%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN052^7 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 11:02:47 AM UTC 2026
% Result : Theorem 1.04s 0.43s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 37
% Syntax : Number of formulae : 192 ( 78 unt; 0 typ; 32 def)
% Number of atoms : 1999 ( 423 equ; 0 cnn)
% Maximal formula atoms : 35 ( 10 avg)
% Number of connectives : 4401 (1137 ~; 854 |; 39 &;2345 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 11 con; 0-3 aty)
% Number of variables : 605 ( 55 ^; 542 !; 8 ?; 605 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_big_f,type,
big_f: mu > $i > $o ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia_s4,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK10_SY18,type,
sK10_SY18: $i > mu > $i > $i ).
thf(tp_sK11_REN,type,
sK11_REN: $o ).
thf(tp_sK12_X,type,
sK12_X: $i > mu ).
thf(tp_sK1_SY267,type,
sK1_SY267: $i ).
thf(tp_sK2_SY320,type,
sK2_SY320: $i ).
thf(tp_sK3_SY352,type,
sK3_SY352: $i ).
thf(tp_sK4_SY360,type,
sK4_SY360: $i ).
thf(tp_sK5_SY347,type,
sK5_SY347: $i ).
thf(tp_sK6_SY362,type,
sK6_SY362: $i ).
thf(tp_sK7_SY365,type,
sK7_SY365: mu ).
thf(tp_sK8_SY367,type,
sK8_SY367: $i ).
thf(tp_sK9_SY72,type,
sK9_SY72: $i > mu > $i > $i ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax) ).
thf(2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(3,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(4,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(5,conjecture,
( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel22) ).
thf(6,negated_conjecture,
( ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [SY267: $i,SY268: $i] :
( ~ ( rel_s4 @ SY267 @ SY268 )
| ~ ! [SY249: $i] :
( ~ ( rel_s4 @ SY268 @ SY249 )
| ! [SY82: mu] :
( ( exists_in_world @ SY82 @ SY249 )
=> ~ ( ~ ! [SY83: $i] :
( ~ ( rel_s4 @ SY249 @ SY83 )
| ~ ! [SY18: $i] :
( ~ ( rel_s4 @ SY83 @ SY18 )
| ( p @ SY18 ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SY83 @ SY70 )
| ( big_f @ SY82 @ SY70 ) ) )
| ~ ! [SY86: $i] :
( ~ ( rel_s4 @ SY249 @ SY86 )
| ~ ! [SY72: $i] :
( ~ ( rel_s4 @ SY86 @ SY72 )
| ( big_f @ SY82 @ SY72 ) )
| ! [SY57: $i] :
( ~ ( rel_s4 @ SY86 @ SY57 )
| ( p @ SY57 ) ) ) ) ) )
| ~ ( ~ ! [SY257: $i] :
( ~ ( rel_s4 @ SY268 @ SY257 )
| ~ ! [SY147: $i] :
( ~ ( rel_s4 @ SY257 @ SY147 )
| ( p @ SY147 ) )
| ! [SY148: $i] :
( ~ ( rel_s4 @ SY257 @ SY148 )
| ! [SY138: mu] :
( ( exists_in_world @ SY138 @ SY148 )
=> ! [SY139: $i] :
( ~ ( rel_s4 @ SY148 @ SY139 )
| ( big_f @ SY138 @ SY139 ) ) ) ) )
| ~ ! [SY262: $i] :
( ~ ( rel_s4 @ SY268 @ SY262 )
| ~ ! [SY213: $i] :
( ~ ( rel_s4 @ SY262 @ SY213 )
| ! [SY188: mu] :
( ( exists_in_world @ SY188 @ SY213 )
=> ! [SY189: $i] :
( ~ ( rel_s4 @ SY213 @ SY189 )
| ( big_f @ SY188 @ SY189 ) ) ) )
| ! [SY216: $i] :
( ~ ( rel_s4 @ SY262 @ SY216 )
| ( p @ SY216 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(8,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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(9,plain,
( ( ! [SY310: $i,SY311: $i,SY312: $i] :
( ( ( rel_s4 @ SY310 @ SY311 )
& ( rel_s4 @ SY311 @ SY312 ) )
=> ( rel_s4 @ SY310 @ SY312 ) ) )
= $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(10,plain,
( ( ! [SY316: $i] : ( rel_s4 @ SY316 @ SY316 ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(11,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(12,plain,
( ( ! [SY320: $i] :
( ~ ( rel_s4 @ sK1_SY267 @ SY320 )
| ~ ! [SY249: $i] :
( ~ ( rel_s4 @ SY320 @ SY249 )
| ! [SY82: mu] :
( ( exists_in_world @ SY82 @ SY249 )
=> ~ ( ~ ! [SY83: $i] :
( ~ ( rel_s4 @ SY249 @ SY83 )
| ~ ! [SY18: $i] :
( ~ ( rel_s4 @ SY83 @ SY18 )
| ( p @ SY18 ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SY83 @ SY70 )
| ( big_f @ SY82 @ SY70 ) ) )
| ~ ! [SY86: $i] :
( ~ ( rel_s4 @ SY249 @ SY86 )
| ~ ! [SY72: $i] :
( ~ ( rel_s4 @ SY86 @ SY72 )
| ( big_f @ SY82 @ SY72 ) )
| ! [SY57: $i] :
( ~ ( rel_s4 @ SY86 @ SY57 )
| ( p @ SY57 ) ) ) ) ) )
| ~ ( ~ ! [SY257: $i] :
( ~ ( rel_s4 @ SY320 @ SY257 )
| ~ ! [SY147: $i] :
( ~ ( rel_s4 @ SY257 @ SY147 )
| ( p @ SY147 ) )
| ! [SY148: $i] :
( ~ ( rel_s4 @ SY257 @ SY148 )
| ! [SY138: mu] :
( ( exists_in_world @ SY138 @ SY148 )
=> ! [SY139: $i] :
( ~ ( rel_s4 @ SY148 @ SY139 )
| ( big_f @ SY138 @ SY139 ) ) ) ) )
| ~ ! [SY262: $i] :
( ~ ( rel_s4 @ SY320 @ SY262 )
| ~ ! [SY213: $i] :
( ~ ( rel_s4 @ SY262 @ SY213 )
| ! [SY188: mu] :
( ( exists_in_world @ SY188 @ SY213 )
=> ! [SY189: $i] :
( ~ ( rel_s4 @ SY213 @ SY189 )
| ( big_f @ SY188 @ SY189 ) ) ) )
| ! [SY216: $i] :
( ~ ( rel_s4 @ SY262 @ SY216 )
| ( p @ SY216 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ~ ( rel_s4 @ sK1_SY267 @ sK2_SY320 )
| ~ ! [SY339: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY339 )
| ! [SY82: mu] :
( ( exists_in_world @ SY82 @ SY339 )
=> ~ ( ~ ! [SY83: $i] :
( ~ ( rel_s4 @ SY339 @ SY83 )
| ~ ! [SY18: $i] :
( ~ ( rel_s4 @ SY83 @ SY18 )
| ( p @ SY18 ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SY83 @ SY70 )
| ( big_f @ SY82 @ SY70 ) ) )
| ~ ! [SY86: $i] :
( ~ ( rel_s4 @ SY339 @ SY86 )
| ~ ! [SY72: $i] :
( ~ ( rel_s4 @ SY86 @ SY72 )
| ( big_f @ SY82 @ SY72 ) )
| ! [SY57: $i] :
( ~ ( rel_s4 @ SY86 @ SY57 )
| ( p @ SY57 ) ) ) ) ) )
| ~ ( ~ ! [SY347: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY347 )
| ~ ! [SY147: $i] :
( ~ ( rel_s4 @ SY347 @ SY147 )
| ( p @ SY147 ) )
| ! [SY148: $i] :
( ~ ( rel_s4 @ SY347 @ SY148 )
| ! [SY138: mu] :
( ( exists_in_world @ SY138 @ SY148 )
=> ! [SY139: $i] :
( ~ ( rel_s4 @ SY148 @ SY139 )
| ( big_f @ SY138 @ SY139 ) ) ) ) )
| ~ ! [SY352: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY352 )
| ~ ! [SY213: $i] :
( ~ ( rel_s4 @ SY352 @ SY213 )
| ! [SY188: mu] :
( ( exists_in_world @ SY188 @ SY213 )
=> ! [SY189: $i] :
( ~ ( rel_s4 @ SY213 @ SY189 )
| ( big_f @ SY188 @ SY189 ) ) ) )
| ! [SY216: $i] :
( ~ ( rel_s4 @ SY352 @ SY216 )
| ( p @ SY216 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY267 @ sK2_SY320 )
| ~ ! [SY339: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY339 )
| ! [SY82: mu] :
( ( exists_in_world @ SY82 @ SY339 )
=> ~ ( ~ ! [SY83: $i] :
( ~ ( rel_s4 @ SY339 @ SY83 )
| ~ ! [SY18: $i] :
( ~ ( rel_s4 @ SY83 @ SY18 )
| ( p @ SY18 ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SY83 @ SY70 )
| ( big_f @ SY82 @ SY70 ) ) )
| ~ ! [SY86: $i] :
( ~ ( rel_s4 @ SY339 @ SY86 )
| ~ ! [SY72: $i] :
( ~ ( rel_s4 @ SY86 @ SY72 )
| ( big_f @ SY82 @ SY72 ) )
| ! [SY57: $i] :
( ~ ( rel_s4 @ SY86 @ SY57 )
| ( p @ SY57 ) ) ) ) ) )
| ~ ( ~ ! [SY347: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY347 )
| ~ ! [SY147: $i] :
( ~ ( rel_s4 @ SY347 @ SY147 )
| ( p @ SY147 ) )
| ! [SY148: $i] :
( ~ ( rel_s4 @ SY347 @ SY148 )
| ! [SY138: mu] :
( ( exists_in_world @ SY138 @ SY148 )
=> ! [SY139: $i] :
( ~ ( rel_s4 @ SY148 @ SY139 )
| ( big_f @ SY138 @ SY139 ) ) ) ) )
| ~ ! [SY352: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY352 )
| ~ ! [SY213: $i] :
( ~ ( rel_s4 @ SY352 @ SY213 )
| ! [SY188: mu] :
( ( exists_in_world @ SY188 @ SY213 )
=> ! [SY189: $i] :
( ~ ( rel_s4 @ SY213 @ SY189 )
| ( big_f @ SY188 @ SY189 ) ) ) )
| ! [SY216: $i] :
( ~ ( rel_s4 @ SY352 @ SY216 )
| ( p @ SY216 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ( rel_s4 @ sK1_SY267 @ sK2_SY320 )
& ! [SY339: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY339 )
| ( ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SY339 )
| ! [SY83: $i] :
( ~ ( rel_s4 @ SY339 @ SY83 )
| ( ( rel_s4 @ SY83 @ ( sK10_SY18 @ SY83 @ SY82 @ SY339 ) )
& ~ ( p @ ( sK10_SY18 @ SY83 @ SY82 @ SY339 ) ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SY83 @ SY70 )
| ( big_f @ SY82 @ SY70 ) ) ) )
& ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SY339 )
| ! [SY86: $i] :
( ~ ( rel_s4 @ SY339 @ SY86 )
| ( ( rel_s4 @ SY86 @ ( sK9_SY72 @ SY86 @ SY82 @ SY339 ) )
& ~ ( big_f @ SY82 @ ( sK9_SY72 @ SY86 @ SY82 @ SY339 ) ) )
| ! [SY57: $i] :
( ~ ( rel_s4 @ SY86 @ SY57 )
| ( p @ SY57 ) ) ) ) ) )
& ( sK11_REN
| ( ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
& ! [SY357: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SY357 )
| ! [SY188: mu] :
( ~ ( exists_in_world @ SY188 @ SY357 )
| ! [SY189: $i] :
( ~ ( rel_s4 @ SY357 @ SY189 )
| ( big_f @ SY188 @ SY189 ) ) ) )
& ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
& ~ ( p @ sK4_SY360 ) ) )
& ( sK11_REN
=> ( ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
& ! [SY361: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SY361 )
| ( p @ SY361 ) )
& ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
& ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
& ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
& ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(17,plain,
( ( ! [SY310: $i,SY311: $i,SY312: $i] :
( ~ ( rel_s4 @ SY310 @ SY311 )
| ~ ( rel_s4 @ SY311 @ SY312 )
| ( rel_s4 @ SY310 @ SY312 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(18,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK12_X @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(19,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK12_X @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [SY316: $i] : ( rel_s4 @ SY316 @ SY316 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(21,plain,
( ( ! [SY310: $i,SY311: $i,SY312: $i] :
( ~ ( rel_s4 @ SY310 @ SY311 )
| ~ ( rel_s4 @ SY311 @ SY312 )
| ( rel_s4 @ SY310 @ SY312 ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(22,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(23,plain,
( ( ( rel_s4 @ sK1_SY267 @ sK2_SY320 )
& ! [SY339: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SY339 )
| ( ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SY339 )
| ! [SY83: $i] :
( ~ ( rel_s4 @ SY339 @ SY83 )
| ( ( rel_s4 @ SY83 @ ( sK10_SY18 @ SY83 @ SY82 @ SY339 ) )
& ~ ( p @ ( sK10_SY18 @ SY83 @ SY82 @ SY339 ) ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SY83 @ SY70 )
| ( big_f @ SY82 @ SY70 ) ) ) )
& ! [SY82: mu] :
( ~ ( exists_in_world @ SY82 @ SY339 )
| ! [SY86: $i] :
( ~ ( rel_s4 @ SY339 @ SY86 )
| ( ( rel_s4 @ SY86 @ ( sK9_SY72 @ SY86 @ SY82 @ SY339 ) )
& ~ ( big_f @ SY82 @ ( sK9_SY72 @ SY86 @ SY82 @ SY339 ) ) )
| ! [SY57: $i] :
( ~ ( rel_s4 @ SY86 @ SY57 )
| ( p @ SY57 ) ) ) ) ) )
& ( sK11_REN
| ( ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
& ! [SY357: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SY357 )
| ! [SY188: mu] :
( ~ ( exists_in_world @ SY188 @ SY357 )
| ! [SY189: $i] :
( ~ ( rel_s4 @ SY357 @ SY189 )
| ( big_f @ SY188 @ SY189 ) ) ) )
& ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
& ~ ( p @ sK4_SY360 ) ) )
& ( sK11_REN
=> ( ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
& ! [SY361: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SY361 )
| ( p @ SY361 ) )
& ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
& ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
& ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
& ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(24,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY267 @ sK2_SY320 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SX0 )
| ~ ( ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( big_f @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( big_f @ SX1 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
| ~ ~ ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(25,plain,
! [SV1: $i] :
( ( exists_in_world @ ( sK12_X @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV2: $i] :
( ( rel_s4 @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ~ ( rel_s4 @ SV3 @ SY368 )
| ~ ( rel_s4 @ SY368 @ SY369 )
| ( rel_s4 @ SV3 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV4: mu] :
( ( ! [SY370: $i,SY371: $i] :
( ~ ( exists_in_world @ SV4 @ SY370 )
| ~ ( rel_s4 @ SY370 @ SY371 )
| ( exists_in_world @ SV4 @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
( ( ~ ( rel_s4 @ sK1_SY267 @ sK2_SY320 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SX0 )
| ~ ( ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( big_f @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( big_f @ SX1 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
| ~ ~ ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV5: $i,SV3: $i] :
( ( ! [SY372: $i] :
( ~ ( rel_s4 @ SV3 @ SV5 )
| ~ ( rel_s4 @ SV5 @ SY372 )
| ( rel_s4 @ SV3 @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV6: $i,SV4: mu] :
( ( ! [SY373: $i] :
( ~ ( exists_in_world @ SV4 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SY373 )
| ( exists_in_world @ SV4 @ SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ( rel_s4 @ sK1_SY267 @ sK2_SY320 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SX0 )
| ~ ( ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( big_f @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( big_f @ SX1 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
| ~ ~ ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ~ ( rel_s4 @ SV3 @ SV5 )
| ~ ( rel_s4 @ SV5 @ SV7 )
| ( rel_s4 @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV8: $i,SV6: $i,SV4: mu] :
( ( ~ ( exists_in_world @ SV4 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SV8 )
| ( exists_in_world @ SV4 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
( ( rel_s4 @ sK1_SY267 @ sK2_SY320 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SX0 )
| ~ ( ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( big_f @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( big_f @ SX1 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
| ~ ~ ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV5 )
| ~ ( rel_s4 @ SV5 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV8: $i,SV6: $i,SV4: mu] :
( ( ( ~ ( exists_in_world @ SV4 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SX0 )
| ~ ( ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( big_f @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( big_f @ SX1 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
| ~ ~ ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV5 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV5 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV8: $i,SV6: $i,SV4: mu] :
( ( ( ~ ( exists_in_world @ SV4 @ SV6 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV6 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(43,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SX0 )
| ~ ( ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( big_f @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( big_f @ SX1 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ~ ~ ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV7: $i,SV5: $i,SV3: $i] :
( ( ( rel_s4 @ SV3 @ SV5 )
= $false )
| ( ( ~ ( rel_s4 @ SV5 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV8: $i,SV6: $i,SV4: mu] :
( ( ( exists_in_world @ SV4 @ SV6 )
= $false )
| ( ( ~ ( rel_s4 @ SV6 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ! [SX0: $i] :
( ~ ( rel_s4 @ sK2_SY320 @ SX0 )
| ~ ( ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( big_f @ SX1 @ SX3 ) ) ) )
| ~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ~ ( ~ ( rel_s4 @ SX2 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( big_f @ SX1 @ ( sK9_SY72 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( ~ ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: $i,SV7: $i,SV5: $i] :
( ( ( rel_s4 @ SV5 @ SV7 )
= $false )
| ( ( rel_s4 @ SV3 @ SV5 )
= $false )
| ( ( rel_s4 @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV4: mu,SV8: $i,SV6: $i] :
( ( ( rel_s4 @ SV6 @ SV8 )
= $false )
| ( ( exists_in_world @ SV4 @ SV6 )
= $false )
| ( ( exists_in_world @ SV4 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV9: $i] :
( ( ~ ( rel_s4 @ sK2_SY320 @ SV9 )
| ~ ( ~ ! [SY374: mu] :
( ~ ( exists_in_world @ SY374 @ SV9 )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SV9 @ SY375 )
| ~ ( ~ ( rel_s4 @ SY375 @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY375 @ SX3 )
| ( big_f @ SY374 @ SX3 ) ) ) )
| ~ ! [SY377: mu] :
( ~ ( exists_in_world @ SY377 @ SV9 )
| ! [SY378: $i] :
( ~ ( rel_s4 @ SV9 @ SY378 )
| ~ ( ~ ( rel_s4 @ SY378 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) )
| ~ ~ ( big_f @ SY377 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY378 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
( ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
| ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV9: $i] :
( ( ( ~ ( rel_s4 @ sK2_SY320 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ! [SY374: mu] :
( ~ ( exists_in_world @ SY374 @ SV9 )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SV9 @ SY375 )
| ~ ( ~ ( rel_s4 @ SY375 @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY375 @ SX3 )
| ( big_f @ SY374 @ SX3 ) ) ) )
| ~ ! [SY377: mu] :
( ~ ( exists_in_world @ SY377 @ SV9 )
| ! [SY378: $i] :
( ~ ( rel_s4 @ SV9 @ SY378 )
| ~ ( ~ ( rel_s4 @ SY378 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) )
| ~ ~ ( big_f @ SY377 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY378 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(54,plain,
( ( ~ ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(55,plain,
( ( ~ ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV9: $i] :
( ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false )
| ( ( ~ ( ~ ! [SY374: mu] :
( ~ ( exists_in_world @ SY374 @ SV9 )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SV9 @ SY375 )
| ~ ( ~ ( rel_s4 @ SY375 @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY375 @ SX3 )
| ( big_f @ SY374 @ SX3 ) ) ) )
| ~ ! [SY377: mu] :
( ~ ( exists_in_world @ SY377 @ SV9 )
| ! [SY378: $i] :
( ~ ( rel_s4 @ SV9 @ SY378 )
| ~ ( ~ ( rel_s4 @ SY378 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) )
| ~ ~ ( big_f @ SY377 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY378 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
( ( sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(58,plain,
( ( ~ sK11_REN
| ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV9: $i] :
( ( ( ~ ! [SY374: mu] :
( ~ ( exists_in_world @ SY374 @ SV9 )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SV9 @ SY375 )
| ~ ( ~ ( rel_s4 @ SY375 @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY375 @ SX3 )
| ( big_f @ SY374 @ SX3 ) ) ) )
| ~ ! [SY377: mu] :
( ~ ( exists_in_world @ SY377 @ SV9 )
| ! [SY378: $i] :
( ~ ( rel_s4 @ SV9 @ SY378 )
| ~ ( ~ ( rel_s4 @ SY378 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) )
| ~ ~ ( big_f @ SY377 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY378 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
( ( sK11_REN = $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(61,plain,
( ( ( ~ sK11_REN ) = $true )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV9: $i] :
( ( ( ~ ! [SY374: mu] :
( ~ ( exists_in_world @ SY374 @ SV9 )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SV9 @ SY375 )
| ~ ( ~ ( rel_s4 @ SY375 @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY375 @ SX3 )
| ( big_f @ SY374 @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV9: $i] :
( ( ( ~ ! [SY377: mu] :
( ~ ( exists_in_world @ SY377 @ SV9 )
| ! [SY378: $i] :
( ~ ( rel_s4 @ SV9 @ SY378 )
| ~ ( ~ ( rel_s4 @ SY378 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) )
| ~ ~ ( big_f @ SY377 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY378 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(64,plain,
( ( ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
( ( sK11_REN = $false )
| ( ( ~ ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV9: $i] :
( ( ( ! [SY374: mu] :
( ~ ( exists_in_world @ SY374 @ SV9 )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SV9 @ SY375 )
| ~ ( ~ ( rel_s4 @ SY375 @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY375 @ SY374 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY375 @ SX3 )
| ( big_f @ SY374 @ SX3 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV9: $i] :
( ( ( ! [SY377: mu] :
( ~ ( exists_in_world @ SY377 @ SV9 )
| ! [SY378: $i] :
( ~ ( rel_s4 @ SV9 @ SY378 )
| ~ ( ~ ( rel_s4 @ SY378 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) )
| ~ ~ ( big_f @ SY377 @ ( sK9_SY72 @ SY378 @ SY377 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY378 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
( ( ( ~ ( rel_s4 @ sK2_SY320 @ sK3_SY352 ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
( ( ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV9: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV9 )
| ! [SY380: $i] :
( ~ ( rel_s4 @ SV9 @ SY380 )
| ~ ( ~ ( rel_s4 @ SY380 @ ( sK10_SY18 @ SY380 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY380 @ SV10 @ SV9 ) ) )
| ! [SY381: $i] :
( ~ ( rel_s4 @ SY380 @ SY381 )
| ( big_f @ SV10 @ SY381 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ SV11 @ SV9 )
| ! [SY382: $i] :
( ~ ( rel_s4 @ SV9 @ SY382 )
| ~ ( ~ ( rel_s4 @ SY382 @ ( sK9_SY72 @ SY382 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SY382 @ SV11 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY382 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(73,plain,
( ( ( rel_s4 @ sK2_SY320 @ sK3_SY352 )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
( ( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(75,plain,
( ( ( ~ ( rel_s4 @ sK2_SY320 @ sK5_SY347 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(76,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(77,plain,
! [SV9: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV9 ) )
= $true )
| ( ( ! [SY380: $i] :
( ~ ( rel_s4 @ SV9 @ SY380 )
| ~ ( ~ ( rel_s4 @ SY380 @ ( sK10_SY18 @ SY380 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY380 @ SV10 @ SV9 ) ) )
| ! [SY381: $i] :
( ~ ( rel_s4 @ SY380 @ SY381 )
| ( big_f @ SV10 @ SY381 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ SV11 @ SV9 ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV9 @ SY382 )
| ~ ( ~ ( rel_s4 @ SY382 @ ( sK9_SY72 @ SY382 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SY382 @ SV11 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY382 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(79,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
( ( ( rel_s4 @ sK2_SY320 @ sK5_SY347 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(81,plain,
( ( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) ) )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(82,plain,
! [SV9: $i,SV10: mu] :
( ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( ! [SY380: $i] :
( ~ ( rel_s4 @ SV9 @ SY380 )
| ~ ( ~ ( rel_s4 @ SY380 @ ( sK10_SY18 @ SY380 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SY380 @ SV10 @ SV9 ) ) )
| ! [SY381: $i] :
( ~ ( rel_s4 @ SY380 @ SY381 )
| ( big_f @ SV10 @ SY381 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV9: $i,SV11: mu] :
( ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( rel_s4 @ SV9 @ SY382 )
| ~ ( ~ ( rel_s4 @ SY382 @ ( sK9_SY72 @ SY382 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SY382 @ SV11 @ SV9 ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY382 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(85,plain,
( ( ( ~ ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(86,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV10: mu,SV12: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV12 )
| ~ ( ~ ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) )
| ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV11: mu,SV13: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV13 )
| ~ ( ~ ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) )
| ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(89,plain,
( ( ( ! [SX0: $i] :
( ~ ( rel_s4 @ sK3_SY352 @ SX0 )
| ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX0 @ SX2 )
| ( big_f @ SX1 @ SX2 ) ) ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(90,plain,
( ( ( ~ ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(91,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(92,plain,
( ( ( ~ ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(93,plain,
! [SV10: mu,SV12: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) )
| ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV11: mu,SV13: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) )
| ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV14: $i] :
( ( ( ~ ( rel_s4 @ sK3_SY352 @ SV14 )
| ! [SY386: mu] :
( ~ ( exists_in_world @ SY386 @ SV14 )
| ! [SY387: $i] :
( ~ ( rel_s4 @ SV14 @ SY387 )
| ( big_f @ SY386 @ SY387 ) ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(96,plain,
( ( ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
| ~ ~ ( p @ sK4_SY360 ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
( ( ( ! [SX0: $i] :
( ~ ( rel_s4 @ sK5_SY347 @ SX0 )
| ( p @ SX0 ) ) )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(98,plain,
( ( ( ~ ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) ) )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV10: mu,SV12: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) )
| ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV11: mu,SV13: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) )
| ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV14: $i] :
( ( ( ~ ( rel_s4 @ sK3_SY352 @ SV14 ) )
= $true )
| ( ( ! [SY386: mu] :
( ~ ( exists_in_world @ SY386 @ SV14 )
| ! [SY387: $i] :
( ~ ( rel_s4 @ SV14 @ SY387 )
| ( big_f @ SY386 @ SY387 ) ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(102,plain,
( ( ( ~ ( rel_s4 @ sK3_SY352 @ sK4_SY360 ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(103,plain,
( ( ( ~ ~ ( p @ sK4_SY360 ) )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(104,plain,
! [SV15: $i] :
( ( ( ~ ( rel_s4 @ sK5_SY347 @ SV15 )
| ( p @ SV15 ) )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(105,plain,
( ( ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
| ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) ) )
= $true )
| ( ( ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV9: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) ) )
= $true )
| ( ( ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV14: $i] :
( ( ( rel_s4 @ sK3_SY352 @ SV14 )
= $false )
| ( ( ! [SY386: mu] :
( ~ ( exists_in_world @ SY386 @ SV14 )
| ! [SY387: $i] :
( ~ ( rel_s4 @ SV14 @ SY387 )
| ( big_f @ SY386 @ SY387 ) ) ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(109,plain,
( ( ( rel_s4 @ sK3_SY352 @ sK4_SY360 )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(110,plain,
( ( ( ~ ( p @ sK4_SY360 ) )
= $true )
| ( sK11_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(111,plain,
! [SV15: $i] :
( ( ( ~ ( rel_s4 @ sK5_SY347 @ SV15 ) )
= $true )
| ( ( p @ SV15 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(112,plain,
( ( ( ~ ( rel_s4 @ sK5_SY347 @ sK6_SY362 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(113,plain,
( ( ( ~ ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(114,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
| ~ ~ ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) )
= $false )
| ( ( ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(115,plain,
! [SV9: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
| ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) )
= $false )
| ( ( ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(116,plain,
! [SV14: $i,SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ SV14 )
| ! [SY388: $i] :
( ~ ( rel_s4 @ SV14 @ SY388 )
| ( big_f @ SV16 @ SY388 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY352 @ SV14 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(117,plain,
( ( ( p @ sK4_SY360 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV15: $i] :
( ( ( rel_s4 @ sK5_SY347 @ SV15 )
= $false )
| ( ( p @ SV15 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(119,plain,
( ( ( rel_s4 @ sK5_SY347 @ sK6_SY362 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(120,plain,
( ( ( ~ ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) ) )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(121,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) )
= $false )
| ( ( ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( ~ ~ ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) )
= $false )
| ( ( ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(123,plain,
! [SV9: $i,SV11: mu,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) )
= $false )
| ( ( ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(124,plain,
! [SV9: $i,SV13: $i,SV11: mu] :
( ( ( ~ ~ ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) )
= $false )
| ( ( ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(125,plain,
! [SV14: $i,SV16: mu] :
( ( ( ~ ( exists_in_world @ SV16 @ SV14 ) )
= $true )
| ( ( ! [SY388: $i] :
( ~ ( rel_s4 @ SV14 @ SY388 )
| ( big_f @ SV16 @ SY388 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY352 @ SV14 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(126,plain,
( ( ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $true )
| ( ( ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(128,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( ~ ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) ) )
= $true )
| ( ( ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV9: $i,SV11: mu,SV13: $i] :
( ( ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $true )
| ( ( ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(130,plain,
! [SV9: $i,SV13: $i,SV11: mu] :
( ( ( ~ ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) ) )
= $true )
| ( ( ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(131,plain,
! [SV14: $i,SV16: mu] :
( ( ( exists_in_world @ SV16 @ SV14 )
= $false )
| ( ( ! [SY388: $i] :
( ~ ( rel_s4 @ SV14 @ SY388 )
| ( big_f @ SV16 @ SY388 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY352 @ SV14 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(132,plain,
( ( ( ~ ( exists_in_world @ sK7_SY365 @ sK6_SY362 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(133,plain,
( ( ( ~ ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(134,plain,
! [SV9: $i,SV10: mu,SV17: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV17 )
| ( big_f @ SV10 @ SV17 ) )
= $true )
| ( ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $false )
| ( ( ! [SY384: $i] :
( ~ ( rel_s4 @ SV12 @ SY384 )
| ( big_f @ SV10 @ SY384 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV9: $i,SV11: mu,SV18: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV18 )
| ( p @ SV18 ) )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV9: $i,SV13: $i,SV11: mu] :
( ( ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $false )
| ( ( ! [SY385: $i] :
( ~ ( rel_s4 @ SV13 @ SY385 )
| ( p @ SY385 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(138,plain,
! [SV16: mu,SV19: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV19 )
| ( big_f @ SV16 @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV16 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY352 @ SV14 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(139,plain,
( ( ( exists_in_world @ sK7_SY365 @ sK6_SY362 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(140,plain,
( ( ( ~ ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) ) )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(141,plain,
! [SV9: $i,SV10: mu,SV17: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV17 ) )
= $true )
| ( ( big_f @ SV10 @ SV17 )
= $true )
| ( ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(142,plain,
! [SV9: $i,SV10: mu,SV20: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV20 )
| ( big_f @ SV10 @ SV20 ) )
= $true )
| ( ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(143,plain,
! [SV9: $i,SV11: mu,SV18: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV18 ) )
= $true )
| ( ( p @ SV18 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV9: $i,SV11: mu,SV21: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV21 )
| ( p @ SV21 ) )
= $true )
| ( ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(145,plain,
! [SV16: mu,SV19: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV19 ) )
= $true )
| ( ( big_f @ SV16 @ SV19 )
= $true )
| ( ( exists_in_world @ SV16 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY352 @ SV14 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(146,plain,
( ( ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
| ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV9: $i,SV10: mu,SV17: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV17 )
= $false )
| ( ( big_f @ SV10 @ SV17 )
= $true )
| ( ( rel_s4 @ SV12 @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV9: $i,SV10: mu,SV20: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV20 ) )
= $true )
| ( ( big_f @ SV10 @ SV20 )
= $true )
| ( ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(149,plain,
! [SV9: $i,SV11: mu,SV18: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV18 )
= $false )
| ( ( p @ SV18 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(150,plain,
! [SV9: $i,SV11: mu,SV21: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV21 ) )
= $true )
| ( ( p @ SV21 )
= $true )
| ( ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(151,plain,
! [SV16: mu,SV19: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV19 )
= $false )
| ( ( big_f @ SV16 @ SV19 )
= $true )
| ( ( exists_in_world @ SV16 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY352 @ SV14 )
= $false )
| ( sK11_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(152,plain,
( ( ( ~ ( rel_s4 @ sK6_SY362 @ sK8_SY367 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(153,plain,
( ( ( ~ ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(154,plain,
! [SV9: $i,SV10: mu,SV20: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV20 )
= $false )
| ( ( big_f @ SV10 @ SV20 )
= $true )
| ( ( p @ ( sK10_SY18 @ SV12 @ SV10 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV9: $i,SV11: mu,SV21: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV21 )
= $false )
| ( ( p @ SV21 )
= $true )
| ( ( big_f @ SV11 @ ( sK9_SY72 @ SV13 @ SV11 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK2_SY320 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(156,plain,
( ( ( rel_s4 @ sK6_SY362 @ sK8_SY367 )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(157,plain,
( ( ( ~ ( big_f @ sK7_SY365 @ sK8_SY367 ) )
= $true )
| ( sK11_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(158,plain,
( ( ( big_f @ sK7_SY365 @ sK8_SY367 )
= $false )
| ( sK11_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(159,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,158,156,155,154,151,149,147,139,119,118,117,109,80,73,50,49,36,26]) ).
thf(160,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN052^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 17:15:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.04/0.43
% 1.04/0.43 No.of.Axioms: 4
% 1.04/0.43
% 1.04/0.43 Length.of.Defs: 5540
% 1.04/0.43
% 1.04/0.43 Contains.Choice.Funs: false
% 1.04/0.43 ...........
% 1.04/0.43
% 1.04/0.43 ********************************
% 1.04/0.43 * All subproblems solved! *
% 1.04/0.43 ********************************
% 1.04/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:159,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.04/0.43
% 1.04/0.43 %**** Beginning of derivation protocol ****
% 1.04/0.43 % SZS output start CNFRefutation
% See solution above
% 1.04/0.43
% 1.04/0.43 %**** End of derivation protocol ****
% 1.04/0.43 %**** no. of clauses in derivation: 160 ****
% 1.04/0.43 %**** clause counter: 159 ****
% 1.04/0.43
% 1.04/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:159,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------