SY536 @ ( sK13_SY405 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY537 )
| ~ ~ ( ~ ! [SY538: $i] :
( ~ ( rel_s4 @ SY537 @ SY538 )
| ( member @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY534 @ SY538 ) )
| ~ ! [SY539: $i] :
( ~ ( rel_s4 @ SY537 @ SY539 )
| ( member @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY536 @ SY539 ) ) ) ) ) )
| ~ ! [SY540: mu] :
( ~ ( exists_in_world @ SY540 @ SY535 )
| ! [SY541: $i] :
( ~ ( rel_s4 @ SY535 @ SY541 )
| ! [SY542: mu] :
( ~ ( exists_in_world @ SY542 @ SY541 )
| ~ ( ~ ( rel_s4 @ SY541 @ ( sK11_SY411 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY542 @ SY534 @ ( sK11_SY411 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY541 @ ( sK10_SY374 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY542 @ SY540 @ ( sK10_SY374 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY541 @ SX6 )
| ( intersect @ SY534 @ SY540 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV3: $i,SV1: $i] :
( ( ( rel_s4 @ SV1 @ SV3 )
= $false )
| ( ( ! [SY529: mu] :
( ~ ( exists_in_world @ SY529 @ SV3 )
| ! [SY530: $i] :
( ~ ( rel_s4 @ SV3 @ SY530 )
| ! [SY531: mu] :
( ~ ( exists_in_world @ SY531 @ SY530 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY530 @ SY532 )
| ~ ( ~ ( rel_s4 @ SY532 @ ( sK9_SY170 @ SY532 @ SY531 @ SY530 @ SY529 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SY529 @ SY531 @ ( sK9_SY170 @ SY532 @ SY531 @ SY530 @ SY529 @ SV3 @ SV1 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY532 @ SX6 )
| ( intersect @ SY531 @ SY529 @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: $i,SV2: $i] :
( ( ( rel_s4 @ SV2 @ SV4 )
= $false )
| ( ( ! [SY534: mu] :
( ~ ( exists_in_world @ SY534 @ SV4 )
| ! [SY535: $i] :
( ~ ( rel_s4 @ SV4 @ SY535 )
| ~ ( ~ ! [SY536: mu] :
( ~ ( exists_in_world @ SY536 @ SY535 )
| ! [SY537: $i] :
( ~ ( rel_s4 @ SY535 @ SY537 )
| ~ ( ~ ( rel_s4 @ SY537 @ ( sK13_SY405 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SY534 @ SY536 @ ( sK13_SY405 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY537 )
| ~ ~ ( ~ ! [SY538: $i] :
( ~ ( rel_s4 @ SY537 @ SY538 )
| ( member @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY534 @ SY538 ) )
| ~ ! [SY539: $i] :
( ~ ( rel_s4 @ SY537 @ SY539 )
| ( member @ ( sK12_SY406 @ SY537 @ SY536 @ SY535 @ SY534 @ SV4 @ SV2 ) @ SY536 @ SY539 ) ) ) ) ) )
| ~ ! [SY540: mu] :
( ~ ( exists_in_world @ SY540 @ SY535 )
| ! [SY541: $i] :
( ~ ( rel_s4 @ SY535 @ SY541 )
| ! [SY542: mu] :
( ~ ( exists_in_world @ SY542 @ SY541 )
| ~ ( ~ ( rel_s4 @ SY541 @ ( sK11_SY411 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY542 @ SY534 @ ( sK11_SY411 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY541 @ ( sK10_SY374 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY542 @ SY540 @ ( sK10_SY374 @ SY542 @ SY541 @ SY540 @ SY535 @ SY534 @ SV4 @ SV2 ) ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY541 @ SX6 )
| ( intersect @ SY534 @ SY540 @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ~ ( exists_in_world @ sK3_SY480 @ sK2_SY471 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ~ ~ ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV1: $i,SV3: $i,SV5: mu] :
( ( ( ~ ( exists_in_world @ SV5 @ SV3 )
| ! [SY544: $i] :
( ~ ( rel_s4 @ SV3 @ SY544 )
| ! [SY545: mu] :
( ~ ( exists_in_world @ SY545 @ SY544 )
| ! [SY546: $i] :
( ~ ( rel_s4 @ SY544 @ SY546 )
| ~ ( ~ ( rel_s4 @ SY546 @ ( sK9_SY170 @ SY546 @ SY545 @ SY544 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SY545 @ ( sK9_SY170 @ SY546 @ SY545 @ SY544 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY546 @ SY547 )
| ( intersect @ SY545 @ SV5 @ SY547 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV2: $i,SV4: $i,SV6: mu] :
( ( ( ~ ( exists_in_world @ SV6 @ SV4 )
| ! [SY548: $i] :
( ~ ( rel_s4 @ SV4 @ SY548 )
| ~ ( ~ ! [SY549: mu] :
( ~ ( exists_in_world @ SY549 @ SY548 )
| ! [SY550: $i] :
( ~ ( rel_s4 @ SY548 @ SY550 )
| ~ ( ~ ( rel_s4 @ SY550 @ ( sK13_SY405 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY549 @ ( sK13_SY405 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SY550 )
| ~ ~ ( ~ ! [SY551: $i] :
( ~ ( rel_s4 @ SY550 @ SY551 )
| ( member @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY551 ) )
| ~ ! [SY552: $i] :
( ~ ( rel_s4 @ SY550 @ SY552 )
| ( member @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SY549 @ SY552 ) ) ) ) ) )
| ~ ! [SY553: mu] :
( ~ ( exists_in_world @ SY553 @ SY548 )
| ! [SY554: $i] :
( ~ ( rel_s4 @ SY548 @ SY554 )
| ! [SY555: mu] :
( ~ ( exists_in_world @ SY555 @ SY554 )
| ~ ( ~ ( rel_s4 @ SY554 @ ( sK11_SY411 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY555 @ SV6 @ ( sK11_SY411 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY554 @ ( sK10_SY374 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY555 @ SY553 @ ( sK10_SY374 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY554 @ SY556 )
| ( intersect @ SV6 @ SY553 @ SY556 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
( ( exists_in_world @ sK3_SY480 @ sK2_SY471 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
( ( ~ ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV1: $i,SV3: $i,SV5: mu] :
( ( ( ~ ( exists_in_world @ SV5 @ SV3 ) )
= $true )
| ( ( ! [SY544: $i] :
( ~ ( rel_s4 @ SV3 @ SY544 )
| ! [SY545: mu] :
( ~ ( exists_in_world @ SY545 @ SY544 )
| ! [SY546: $i] :
( ~ ( rel_s4 @ SY544 @ SY546 )
| ~ ( ~ ( rel_s4 @ SY546 @ ( sK9_SY170 @ SY546 @ SY545 @ SY544 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SY545 @ ( sK9_SY170 @ SY546 @ SY545 @ SY544 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY546 @ SY547 )
| ( intersect @ SY545 @ SV5 @ SY547 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: $i,SV4: $i,SV6: mu] :
( ( ( ~ ( exists_in_world @ SV6 @ SV4 ) )
= $true )
| ( ( ! [SY548: $i] :
( ~ ( rel_s4 @ SV4 @ SY548 )
| ~ ( ~ ! [SY549: mu] :
( ~ ( exists_in_world @ SY549 @ SY548 )
| ! [SY550: $i] :
( ~ ( rel_s4 @ SY548 @ SY550 )
| ~ ( ~ ( rel_s4 @ SY550 @ ( sK13_SY405 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY549 @ ( sK13_SY405 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SY550 )
| ~ ~ ( ~ ! [SY551: $i] :
( ~ ( rel_s4 @ SY550 @ SY551 )
| ( member @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY551 ) )
| ~ ! [SY552: $i] :
( ~ ( rel_s4 @ SY550 @ SY552 )
| ( member @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SY549 @ SY552 ) ) ) ) ) )
| ~ ! [SY553: mu] :
( ~ ( exists_in_world @ SY553 @ SY548 )
| ! [SY554: $i] :
( ~ ( rel_s4 @ SY548 @ SY554 )
| ! [SY555: mu] :
( ~ ( exists_in_world @ SY555 @ SY554 )
| ~ ( ~ ( rel_s4 @ SY554 @ ( sK11_SY411 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY555 @ SV6 @ ( sK11_SY411 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY554 @ ( sK10_SY374 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY555 @ SY553 @ ( sK10_SY374 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY554 @ SY556 )
| ( intersect @ SV6 @ SY553 @ SY556 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV1: $i,SV3: $i,SV5: mu] :
( ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( ! [SY544: $i] :
( ~ ( rel_s4 @ SV3 @ SY544 )
| ! [SY545: mu] :
( ~ ( exists_in_world @ SY545 @ SY544 )
| ! [SY546: $i] :
( ~ ( rel_s4 @ SY544 @ SY546 )
| ~ ( ~ ( rel_s4 @ SY546 @ ( sK9_SY170 @ SY546 @ SY545 @ SY544 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SY545 @ ( sK9_SY170 @ SY546 @ SY545 @ SY544 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY546 @ SY547 )
| ( intersect @ SY545 @ SV5 @ SY547 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
! [SV2: $i,SV4: $i,SV6: mu] :
( ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( ! [SY548: $i] :
( ~ ( rel_s4 @ SV4 @ SY548 )
| ~ ( ~ ! [SY549: mu] :
( ~ ( exists_in_world @ SY549 @ SY548 )
| ! [SY550: $i] :
( ~ ( rel_s4 @ SY548 @ SY550 )
| ~ ( ~ ( rel_s4 @ SY550 @ ( sK13_SY405 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY549 @ ( sK13_SY405 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SY550 )
| ~ ~ ( ~ ! [SY551: $i] :
( ~ ( rel_s4 @ SY550 @ SY551 )
| ( member @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY551 ) )
| ~ ! [SY552: $i] :
( ~ ( rel_s4 @ SY550 @ SY552 )
| ( member @ ( sK12_SY406 @ SY550 @ SY549 @ SY548 @ SV6 @ SV4 @ SV2 ) @ SY549 @ SY552 ) ) ) ) ) )
| ~ ! [SY553: mu] :
( ~ ( exists_in_world @ SY553 @ SY548 )
| ! [SY554: $i] :
( ~ ( rel_s4 @ SY548 @ SY554 )
| ! [SY555: mu] :
( ~ ( exists_in_world @ SY555 @ SY554 )
| ~ ( ~ ( rel_s4 @ SY554 @ ( sK11_SY411 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY555 @ SV6 @ ( sK11_SY411 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY554 @ ( sK10_SY374 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY555 @ SY553 @ ( sK10_SY374 @ SY555 @ SY554 @ SY553 @ SY548 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY554 @ SY556 )
| ( intersect @ SV6 @ SY553 @ SY556 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
( ( ~ ( rel_s4 @ sK2_SY471 @ sK4_SY488 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
( ( ~ ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV1: $i,SV5: mu,SV7: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV7 )
| ! [SY557: mu] :
( ~ ( exists_in_world @ SY557 @ SV7 )
| ! [SY558: $i] :
( ~ ( rel_s4 @ SV7 @ SY558 )
| ~ ( ~ ( rel_s4 @ SY558 @ ( sK9_SY170 @ SY558 @ SY557 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SY557 @ ( sK9_SY170 @ SY558 @ SY557 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY558 @ SY547 )
| ( intersect @ SY557 @ SV5 @ SY547 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV2: $i,SV6: mu,SV8: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV8 )
| ~ ( ~ ! [SY560: mu] :
( ~ ( exists_in_world @ SY560 @ SV8 )
| ! [SY561: $i] :
( ~ ( rel_s4 @ SV8 @ SY561 )
| ~ ( ~ ( rel_s4 @ SY561 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY560 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY561 )
| ~ ~ ( ~ ! [SY562: $i] :
( ~ ( rel_s4 @ SY561 @ SY562 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY562 ) )
| ~ ! [SY563: $i] :
( ~ ( rel_s4 @ SY561 @ SY563 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY560 @ SY563 ) ) ) ) ) )
| ~ ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV8 )
| ! [SY565: $i] :
( ~ ( rel_s4 @ SV8 @ SY565 )
| ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SY565 )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SV6 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SY564 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY565 @ SY556 )
| ( intersect @ SV6 @ SY564 @ SY556 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
( ( rel_s4 @ sK2_SY471 @ sK4_SY488 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( ~ ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV1: $i,SV5: mu,SV7: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV7 ) )
= $true )
| ( ( ! [SY557: mu] :
( ~ ( exists_in_world @ SY557 @ SV7 )
| ! [SY558: $i] :
( ~ ( rel_s4 @ SV7 @ SY558 )
| ~ ( ~ ( rel_s4 @ SY558 @ ( sK9_SY170 @ SY558 @ SY557 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SY557 @ ( sK9_SY170 @ SY558 @ SY557 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY558 @ SY547 )
| ( intersect @ SY557 @ SV5 @ SY547 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV2: $i,SV6: mu,SV8: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ! [SY560: mu] :
( ~ ( exists_in_world @ SY560 @ SV8 )
| ! [SY561: $i] :
( ~ ( rel_s4 @ SV8 @ SY561 )
| ~ ( ~ ( rel_s4 @ SY561 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY560 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY561 )
| ~ ~ ( ~ ! [SY562: $i] :
( ~ ( rel_s4 @ SY561 @ SY562 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY562 ) )
| ~ ! [SY563: $i] :
( ~ ( rel_s4 @ SY561 @ SY563 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY560 @ SY563 ) ) ) ) ) )
| ~ ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV8 )
| ! [SY565: $i] :
( ~ ( rel_s4 @ SV8 @ SY565 )
| ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SY565 )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SV6 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SY564 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY565 @ SY556 )
| ( intersect @ SV6 @ SY564 @ SY556 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(57,plain,
( ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
| ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV1: $i,SV5: mu,SV7: $i,SV3: $i] :
( ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( ! [SY557: mu] :
( ~ ( exists_in_world @ SY557 @ SV7 )
| ! [SY558: $i] :
( ~ ( rel_s4 @ SV7 @ SY558 )
| ~ ( ~ ( rel_s4 @ SY558 @ ( sK9_SY170 @ SY558 @ SY557 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SY557 @ ( sK9_SY170 @ SY558 @ SY557 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY558 @ SY547 )
| ( intersect @ SY557 @ SV5 @ SY547 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV2: $i,SV6: mu,SV8: $i,SV4: $i] :
( ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( ~ ( ~ ! [SY560: mu] :
( ~ ( exists_in_world @ SY560 @ SV8 )
| ! [SY561: $i] :
( ~ ( rel_s4 @ SV8 @ SY561 )
| ~ ( ~ ( rel_s4 @ SY561 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY560 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY561 )
| ~ ~ ( ~ ! [SY562: $i] :
( ~ ( rel_s4 @ SY561 @ SY562 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY562 ) )
| ~ ! [SY563: $i] :
( ~ ( rel_s4 @ SY561 @ SY563 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY560 @ SY563 ) ) ) ) ) )
| ~ ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV8 )
| ! [SY565: $i] :
( ~ ( rel_s4 @ SV8 @ SY565 )
| ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SY565 )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SV6 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SY564 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY565 @ SY556 )
| ( intersect @ SV6 @ SY564 @ SY556 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
( ( ~ ( exists_in_world @ sK5_SY495 @ sK4_SY488 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(61,plain,
( ( ~ ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(62,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV7: $i,SV9: mu] :
( ( ( ~ ( exists_in_world @ SV9 @ SV7 )
| ! [SY568: $i] :
( ~ ( rel_s4 @ SV7 @ SY568 )
| ~ ( ~ ( rel_s4 @ SY568 @ ( sK9_SY170 @ SY568 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SY568 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY568 @ SY569 )
| ( intersect @ SV9 @ SV5 @ SY569 ) ) ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i] :
( ( ( ~ ! [SY560: mu] :
( ~ ( exists_in_world @ SY560 @ SV8 )
| ! [SY561: $i] :
( ~ ( rel_s4 @ SV8 @ SY561 )
| ~ ( ~ ( rel_s4 @ SY561 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY560 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY561 )
| ~ ~ ( ~ ! [SY562: $i] :
( ~ ( rel_s4 @ SY561 @ SY562 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY562 ) )
| ~ ! [SY563: $i] :
( ~ ( rel_s4 @ SY561 @ SY563 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY560 @ SY563 ) ) ) ) ) )
| ~ ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV8 )
| ! [SY565: $i] :
( ~ ( rel_s4 @ SV8 @ SY565 )
| ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SY565 )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SV6 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SY564 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY565 @ SY556 )
| ( intersect @ SV6 @ SY564 @ SY556 ) ) ) ) )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
( ( exists_in_world @ sK5_SY495 @ sK4_SY488 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(65,plain,
( ( ~ ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV7: $i,SV9: mu] :
( ( ( ~ ( exists_in_world @ SV9 @ SV7 ) )
= $true )
| ( ( ! [SY568: $i] :
( ~ ( rel_s4 @ SV7 @ SY568 )
| ~ ( ~ ( rel_s4 @ SY568 @ ( sK9_SY170 @ SY568 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SY568 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY568 @ SY569 )
| ( intersect @ SV9 @ SV5 @ SY569 ) ) ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i] :
( ( ( ~ ! [SY560: mu] :
( ~ ( exists_in_world @ SY560 @ SV8 )
| ! [SY561: $i] :
( ~ ( rel_s4 @ SV8 @ SY561 )
| ~ ( ~ ( rel_s4 @ SY561 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY560 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY561 )
| ~ ~ ( ~ ! [SY562: $i] :
( ~ ( rel_s4 @ SY561 @ SY562 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY562 ) )
| ~ ! [SY563: $i] :
( ~ ( rel_s4 @ SY561 @ SY563 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY560 @ SY563 ) ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i] :
( ( ( ~ ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV8 )
| ! [SY565: $i] :
( ~ ( rel_s4 @ SV8 @ SY565 )
| ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SY565 )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SV6 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SY564 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY565 @ SY556 )
| ( intersect @ SV6 @ SY564 @ SY556 ) ) ) ) )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
( ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV7: $i,SV9: mu] :
( ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( ! [SY568: $i] :
( ~ ( rel_s4 @ SV7 @ SY568 )
| ~ ( ~ ( rel_s4 @ SY568 @ ( sK9_SY170 @ SY568 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SY568 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY568 @ SY569 )
| ( intersect @ SV9 @ SV5 @ SY569 ) ) ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i] :
( ( ( ! [SY560: mu] :
( ~ ( exists_in_world @ SY560 @ SV8 )
| ! [SY561: $i] :
( ~ ( rel_s4 @ SV8 @ SY561 )
| ~ ( ~ ( rel_s4 @ SY561 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SY560 @ ( sK13_SY405 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY561 )
| ~ ~ ( ~ ! [SY562: $i] :
( ~ ( rel_s4 @ SY561 @ SY562 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY562 ) )
| ~ ! [SY563: $i] :
( ~ ( rel_s4 @ SY561 @ SY563 )
| ( member @ ( sK12_SY406 @ SY561 @ SY560 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY560 @ SY563 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i] :
( ( ( ! [SY564: mu] :
( ~ ( exists_in_world @ SY564 @ SV8 )
| ! [SY565: $i] :
( ~ ( rel_s4 @ SV8 @ SY565 )
| ! [SY566: mu] :
( ~ ( exists_in_world @ SY566 @ SY565 )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SV6 @ ( sK11_SY411 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY565 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY566 @ SY564 @ ( sK10_SY374 @ SY566 @ SY565 @ SY564 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY556: $i] :
( ~ ( rel_s4 @ SY565 @ SY556 )
| ( intersect @ SV6 @ SY564 @ SY556 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
( ( ~ ( rel_s4 @ sK4_SY488 @ sK6_SY501 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(74,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(75,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV9: mu,SV10: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV10 )
| ~ ( ~ ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ SV11 @ SV8 )
| ! [SY571: $i] :
( ~ ( rel_s4 @ SV8 @ SY571 )
| ~ ( ~ ( rel_s4 @ SY571 @ ( sK13_SY405 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY571 )
| ~ ~ ( ~ ! [SY572: $i] :
( ~ ( rel_s4 @ SY571 @ SY572 )
| ( member @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY572 ) )
| ~ ! [SY573: $i] :
( ~ ( rel_s4 @ SY571 @ SY573 )
| ( member @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY573 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu] :
( ( ( ~ ( exists_in_world @ SV12 @ SV8 )
| ! [SY574: $i] :
( ~ ( rel_s4 @ SV8 @ SY574 )
| ! [SY575: mu] :
( ~ ( exists_in_world @ SY575 @ SY574 )
| ~ ( ~ ( rel_s4 @ SY574 @ ( sK11_SY411 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY575 @ SV6 @ ( sK11_SY411 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY574 @ ( sK10_SY374 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY575 @ SV12 @ ( sK10_SY374 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY576: $i] :
( ~ ( rel_s4 @ SY574 @ SY576 )
| ( intersect @ SV6 @ SV12 @ SY576 ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(78,plain,
( ( rel_s4 @ sK4_SY488 @ sK6_SY501 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(79,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV9: mu,SV10: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ SV11 @ SV8 ) )
= $true )
| ( ( ! [SY571: $i] :
( ~ ( rel_s4 @ SV8 @ SY571 )
| ~ ( ~ ( rel_s4 @ SY571 @ ( sK13_SY405 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY571 )
| ~ ~ ( ~ ! [SY572: $i] :
( ~ ( rel_s4 @ SY571 @ SY572 )
| ( member @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY572 ) )
| ~ ! [SY573: $i] :
( ~ ( rel_s4 @ SY571 @ SY573 )
| ( member @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY573 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu] :
( ( ( ~ ( exists_in_world @ SV12 @ SV8 ) )
= $true )
| ( ( ! [SY574: $i] :
( ~ ( rel_s4 @ SV8 @ SY574 )
| ! [SY575: mu] :
( ~ ( exists_in_world @ SY575 @ SY574 )
| ~ ( ~ ( rel_s4 @ SY574 @ ( sK11_SY411 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY575 @ SV6 @ ( sK11_SY411 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY574 @ ( sK10_SY374 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY575 @ SV12 @ ( sK10_SY374 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY576: $i] :
( ~ ( rel_s4 @ SY574 @ SY576 )
| ( intersect @ SV6 @ SV12 @ SY576 ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) )
| ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV9: mu,SV10: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
| ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu] :
( ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( ! [SY571: $i] :
( ~ ( rel_s4 @ SV8 @ SY571 )
| ~ ( ~ ( rel_s4 @ SY571 @ ( sK13_SY405 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SY571 )
| ~ ~ ( ~ ! [SY572: $i] :
( ~ ( rel_s4 @ SY571 @ SY572 )
| ( member @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY572 ) )
| ~ ! [SY573: $i] :
( ~ ( rel_s4 @ SY571 @ SY573 )
| ( member @ ( sK12_SY406 @ SY571 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY573 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu] :
( ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( ! [SY574: $i] :
( ~ ( rel_s4 @ SV8 @ SY574 )
| ! [SY575: mu] :
( ~ ( exists_in_world @ SY575 @ SY574 )
| ~ ( ~ ( rel_s4 @ SY574 @ ( sK11_SY411 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY575 @ SV6 @ ( sK11_SY411 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SY574 @ ( sK10_SY374 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY575 @ SV12 @ ( sK10_SY374 @ SY575 @ SY574 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY576: $i] :
( ~ ( rel_s4 @ SY574 @ SY576 )
| ( intersect @ SV6 @ SV12 @ SY576 ) ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(88,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(89,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV7: $i,SV9: mu,SV10: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) ) )
= $true )
| ( ( ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV11: mu,SV13: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV13 )
| ~ ( ~ ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV12: mu,SV14: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV14 )
| ! [SY579: mu] :
( ~ ( exists_in_world @ SY579 @ SV14 )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV6 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV12 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(92,plain,
( ( ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY501 @ SX0 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(93,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK3_SY480 @ ( sK8_SY508 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SX0 ) )
| ~ ~ ( member @ SX0 @ sK5_SY495 @ ( sK7_SY509 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV7: $i,SV9: mu,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
| ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV11: mu,SV13: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV12: mu,SV14: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV14 ) )
= $true )
| ( ( ! [SY579: mu] :
( ~ ( exists_in_world @ SY579 @ SV14 )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV6 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV12 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV15: $i] :
( ( ~ ( rel_s4 @ sK6_SY501 @ SV15 )
| ( intersect @ sK3_SY480 @ sK5_SY495 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV16: mu] :
( ( ~ ( exists_in_world @ SV16 @ sK6_SY501 )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV7: $i,SV9: mu,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV10: $i,SV9: mu,SV5: mu] :
( ( ( ~ ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
= $false )
| ( ( ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(101,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV11: mu,SV13: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV12: mu,SV14: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( ! [SY579: mu] :
( ~ ( exists_in_world @ SY579 @ SV14 )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV6 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV12 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
| ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV15: $i] :
( ( ( ~ ( rel_s4 @ sK6_SY501 @ SV15 ) )
= $true )
| ( ( intersect @ sK3_SY480 @ sK5_SY495 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ sK6_SY501 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV1: $i,SV3: $i,SV5: mu,SV7: $i,SV9: mu,SV10: $i] :
( ( ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV10: $i,SV9: mu,SV5: mu] :
( ( ( ~ ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) ) )
= $true )
| ( ( ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(107,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV14: $i] :
( ( ( ! [SY579: mu] :
( ~ ( exists_in_world @ SY579 @ SV14 )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV6 @ ( sK11_SY411 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SY579 @ SV12 @ ( sK10_SY374 @ SY579 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) ) )
= $true )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV15: $i] :
( ( ( rel_s4 @ sK6_SY501 @ SV15 )
= $false )
| ( ( intersect @ sK3_SY480 @ sK5_SY495 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV16: mu] :
( ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) ) )
| ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV5: mu,SV9: mu,SV17: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV17 )
| ( intersect @ SV9 @ SV5 @ SV17 ) )
= $true )
| ( ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV10: $i,SV9: mu,SV5: mu] :
( ( ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $false )
| ( ( ! [SY570: $i] :
( ~ ( rel_s4 @ SV10 @ SY570 )
| ( intersect @ SV9 @ SV5 @ SY570 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV14: $i,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ SV14 )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(115,plain,
! [SV16: mu] :
( ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV5: mu,SV9: mu,SV17: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV17 ) )
= $true )
| ( ( intersect @ SV9 @ SV5 @ SV17 )
= $true )
| ( ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV5: mu,SV9: mu,SV19: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV19 )
| ( intersect @ SV9 @ SV5 @ SV19 ) )
= $true )
| ( ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $false )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(119,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV13: $i,SV11: mu,SV6: mu] :
( ( ( ~ ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(120,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV14: $i,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(121,plain,
! [SV16: mu] :
( ( ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(122,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV5: mu,SV9: mu,SV17: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV17 )
= $false )
| ( ( intersect @ SV9 @ SV5 @ SV17 )
= $true )
| ( ( rel_s4 @ SV10 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(123,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV5: mu,SV9: mu,SV19: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV19 ) )
= $true )
| ( ( intersect @ SV9 @ SV5 @ SV19 )
= $true )
| ( ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $false )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(124,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(125,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV13: $i,SV11: mu,SV6: mu] :
( ( ( ~ ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(126,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV14: $i,SV18: mu] :
( ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
| ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV16: mu] :
( ( ( ~ ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV16: mu] :
( ( ( ~ ~ ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV1: $i,SV3: $i,SV7: $i,SV5: mu,SV9: mu,SV19: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV19 )
= $false )
| ( ( intersect @ SV9 @ SV5 @ SV19 )
= $true )
| ( ( intersect @ SV5 @ SV9 @ ( sK9_SY170 @ SV10 @ SV9 @ SV7 @ SV5 @ SV3 @ SV1 ) )
= $false )
| ( ( rel_s4 @ SV7 @ SV10 )
= $false )
| ( ( exists_in_world @ SV9 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $false )
| ( ( exists_in_world @ SV5 @ SV3 )
= $false )
| ( ( rel_s4 @ SV1 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) )
= $false )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV13: $i,SV11: mu,SV6: mu] :
( ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV16: mu] :
( ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(134,plain,
! [SV16: mu] :
( ( ( ~ ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(135,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 ) )
= $false )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(136,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) )
= $false )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(137,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
| ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) )
= $false )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV16: mu] :
( ( ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(140,plain,
! [SV16: mu] :
( ( ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(141,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(142,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(143,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 ) )
= $false )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(144,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) )
= $false )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(145,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(146,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV12: mu,SV14: $i,SV6: mu,SV18: mu] :
( ( ( ~ ~ ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(147,plain,
! [SV16: mu] :
( ( ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(148,plain,
! [SV16: mu] :
( ( ( ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(149,plain,
! [SV16: mu] :
( ( ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
| ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) )
= $false )
| ( ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) )
= $false )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(151,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( exists_in_world @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV13 )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(152,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) ) )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(153,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(154,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV12: mu,SV14: $i,SV6: mu,SV18: mu] :
( ( ( ~ ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV16: mu] :
( ( ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
= $true )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV16: mu] :
( ( ( ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) )
= $true )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(157,plain,
! [SV16: mu] :
( ( ( ~ ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) ) )
= $false )
| ( ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(158,plain,
! [SV16: mu] :
( ( ( ~ ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) )
= $false )
| ( ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(159,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) ) )
= $false )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(160,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) )
= $false )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(161,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) )
| ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) )
= $false )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV12: mu,SV14: $i,SV6: mu,SV18: mu] :
( ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV16: mu] :
( ( ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) )
= $false )
| ( ( rel_s4 @ sK6_SY501 @ ( sK8_SY508 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV16: mu] :
( ( ( rel_s4 @ sK6_SY501 @ ( sK7_SY509 @ SV16 ) )
= $true )
| ( ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(166,plain,
! [SV16: mu] :
( ( ( ~ ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) ) )
= $true )
| ( ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(167,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(168,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(169,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) ) )
= $false )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(170,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ~ ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) )
= $false )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(171,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(172,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV14: $i,SV12: mu,SV18: mu] :
( ( ( ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(173,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
| ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV16: mu] :
( ( ( member @ SV16 @ sK5_SY495 @ ( sK7_SY509 @ SV16 ) )
= $false )
| ( ( member @ SV16 @ sK3_SY480 @ ( sK8_SY508 @ SV16 ) )
= $false )
| ( ( exists_in_world @ SV16 @ sK6_SY501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV20: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV20 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SV20 ) )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV21: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV21 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SV21 ) )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ! [SY577: $i] :
( ~ ( rel_s4 @ SV13 @ SY577 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SY577 ) ) )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(178,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV13: $i] :
( ( ( ! [SY578: $i] :
( ~ ( rel_s4 @ SV13 @ SY578 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SY578 ) ) )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(179,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(180,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV14: $i,SV12: mu,SV18: mu] :
( ( ( ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $true )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(181,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(182,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV14: $i,SV12: mu,SV18: mu] :
( ( ( ~ ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(183,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV20: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV20 ) )
= $true )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SV20 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(184,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV21: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV21 ) )
= $true )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SV21 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV22: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV22 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SV22 ) )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV23: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV23 )
| ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SV23 ) )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(187,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV24: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV24 )
| ( intersect @ SV6 @ SV12 @ SV24 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV14: $i,SV12: mu,SV18: mu] :
( ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV12: mu,SV18: mu,SV14: $i] :
( ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(190,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV14: $i,SV12: mu,SV18: mu] :
( ( ( ~ ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) ) )
= $true )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(191,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV20: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV20 )
= $false )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SV20 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV21: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV21 )
= $false )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SV21 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV22: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV22 ) )
= $true )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SV22 )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV23: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV23 ) )
= $true )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SV23 )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV24: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV24 ) )
= $true )
| ( ( intersect @ SV6 @ SV12 @ SV24 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV25: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV25 )
| ( intersect @ SV6 @ SV12 @ SV25 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV26: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV26 )
| ( intersect @ SV6 @ SV12 @ SV26 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV14: $i,SV12: mu,SV18: mu] :
( ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY580: $i] :
( ~ ( rel_s4 @ SV14 @ SY580 )
| ( intersect @ SV6 @ SV12 @ SY580 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV22: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV22 )
= $false )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV6 @ SV22 )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV2: $i,SV4: $i,SV6: mu,SV8: $i,SV11: mu,SV23: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV23 )
= $false )
| ( ( member @ ( sK12_SY406 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) @ SV11 @ SV23 )
= $true )
| ( ( intersect @ SV6 @ SV11 @ ( sK13_SY405 @ SV13 @ SV11 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV24: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV24 )
= $false )
| ( ( intersect @ SV6 @ SV12 @ SV24 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV25: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV25 ) )
= $true )
| ( ( intersect @ SV6 @ SV12 @ SV25 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV26: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV26 ) )
= $true )
| ( ( intersect @ SV6 @ SV12 @ SV26 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(204,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV27: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV27 )
| ( intersect @ SV6 @ SV12 @ SV27 ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV25: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV25 )
= $false )
| ( ( intersect @ SV6 @ SV12 @ SV25 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(206,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV26: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV26 )
= $false )
| ( ( intersect @ SV6 @ SV12 @ SV26 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV14 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV27: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV27 ) )
= $true )
| ( ( intersect @ SV6 @ SV12 @ SV27 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(208,plain,
! [SV2: $i,SV4: $i,SV8: $i,SV18: mu,SV12: mu,SV6: mu,SV27: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV27 )
= $false )
| ( ( intersect @ SV6 @ SV12 @ SV27 )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( member @ SV18 @ SV6 @ ( sK11_SY411 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( member @ SV18 @ SV12 @ ( sK10_SY374 @ SV18 @ SV14 @ SV12 @ SV8 @ SV6 @ SV4 @ SV2 ) )
= $false )
| ( ( rel_s4 @ SV8 @ SV14 )
= $false )
| ( ( exists_in_world @ SV12 @ SV8 )
= $false )
| ( ( rel_s4 @ SV4 @ SV8 )
= $false )
| ( ( exists_in_world @ SV6 @ SV4 )
= $false )
| ( ( rel_s4 @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(209,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,208,206,205,201,200,199,192,191,174,165,164,155,151,141,129,122,109,78,64,53,42]) ).
thf(210,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET575^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 14:47:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.13/0.42
% 1.13/0.42 No.of.Axioms: 6
% 1.13/0.42
% 1.13/0.42 Length.of.Defs: 5508
% 1.13/0.42
% 1.13/0.42 Contains.Choice.Funs: false
% 1.13/0.42 ....................
% 1.13/0.42
% 1.13/0.42 ********************************
% 1.13/0.42 * All subproblems solved! *
% 1.13/0.42 ********************************
% 1.13/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:209,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.13/0.42
% 1.13/0.42 %**** Beginning of derivation protocol ****
% 1.13/0.42 % SZS output start CNFRefutation
% See solution above
% 1.13/0.42
% 1.13/0.42 %**** End of derivation protocol ****
% 1.13/0.42 %**** no. of clauses in derivation: 206 ****
% 1.13/0.42 %**** clause counter: 209 ****
% 1.13/0.42
% 1.13/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:209,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------