TSTP Solution File: SYN397^7 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN397^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 08:25:57 EDT 2022
% Result : Theorem 1.29s 1.50s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 109
% Syntax : Number of formulae : 434 ( 58 unt; 72 typ; 32 def)
% Number of atoms : 4420 (1091 equ; 0 cnn)
% Maximal formula atoms : 28 ( 12 avg)
% Number of connectives : 8445 (1671 ~;1773 |; 9 &;4982 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 226 ( 226 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 71 usr; 19 con; 0-5 aty)
% Number of variables : 1502 ( 65 ^1430 !; 7 ?;1502 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_f,type,
f: 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_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK10_SY13,type,
sK10_SY13: $i ).
thf(tp_sK11_SY49,type,
sK11_SY49: $i ).
thf(tp_sK12_SY43,type,
sK12_SY43: mu ).
thf(tp_sK13_SY13,type,
sK13_SY13: $i ).
thf(tp_sK14_SY61,type,
sK14_SY61: $i ).
thf(tp_sK15_SY56,type,
sK15_SY56: mu > $i > $i ).
thf(tp_sK16_SY64,type,
sK16_SY64: mu ).
thf(tp_sK17_SY76,type,
sK17_SY76: $i ).
thf(tp_sK18_SY13,type,
sK18_SY13: $i > $i ).
thf(tp_sK19_SY13,type,
sK19_SY13: mu > $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i > mu ).
thf(tp_sK20_SY79,type,
sK20_SY79: mu ).
thf(tp_sK21_SY13,type,
sK21_SY13: mu > $i > $i ).
thf(tp_sK22_SY94,type,
sK22_SY94: $i > $i ).
thf(tp_sK23_SY84,type,
sK23_SY84: $i > mu > $i > $i ).
thf(tp_sK24_SY88,type,
sK24_SY88: mu ).
thf(tp_sK25_SY104,type,
sK25_SY104: $i > mu > $i ).
thf(tp_sK26_SY114,type,
sK26_SY114: $i > mu > $i ).
thf(tp_sK27_SY117,type,
sK27_SY117: $i > mu > $i > $i ).
thf(tp_sK28_SY118,type,
sK28_SY118: $i > mu ).
thf(tp_sK29_SY126,type,
sK29_SY126: mu > $i > mu ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK30_SY128,type,
sK30_SY128: $i > mu > $i > $i ).
thf(tp_sK31_SY129,type,
sK31_SY129: mu > $i > mu ).
thf(tp_sK32_SY137,type,
sK32_SY137: $i > mu > $i > $i ).
thf(tp_sK33_SY147,type,
sK33_SY147: $i > $i > mu > $i > $i ).
thf(tp_sK34_SY148,type,
sK34_SY148: $i > mu > $i > mu > $i > $i ).
thf(tp_sK35_SY149,type,
sK35_SY149: $i > mu > $i > mu > $i > $i ).
thf(tp_sK3_SY5,type,
sK3_SY5: $i ).
thf(tp_sK4_SY25,type,
sK4_SY25: $i ).
thf(tp_sK5_SY13,type,
sK5_SY13: $i ).
thf(tp_sK6_SY29,type,
sK6_SY29: mu ).
thf(tp_sK7_SY36,type,
sK7_SY36: $i ).
thf(tp_sK8_SY13,type,
sK8_SY13: $i ).
thf(tp_sK9_SY41,type,
sK9_SY41: $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
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish204) ).
thf(6,negated_conjecture,
( ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
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(extcnf_combined,[status(esa)],[1]) ).
thf(9,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(12,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(13,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)],[8]) ).
thf(14,plain,
( ( ~ ( mvalid
@ ( mand
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( f @ Y ) ) ) ) ) )
@ ( mbox_s4
@ ( mnot
@ ( mexists_ind
@ ^ [X: mu] : ( mbox_s4 @ ( f @ X ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(15,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( rel_s4 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(17,plain,
( ( ! [SX0: $i] : ( rel_s4 @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(18,plain,
! [SV1: $i] :
( ( exists_in_world @ ( sK1_X @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(19,plain,
! [SV2: mu] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ( exists_in_world @ SV2 @ SY0 )
| ~ ( rel_s4 @ SY0 @ SY1 )
| ( exists_in_world @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(21,plain,
! [SV3: $i] :
( ( ! [SY2: $i,SY3: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV3 @ SY2 )
| ~ ( rel_s4 @ SY2 @ SY3 ) )
| ( rel_s4 @ SV3 @ SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV4: $i] :
( ( rel_s4 @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV5: $i,SV2: mu] :
( ( ! [SY4: $i] :
( ~ ( exists_in_world @ SV2 @ SV5 )
| ~ ( rel_s4 @ SV5 @ SY4 )
| ( exists_in_world @ SV2 @ SY4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( ~ ! [SY5: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY5 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
| ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(25,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY21: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV3 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SY21 ) )
| ( rel_s4 @ SV3 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV7: $i,SV5: $i,SV2: mu] :
( ( ~ ( exists_in_world @ SV2 @ SV5 )
| ~ ( rel_s4 @ SV5 @ SV7 )
| ( exists_in_world @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ! [SY5: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY5 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
| ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV3 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SV8 ) )
| ( rel_s4 @ SV3 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV7: $i,SV5: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV5 )
| ~ ( rel_s4 @ SV5 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( ( ~ ! [SY5: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY5 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV3 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SV8 ) ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV7: $i,SV5: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV5 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV5 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( ! [SY5: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY5 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV3 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SV8 ) ) )
= $false )
| ( ( rel_s4 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV7: $i,SV5: $i,SV2: mu] :
( ( ( exists_in_world @ SV2 @ SV5 )
= $false )
| ( ( ~ ( rel_s4 @ SV5 @ SV7 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
| ~ ! [SY22: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY22 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY22 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY22 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SY25: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY25 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY25 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY25 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(37,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV2: mu,SV7: $i,SV5: $i] :
( ( ( rel_s4 @ SV5 @ SV7 )
= $false )
| ( ( exists_in_world @ SV2 @ SV5 )
= $false )
| ( ( exists_in_world @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK3_SY5 ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
( ( ( ~ ! [SY22: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY22 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY22 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY22 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) )
| ! [SY25: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY25 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY25 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY25 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV6 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV6 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
( ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,plain,
( ( ( ~ ! [SY22: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY22 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY22 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY22 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( ( ! [SY25: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY25 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY25 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY25 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( rel_s4 @ SV3 @ SV6 )
= $false )
| ( ( ~ ( rel_s4 @ SV6 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
( ( ( ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( ( ! [SY22: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY22 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY22 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY22 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(48,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
| ! [SY29: mu] :
( ~ ( exists_in_world @ SY29 @ sK4_SY25 )
| ! [SY30: $i] :
( ~ ( rel_s4 @ sK4_SY25 @ SY30 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY30 @ SX5 )
| ( f @ SY29 @ SX5 ) ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(49,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( rel_s4 @ SV6 @ SV8 )
= $false )
| ( ( rel_s4 @ SV3 @ SV6 )
= $false )
| ( ( rel_s4 @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK5_SY13 )
| ~ ! [SY32: $i] :
( ~ ( rel_s4 @ sK5_SY13 @ SY32 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY32 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY32 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY36: $i] :
( ~ ( rel_s4 @ sK5_SY13 @ SY36 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY36 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY36 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(51,plain,
! [SV9: $i] :
( ( ( ~ ( rel_s4 @ sK3_SY5 @ SV9 )
| ~ ~ ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV9 )
| ~ ! [SY40: $i] :
( ~ ( rel_s4 @ SV9 @ SY40 )
| ( f @ SY39 @ SY40 ) ) ) )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK4_SY25 ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( ( ! [SY29: mu] :
( ~ ( exists_in_world @ SY29 @ sK4_SY25 )
| ! [SY30: $i] :
( ~ ( rel_s4 @ sK4_SY25 @ SY30 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY30 @ SX5 )
| ( f @ SY29 @ SX5 ) ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(54,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK5_SY13 ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
( ( ( ~ ! [SY32: $i] :
( ~ ( rel_s4 @ sK5_SY13 @ SY32 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY32 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY32 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY36: $i] :
( ~ ( rel_s4 @ sK5_SY13 @ SY36 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY36 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY36 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV9: $i] :
( ( ( ~ ( rel_s4 @ sK3_SY5 @ SV9 ) )
= $true )
| ( ( ~ ~ ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV9 )
| ~ ! [SY40: $i] :
( ~ ( rel_s4 @ SV9 @ SY40 )
| ( f @ SY39 @ SY40 ) ) ) )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(57,plain,
( ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(58,plain,
( ( ( ~ ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
| ! [SY41: $i] :
( ~ ( rel_s4 @ sK4_SY25 @ SY41 )
| ~ ! [SY42: $i] :
( ~ ( rel_s4 @ SY41 @ SY42 )
| ( f @ sK6_SY29 @ SY42 ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[53]) ).
thf(59,plain,
( ( ( rel_s4 @ sK2_SX0 @ sK5_SY13 )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(60,plain,
( ( ( ~ ! [SY32: $i] :
( ~ ( rel_s4 @ sK5_SY13 @ SY32 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY32 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY32 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(61,plain,
( ( ( ! [SY36: $i] :
( ~ ( rel_s4 @ sK5_SY13 @ SY36 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY36 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY36 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(62,plain,
! [SV9: $i] :
( ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ~ ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV9 )
| ~ ! [SY40: $i] :
( ~ ( rel_s4 @ SV9 @ SY40 )
| ( f @ SY39 @ SY40 ) ) ) )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(63,plain,
( ( ( ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
( ( ( ~ ( exists_in_world @ sK6_SY29 @ sK4_SY25 ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
( ( ( ! [SY41: $i] :
( ~ ( rel_s4 @ sK4_SY25 @ SY41 )
| ~ ! [SY42: $i] :
( ~ ( rel_s4 @ SY41 @ SY42 )
| ( f @ sK6_SY29 @ SY42 ) ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
( ( ( ! [SY32: $i] :
( ~ ( rel_s4 @ sK5_SY13 @ SY32 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY32 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY32 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
( ( ( ~ ( rel_s4 @ sK5_SY13 @ sK7_SY36 )
| ~ ~ ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ sK7_SY36 )
| ~ ! [SY44: $i] :
( ~ ( rel_s4 @ sK7_SY36 @ SY44 )
| ( f @ SY43 @ SY44 ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(68,plain,
! [SV9: $i] :
( ( ( ~ ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV9 )
| ~ ! [SY40: $i] :
( ~ ( rel_s4 @ SV9 @ SY40 )
| ( f @ SY39 @ SY40 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK8_SY13 )
| ~ ! [SY45: $i] :
( ~ ( rel_s4 @ sK8_SY13 @ SY45 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY45 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY45 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY49: $i] :
( ~ ( rel_s4 @ sK8_SY13 @ SY49 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY49 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY49 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(70,plain,
( ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
( ( ( ~ ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
| ~ ! [SY52: $i] :
( ~ ( rel_s4 @ sK9_SY41 @ SY52 )
| ( f @ sK6_SY29 @ SY52 ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(72,plain,
! [SV10: $i] :
( ( ( ~ ( rel_s4 @ sK5_SY13 @ SV10 )
| ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV10 )
| ! [SY54: $i] :
( ~ ( rel_s4 @ SV10 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( f @ SY53 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
( ( ( ~ ( rel_s4 @ sK5_SY13 @ sK7_SY36 ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(74,plain,
( ( ( ~ ~ ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ sK7_SY36 )
| ~ ! [SY44: $i] :
( ~ ( rel_s4 @ sK7_SY36 @ SY44 )
| ( f @ SY43 @ SY44 ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[67]) ).
thf(75,plain,
! [SV9: $i] :
( ( ( ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV9 )
| ~ ! [SY40: $i] :
( ~ ( rel_s4 @ SV9 @ SY40 )
| ( f @ SY39 @ SY40 ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(76,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK8_SY13 ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(77,plain,
( ( ( ~ ! [SY45: $i] :
( ~ ( rel_s4 @ sK8_SY13 @ SY45 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY45 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY45 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY49: $i] :
( ~ ( rel_s4 @ sK8_SY13 @ SY49 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY49 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY49 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(78,plain,
( ( ( ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(79,plain,
( ( ( ~ ( rel_s4 @ sK4_SY25 @ sK9_SY41 ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(80,plain,
( ( ( ~ ! [SY52: $i] :
( ~ ( rel_s4 @ sK9_SY41 @ SY52 )
| ( f @ sK6_SY29 @ SY52 ) ) )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(81,plain,
! [SV10: $i] :
( ( ( ~ ( rel_s4 @ sK5_SY13 @ SV10 ) )
= $true )
| ( ( ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV10 )
| ! [SY54: $i] :
( ~ ( rel_s4 @ SV10 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( f @ SY53 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
( ( ( rel_s4 @ sK5_SY13 @ sK7_SY36 )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(83,plain,
( ( ( ~ ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ sK7_SY36 )
| ~ ! [SY44: $i] :
( ~ ( rel_s4 @ sK7_SY36 @ SY44 )
| ( f @ SY43 @ SY44 ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(84,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ SV11 @ SV9 )
| ~ ! [SY56: $i] :
( ~ ( rel_s4 @ SV9 @ SY56 )
| ( f @ SV11 @ SY56 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(85,plain,
( ( ( rel_s4 @ sK2_SX0 @ sK8_SY13 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(86,plain,
( ( ( ~ ! [SY45: $i] :
( ~ ( rel_s4 @ sK8_SY13 @ SY45 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY45 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY45 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(87,plain,
( ( ( ! [SY49: $i] :
( ~ ( rel_s4 @ sK8_SY13 @ SY49 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY49 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY49 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(88,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK10_SY13 )
| ~ ! [SY57: $i] :
( ~ ( rel_s4 @ sK10_SY13 @ SY57 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY57 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY57 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY61: $i] :
( ~ ( rel_s4 @ sK10_SY13 @ SY61 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY61 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY61 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[78]) ).
thf(89,plain,
( ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(90,plain,
( ( ( ! [SY52: $i] :
( ~ ( rel_s4 @ sK9_SY41 @ SY52 )
| ( f @ sK6_SY29 @ SY52 ) ) )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(91,plain,
! [SV10: $i] :
( ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV10 )
| ! [SY54: $i] :
( ~ ( rel_s4 @ SV10 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( f @ SY53 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(92,plain,
( ( ( ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ sK7_SY36 )
| ~ ! [SY44: $i] :
( ~ ( rel_s4 @ sK7_SY36 @ SY44 )
| ( f @ SY43 @ SY44 ) ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ SV11 @ SV9 ) )
= $true )
| ( ( ~ ! [SY56: $i] :
( ~ ( rel_s4 @ SV9 @ SY56 )
| ( f @ SV11 @ SY56 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(94,plain,
( ( ( ! [SY45: $i] :
( ~ ( rel_s4 @ sK8_SY13 @ SY45 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY45 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY45 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(95,plain,
( ( ( ~ ( rel_s4 @ sK8_SY13 @ sK11_SY49 )
| ~ ~ ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ sK11_SY49 )
| ~ ! [SY65: $i] :
( ~ ( rel_s4 @ sK11_SY49 @ SY65 )
| ( f @ SY64 @ SY65 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(96,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK10_SY13 ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(97,plain,
( ( ( ~ ! [SY57: $i] :
( ~ ( rel_s4 @ sK10_SY13 @ SY57 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY57 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY57 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY61: $i] :
( ~ ( rel_s4 @ sK10_SY13 @ SY61 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY61 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY61 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(98,plain,
( ( ( ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s4 @ sK9_SY41 @ SV12 )
| ( f @ sK6_SY29 @ SV12 ) )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV10: $i,SV13: mu] :
( ( ( ~ ( exists_in_world @ SV13 @ SV10 )
| ! [SY66: $i] :
( ~ ( rel_s4 @ SV10 @ SY66 )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SY66 @ SY67 )
| ( f @ SV13 @ SY67 ) ) ) )
= $true )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(101,plain,
( ( ( ~ ( exists_in_world @ sK12_SY43 @ sK7_SY36 )
| ~ ! [SY68: $i] :
( ~ ( rel_s4 @ sK7_SY36 @ SY68 )
| ( f @ sK12_SY43 @ SY68 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(102,plain,
! [SV9: $i,SV11: mu] :
( ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( ~ ! [SY56: $i] :
( ~ ( rel_s4 @ SV9 @ SY56 )
| ( f @ SV11 @ SY56 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV14: $i] :
( ( ( ~ ( rel_s4 @ sK8_SY13 @ SV14 )
| ! [SY69: mu] :
( ~ ( exists_in_world @ SY69 @ SV14 )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SV14 @ SY70 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY70 @ SX5 )
| ( f @ SY69 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(104,plain,
( ( ( ~ ( rel_s4 @ sK8_SY13 @ sK11_SY49 ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(105,plain,
( ( ( ~ ~ ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ sK11_SY49 )
| ~ ! [SY65: $i] :
( ~ ( rel_s4 @ sK11_SY49 @ SY65 )
| ( f @ SY64 @ SY65 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(106,plain,
( ( ( rel_s4 @ sK2_SX0 @ sK10_SY13 )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(107,plain,
( ( ( ~ ! [SY57: $i] :
( ~ ( rel_s4 @ sK10_SY13 @ SY57 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY57 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY57 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(108,plain,
( ( ( ! [SY61: $i] :
( ~ ( rel_s4 @ sK10_SY13 @ SY61 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY61 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY61 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(109,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK13_SY13 )
| ~ ! [SY72: $i] :
( ~ ( rel_s4 @ sK13_SY13 @ SY72 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY72 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY72 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY76: $i] :
( ~ ( rel_s4 @ sK13_SY13 @ SY76 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY76 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY76 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(110,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s4 @ sK9_SY41 @ SV12 ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV10: $i,SV13: mu] :
( ( ( ~ ( exists_in_world @ SV13 @ SV10 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( rel_s4 @ SV10 @ SY66 )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SY66 @ SY67 )
| ( f @ SV13 @ SY67 ) ) ) )
= $true )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(112,plain,
( ( ( ~ ( exists_in_world @ sK12_SY43 @ sK7_SY36 ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(113,plain,
( ( ( ~ ! [SY68: $i] :
( ~ ( rel_s4 @ sK7_SY36 @ SY68 )
| ( f @ sK12_SY43 @ SY68 ) ) )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(114,plain,
! [SV11: mu,SV9: $i] :
( ( ( ! [SY56: $i] :
( ~ ( rel_s4 @ SV9 @ SY56 )
| ( f @ SV11 @ SY56 ) ) )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV14: $i] :
( ( ( ~ ( rel_s4 @ sK8_SY13 @ SV14 ) )
= $true )
| ( ( ! [SY69: mu] :
( ~ ( exists_in_world @ SY69 @ SV14 )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SV14 @ SY70 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY70 @ SX5 )
| ( f @ SY69 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(116,plain,
( ( ( rel_s4 @ sK8_SY13 @ sK11_SY49 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(117,plain,
( ( ( ~ ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ sK11_SY49 )
| ~ ! [SY65: $i] :
( ~ ( rel_s4 @ sK11_SY49 @ SY65 )
| ( f @ SY64 @ SY65 ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(118,plain,
( ( ( ! [SY57: $i] :
( ~ ( rel_s4 @ sK10_SY13 @ SY57 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY57 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY57 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(119,plain,
( ( ( ~ ( rel_s4 @ sK10_SY13 @ sK14_SY61 )
| ~ ~ ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ sK14_SY61 )
| ~ ! [SY80: $i] :
( ~ ( rel_s4 @ sK14_SY61 @ SY80 )
| ( f @ SY79 @ SY80 ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(120,plain,
( ( ( ~ ( rel_s4 @ sK2_SX0 @ sK13_SY13 ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(121,plain,
( ( ( ~ ! [SY72: $i] :
( ~ ( rel_s4 @ sK13_SY13 @ SY72 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY72 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY72 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY76: $i] :
( ~ ( rel_s4 @ sK13_SY13 @ SY76 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY76 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY76 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(122,plain,
! [SV12: $i] :
( ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV10: $i,SV13: mu] :
( ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( rel_s4 @ SV10 @ SY66 )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SY66 @ SY67 )
| ( f @ SV13 @ SY67 ) ) ) )
= $true )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(124,plain,
( ( ( exists_in_world @ sK12_SY43 @ sK7_SY36 )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(125,plain,
( ( ( ! [SY68: $i] :
( ~ ( rel_s4 @ sK7_SY36 @ SY68 )
| ( f @ sK12_SY43 @ SY68 ) ) )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(126,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
| ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(127,plain,
! [SV14: $i] :
( ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( ! [SY69: mu] :
( ~ ( exists_in_world @ SY69 @ SV14 )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SV14 @ SY70 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY70 @ SX5 )
| ( f @ SY69 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(128,plain,
( ( ( ! [SY64: mu] :
( ~ ( exists_in_world @ SY64 @ sK11_SY49 )
| ~ ! [SY65: $i] :
( ~ ( rel_s4 @ sK11_SY49 @ SY65 )
| ( f @ SY64 @ SY65 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(129,plain,
! [SV15: $i] :
( ( ( ~ ( rel_s4 @ sK10_SY13 @ SV15 )
| ! [SY81: mu] :
( ~ ( exists_in_world @ SY81 @ SV15 )
| ! [SY82: $i] :
( ~ ( rel_s4 @ SV15 @ SY82 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY82 @ SX5 )
| ( f @ SY81 @ SX5 ) ) ) ) )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(130,plain,
( ( ( ~ ( rel_s4 @ sK10_SY13 @ sK14_SY61 ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(131,plain,
( ( ( ~ ~ ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ sK14_SY61 )
| ~ ! [SY80: $i] :
( ~ ( rel_s4 @ sK14_SY61 @ SY80 )
| ( f @ SY79 @ SY80 ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(132,plain,
( ( ( rel_s4 @ sK2_SX0 @ sK13_SY13 )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(133,plain,
( ( ( ~ ! [SY72: $i] :
( ~ ( rel_s4 @ sK13_SY13 @ SY72 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY72 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY72 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(134,plain,
( ( ( ! [SY76: $i] :
( ~ ( rel_s4 @ sK13_SY13 @ SY76 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY76 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY76 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(135,plain,
! [SV12: $i] :
( ( ( ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(136,plain,
! [SV13: mu,SV16: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV16 )
| ~ ! [SY84: $i] :
( ~ ( rel_s4 @ SV16 @ SY84 )
| ( f @ SV13 @ SY84 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(137,plain,
! [SV17: $i] :
( ( ( ~ ( rel_s4 @ sK7_SY36 @ SV17 )
| ( f @ sK12_SY43 @ SV17 ) )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) ) )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(139,plain,
! [SV9: $i,SV11: mu] :
( ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(140,plain,
! [SV14: $i,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ SV14 )
| ! [SY85: $i] :
( ~ ( rel_s4 @ SV14 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( rel_s4 @ SY85 @ SY86 )
| ( f @ SV18 @ SY86 ) ) ) )
= $true )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(141,plain,
( ( ( ~ ( exists_in_world @ sK16_SY64 @ sK11_SY49 )
| ~ ! [SY87: $i] :
( ~ ( rel_s4 @ sK11_SY49 @ SY87 )
| ( f @ sK16_SY64 @ SY87 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(142,plain,
! [SV15: $i] :
( ( ( ~ ( rel_s4 @ sK10_SY13 @ SV15 ) )
= $true )
| ( ( ! [SY81: mu] :
( ~ ( exists_in_world @ SY81 @ SV15 )
| ! [SY82: $i] :
( ~ ( rel_s4 @ SV15 @ SY82 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY82 @ SX5 )
| ( f @ SY81 @ SX5 ) ) ) ) )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(143,plain,
( ( ( rel_s4 @ sK10_SY13 @ sK14_SY61 )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(144,plain,
( ( ( ~ ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ sK14_SY61 )
| ~ ! [SY80: $i] :
( ~ ( rel_s4 @ sK14_SY61 @ SY80 )
| ( f @ SY79 @ SY80 ) ) ) )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(145,plain,
( ( ( ! [SY72: $i] :
( ~ ( rel_s4 @ sK13_SY13 @ SY72 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY72 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY72 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(146,plain,
( ( ( ~ ( rel_s4 @ sK13_SY13 @ sK17_SY76 )
| ~ ~ ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ sK17_SY76 )
| ~ ! [SY89: $i] :
( ~ ( rel_s4 @ sK17_SY76 @ SY89 )
| ( f @ SY88 @ SY89 ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[134]) ).
thf(147,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s4 @ sK2_SX0 @ ( sK18_SY13 @ SV12 ) )
| ~ ! [SY90: $i] :
( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SY90 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY90 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY90 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY94: $i] :
( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SY94 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY94 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY94 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[135]) ).
thf(148,plain,
! [SV13: mu,SV16: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV16 ) )
= $true )
| ( ( ~ ! [SY84: $i] :
( ~ ( rel_s4 @ SV16 @ SY84 )
| ( f @ SV13 @ SY84 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV17: $i] :
( ( ( ~ ( rel_s4 @ sK7_SY36 @ SV17 ) )
= $true )
| ( ( f @ sK12_SY43 @ SV17 )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV11: mu,SV9: $i] :
( ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ~ ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(151,plain,
! [SV11: mu,SV9: $i] :
( ( ( ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV14: $i,SV18: mu] :
( ( ( ~ ( exists_in_world @ SV18 @ SV14 ) )
= $true )
| ( ( ! [SY85: $i] :
( ~ ( rel_s4 @ SV14 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( rel_s4 @ SY85 @ SY86 )
| ( f @ SV18 @ SY86 ) ) ) )
= $true )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(153,plain,
( ( ( ~ ( exists_in_world @ sK16_SY64 @ sK11_SY49 ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(154,plain,
( ( ( ~ ! [SY87: $i] :
( ~ ( rel_s4 @ sK11_SY49 @ SY87 )
| ( f @ sK16_SY64 @ SY87 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(155,plain,
! [SV15: $i] :
( ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( ! [SY81: mu] :
( ~ ( exists_in_world @ SY81 @ SV15 )
| ! [SY82: $i] :
( ~ ( rel_s4 @ SV15 @ SY82 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY82 @ SX5 )
| ( f @ SY81 @ SX5 ) ) ) ) )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(156,plain,
( ( ( ! [SY79: mu] :
( ~ ( exists_in_world @ SY79 @ sK14_SY61 )
| ~ ! [SY80: $i] :
( ~ ( rel_s4 @ sK14_SY61 @ SY80 )
| ( f @ SY79 @ SY80 ) ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV19: $i] :
( ( ( ~ ( rel_s4 @ sK13_SY13 @ SV19 )
| ! [SY97: mu] :
( ~ ( exists_in_world @ SY97 @ SV19 )
| ! [SY98: $i] :
( ~ ( rel_s4 @ SV19 @ SY98 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY98 @ SX5 )
| ( f @ SY97 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(158,plain,
( ( ( ~ ( rel_s4 @ sK13_SY13 @ sK17_SY76 ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(159,plain,
( ( ( ~ ~ ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ sK17_SY76 )
| ~ ! [SY89: $i] :
( ~ ( rel_s4 @ sK17_SY76 @ SY89 )
| ( f @ SY88 @ SY89 ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(160,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s4 @ sK2_SX0 @ ( sK18_SY13 @ SV12 ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(161,plain,
! [SV12: $i] :
( ( ( ~ ! [SY90: $i] :
( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SY90 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY90 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY90 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY94: $i] :
( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SY94 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY94 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY94 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(162,plain,
! [SV13: mu,SV16: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV16 )
= $false )
| ( ( ~ ! [SY84: $i] :
( ~ ( rel_s4 @ SV16 @ SY84 )
| ( f @ SV13 @ SY84 ) ) )
= $true )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(163,plain,
! [SV17: $i] :
( ( ( rel_s4 @ sK7_SY36 @ SV17 )
= $false )
| ( ( f @ sK12_SY43 @ SV17 )
= $true )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV11: mu,SV9: $i] :
( ( ( ! [SY13: $i] :
( ~ ( rel_s4 @ sK2_SX0 @ SY13 )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( rel_s4 @ SY13 @ SX2 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ sK2_SX0 @ ( sK19_SY13 @ SV11 @ SV9 ) )
| ~ ! [SY100: $i] :
( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SY100 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY100 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY100 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY104: $i] :
( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SY104 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY104 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY104 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[151]) ).
thf(166,plain,
! [SV14: $i,SV18: mu] :
( ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( ! [SY85: $i] :
( ~ ( rel_s4 @ SV14 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( rel_s4 @ SY85 @ SY86 )
| ( f @ SV18 @ SY86 ) ) ) )
= $true )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(167,plain,
( ( ( exists_in_world @ sK16_SY64 @ sK11_SY49 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(168,plain,
( ( ( ! [SY87: $i] :
( ~ ( rel_s4 @ sK11_SY49 @ SY87 )
| ( f @ sK16_SY64 @ SY87 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(169,plain,
! [SV15: $i,SV20: mu] :
( ( ( ~ ( exists_in_world @ SV20 @ SV15 )
| ! [SY107: $i] :
( ~ ( rel_s4 @ SV15 @ SY107 )
| ~ ! [SY108: $i] :
( ~ ( rel_s4 @ SY107 @ SY108 )
| ( f @ SV20 @ SY108 ) ) ) )
= $true )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(170,plain,
( ( ( ~ ( exists_in_world @ sK20_SY79 @ sK14_SY61 )
| ~ ! [SY109: $i] :
( ~ ( rel_s4 @ sK14_SY61 @ SY109 )
| ( f @ sK20_SY79 @ SY109 ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[156]) ).
thf(171,plain,
! [SV19: $i] :
( ( ( ~ ( rel_s4 @ sK13_SY13 @ SV19 ) )
= $true )
| ( ( ! [SY97: mu] :
( ~ ( exists_in_world @ SY97 @ SV19 )
| ! [SY98: $i] :
( ~ ( rel_s4 @ SV19 @ SY98 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY98 @ SX5 )
| ( f @ SY97 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(172,plain,
( ( ( rel_s4 @ sK13_SY13 @ sK17_SY76 )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(173,plain,
( ( ( ~ ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ sK17_SY76 )
| ~ ! [SY89: $i] :
( ~ ( rel_s4 @ sK17_SY76 @ SY89 )
| ( f @ SY88 @ SY89 ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(174,plain,
! [SV12: $i] :
( ( ( rel_s4 @ sK2_SX0 @ ( sK18_SY13 @ SV12 ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(175,plain,
! [SV12: $i] :
( ( ( ~ ! [SY90: $i] :
( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SY90 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY90 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY90 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(176,plain,
! [SV12: $i] :
( ( ( ! [SY94: $i] :
( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SY94 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY94 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY94 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(177,plain,
! [SV10: $i,SV13: mu,SV16: $i] :
( ( ( ! [SY84: $i] :
( ~ ( rel_s4 @ SV16 @ SY84 )
| ( f @ SV13 @ SY84 ) ) )
= $false )
| ( ( rel_s4 @ SV10 @ SV16 )
= $false )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ sK2_SX0 @ ( sK21_SY13 @ SV11 @ SV9 ) )
| ~ ! [SY110: $i] :
( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SY110 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY110 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY110 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY114: $i] :
( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SY114 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY114 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY114 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[164]) ).
thf(179,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ sK2_SX0 @ ( sK19_SY13 @ SV11 @ SV9 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(180,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SY100 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY100 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY100 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY104: $i] :
( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SY104 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY104 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY104 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(181,plain,
! [SV18: mu,SV21: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV21 )
| ~ ! [SY117: $i] :
( ~ ( rel_s4 @ SV21 @ SY117 )
| ( f @ SV18 @ SY117 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(182,plain,
! [SV22: $i] :
( ( ( ~ ( rel_s4 @ sK11_SY49 @ SV22 )
| ( f @ sK16_SY64 @ SV22 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(183,plain,
! [SV15: $i,SV20: mu] :
( ( ( ~ ( exists_in_world @ SV20 @ SV15 ) )
= $true )
| ( ( ! [SY107: $i] :
( ~ ( rel_s4 @ SV15 @ SY107 )
| ~ ! [SY108: $i] :
( ~ ( rel_s4 @ SY107 @ SY108 )
| ( f @ SV20 @ SY108 ) ) ) )
= $true )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(184,plain,
( ( ( ~ ( exists_in_world @ sK20_SY79 @ sK14_SY61 ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(185,plain,
( ( ( ~ ! [SY109: $i] :
( ~ ( rel_s4 @ sK14_SY61 @ SY109 )
| ( f @ sK20_SY79 @ SY109 ) ) )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(186,plain,
! [SV19: $i] :
( ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( ! [SY97: mu] :
( ~ ( exists_in_world @ SY97 @ SV19 )
| ! [SY98: $i] :
( ~ ( rel_s4 @ SV19 @ SY98 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY98 @ SX5 )
| ( f @ SY97 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(187,plain,
( ( ( ! [SY88: mu] :
( ~ ( exists_in_world @ SY88 @ sK17_SY76 )
| ~ ! [SY89: $i] :
( ~ ( rel_s4 @ sK17_SY76 @ SY89 )
| ( f @ SY88 @ SY89 ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(188,plain,
! [SV12: $i] :
( ( ( ! [SY90: $i] :
( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SY90 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY90 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY90 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(189,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ ( sK22_SY94 @ SV12 ) )
| ~ ~ ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ ( sK22_SY94 @ SV12 ) )
| ~ ! [SY119: $i] :
( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SY119 )
| ( f @ SY118 @ SY119 ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[176]) ).
thf(190,plain,
! [SV13: mu,SV10: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ ( sK23_SY84 @ SV10 @ SV13 @ SV16 ) )
| ( f @ SV13 @ ( sK23_SY84 @ SV10 @ SV13 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ SV10 @ SV16 )
= $false )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[177]) ).
thf(191,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ sK2_SX0 @ ( sK21_SY13 @ SV11 @ SV9 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(192,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ! [SY110: $i] :
( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SY110 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY110 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY110 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) )
| ! [SY114: $i] :
( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SY114 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY114 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY114 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(193,plain,
! [SV9: $i,SV11: mu] :
( ( ( rel_s4 @ sK2_SX0 @ ( sK19_SY13 @ SV11 @ SV9 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(194,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ! [SY100: $i] :
( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SY100 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY100 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY100 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(195,plain,
! [SV9: $i,SV11: mu] :
( ( ( ! [SY104: $i] :
( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SY104 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY104 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY104 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(196,plain,
! [SV18: mu,SV21: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV21 ) )
= $true )
| ( ( ~ ! [SY117: $i] :
( ~ ( rel_s4 @ SV21 @ SY117 )
| ( f @ SV18 @ SY117 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(197,plain,
! [SV22: $i] :
( ( ( ~ ( rel_s4 @ sK11_SY49 @ SV22 ) )
= $true )
| ( ( f @ sK16_SY64 @ SV22 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(198,plain,
! [SV15: $i,SV20: mu] :
( ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( ! [SY107: $i] :
( ~ ( rel_s4 @ SV15 @ SY107 )
| ~ ! [SY108: $i] :
( ~ ( rel_s4 @ SY107 @ SY108 )
| ( f @ SV20 @ SY108 ) ) ) )
= $true )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(199,plain,
( ( ( exists_in_world @ sK20_SY79 @ sK14_SY61 )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(200,plain,
( ( ( ! [SY109: $i] :
( ~ ( rel_s4 @ sK14_SY61 @ SY109 )
| ( f @ sK20_SY79 @ SY109 ) ) )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(201,plain,
! [SV19: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV19 )
| ! [SY120: $i] :
( ~ ( rel_s4 @ SV19 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( rel_s4 @ SY120 @ SY121 )
| ( f @ SV23 @ SY121 ) ) ) )
= $true )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(202,plain,
( ( ( ~ ( exists_in_world @ sK24_SY88 @ sK17_SY76 )
| ~ ! [SY122: $i] :
( ~ ( rel_s4 @ sK17_SY76 @ SY122 )
| ( f @ sK24_SY88 @ SY122 ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[187]) ).
thf(203,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
| ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV24 )
| ! [SY124: $i] :
( ~ ( rel_s4 @ SV24 @ SY124 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY124 @ SX5 )
| ( f @ SY123 @ SX5 ) ) ) ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(204,plain,
! [SV12: $i] :
( ( ( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ ( sK22_SY94 @ SV12 ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(205,plain,
! [SV12: $i] :
( ( ( ~ ~ ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ ( sK22_SY94 @ SV12 ) )
| ~ ! [SY119: $i] :
( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SY119 )
| ( f @ SY118 @ SY119 ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(206,plain,
! [SV13: mu,SV10: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ ( sK23_SY84 @ SV10 @ SV13 @ SV16 ) ) )
= $false )
| ( ( rel_s4 @ SV10 @ SV16 )
= $false )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(207,plain,
! [SV16: $i,SV10: $i,SV13: mu] :
( ( ( f @ SV13 @ ( sK23_SY84 @ SV10 @ SV13 @ SV16 ) )
= $false )
| ( ( rel_s4 @ SV10 @ SV16 )
= $false )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(208,plain,
! [SV9: $i,SV11: mu] :
( ( ( rel_s4 @ sK2_SX0 @ ( sK21_SY13 @ SV11 @ SV9 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(209,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ! [SY110: $i] :
( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SY110 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY110 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY110 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(210,plain,
! [SV9: $i,SV11: mu] :
( ( ( ! [SY114: $i] :
( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SY114 )
| ~ ~ ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY114 )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY114 @ SX4 )
| ( f @ SX3 @ SX4 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(211,plain,
! [SV9: $i,SV11: mu] :
( ( ( ! [SY100: $i] :
( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SY100 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY100 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY100 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(212,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ ( sK25_SY104 @ SV9 @ SV11 ) )
| ~ ~ ! [SY126: mu] :
( ~ ( exists_in_world @ SY126 @ ( sK25_SY104 @ SV9 @ SV11 ) )
| ~ ! [SY127: $i] :
( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SY127 )
| ( f @ SY126 @ SY127 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[195]) ).
thf(213,plain,
! [SV18: mu,SV21: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV21 )
= $false )
| ( ( ~ ! [SY117: $i] :
( ~ ( rel_s4 @ SV21 @ SY117 )
| ( f @ SV18 @ SY117 ) ) )
= $true )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV22: $i] :
( ( ( rel_s4 @ sK11_SY49 @ SV22 )
= $false )
| ( ( f @ sK16_SY64 @ SV22 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV20: mu,SV25: $i,SV15: $i] :
( ( ( ~ ( rel_s4 @ SV15 @ SV25 )
| ~ ! [SY128: $i] :
( ~ ( rel_s4 @ SV25 @ SY128 )
| ( f @ SV20 @ SY128 ) ) )
= $true )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(216,plain,
! [SV26: $i] :
( ( ( ~ ( rel_s4 @ sK14_SY61 @ SV26 )
| ( f @ sK20_SY79 @ SV26 ) )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(217,plain,
! [SV19: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV19 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( rel_s4 @ SV19 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( rel_s4 @ SY120 @ SY121 )
| ( f @ SV23 @ SY121 ) ) ) )
= $true )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(218,plain,
( ( ( ~ ( exists_in_world @ sK24_SY88 @ sK17_SY76 ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(219,plain,
( ( ( ~ ! [SY122: $i] :
( ~ ( rel_s4 @ sK17_SY76 @ SY122 )
| ( f @ sK24_SY88 @ SY122 ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(220,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 ) )
= $true )
| ( ( ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV24 )
| ! [SY124: $i] :
( ~ ( rel_s4 @ SV24 @ SY124 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY124 @ SX5 )
| ( f @ SY123 @ SX5 ) ) ) ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(221,plain,
! [SV12: $i] :
( ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ ( sK22_SY94 @ SV12 ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(222,plain,
! [SV12: $i] :
( ( ( ~ ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ ( sK22_SY94 @ SV12 ) )
| ~ ! [SY119: $i] :
( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SY119 )
| ( f @ SY118 @ SY119 ) ) ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(223,plain,
! [SV13: mu,SV10: $i,SV16: $i] :
( ( ( rel_s4 @ SV16 @ ( sK23_SY84 @ SV10 @ SV13 @ SV16 ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV16 )
= $false )
| ( ( exists_in_world @ SV13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK5_SY13 @ SV10 )
= $false )
| ( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(224,plain,
! [SV9: $i,SV11: mu] :
( ( ( ! [SY110: $i] :
( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SY110 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SY110 )
| ! [SX4: $i] :
( ~ ( rel_s4 @ SY110 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( f @ SX3 @ SX5 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(225,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ ( sK26_SY114 @ SV9 @ SV11 ) )
| ~ ~ ! [SY129: mu] :
( ~ ( exists_in_world @ SY129 @ ( sK26_SY114 @ SV9 @ SV11 ) )
| ~ ! [SY130: $i] :
( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SY130 )
| ( f @ SY129 @ SY130 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[210]) ).
thf(226,plain,
! [SV27: $i,SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
| ! [SY131: mu] :
( ~ ( exists_in_world @ SY131 @ SV27 )
| ! [SY132: $i] :
( ~ ( rel_s4 @ SV27 @ SY132 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY132 @ SX5 )
| ( f @ SY131 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(227,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ ( sK25_SY104 @ SV9 @ SV11 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(228,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ~ ! [SY126: mu] :
( ~ ( exists_in_world @ SY126 @ ( sK25_SY104 @ SV9 @ SV11 ) )
| ~ ! [SY127: $i] :
( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SY127 )
| ( f @ SY126 @ SY127 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(229,plain,
! [SV14: $i,SV18: mu,SV21: $i] :
( ( ( ! [SY117: $i] :
( ~ ( rel_s4 @ SV21 @ SY117 )
| ( f @ SV18 @ SY117 ) ) )
= $false )
| ( ( rel_s4 @ SV14 @ SV21 )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(230,plain,
! [SV20: mu,SV25: $i,SV15: $i] :
( ( ( ~ ( rel_s4 @ SV15 @ SV25 ) )
= $true )
| ( ( ~ ! [SY128: $i] :
( ~ ( rel_s4 @ SV25 @ SY128 )
| ( f @ SV20 @ SY128 ) ) )
= $true )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(231,plain,
! [SV26: $i] :
( ( ( ~ ( rel_s4 @ sK14_SY61 @ SV26 ) )
= $true )
| ( ( f @ sK20_SY79 @ SV26 )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(232,plain,
! [SV19: $i,SV23: mu] :
( ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( rel_s4 @ SV19 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( rel_s4 @ SY120 @ SY121 )
| ( f @ SV23 @ SY121 ) ) ) )
= $true )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(233,plain,
( ( ( exists_in_world @ sK24_SY88 @ sK17_SY76 )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(234,plain,
( ( ( ! [SY122: $i] :
( ~ ( rel_s4 @ sK17_SY76 @ SY122 )
| ( f @ sK24_SY88 @ SY122 ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(235,plain,
! [SV24: $i,SV12: $i] :
( ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( ! [SY123: mu] :
( ~ ( exists_in_world @ SY123 @ SV24 )
| ! [SY124: $i] :
( ~ ( rel_s4 @ SV24 @ SY124 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY124 @ SX5 )
| ( f @ SY123 @ SX5 ) ) ) ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(236,plain,
! [SV12: $i] :
( ( ( ! [SY118: mu] :
( ~ ( exists_in_world @ SY118 @ ( sK22_SY94 @ SV12 ) )
| ~ ! [SY119: $i] :
( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SY119 )
| ( f @ SY118 @ SY119 ) ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(237,plain,
! [SV28: $i,SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
| ! [SY134: mu] :
( ~ ( exists_in_world @ SY134 @ SV28 )
| ! [SY135: $i] :
( ~ ( rel_s4 @ SV28 @ SY135 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY135 @ SX5 )
| ( f @ SY134 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(238,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ ( sK26_SY114 @ SV9 @ SV11 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(239,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ~ ! [SY129: mu] :
( ~ ( exists_in_world @ SY129 @ ( sK26_SY114 @ SV9 @ SV11 ) )
| ~ ! [SY130: $i] :
( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SY130 )
| ( f @ SY129 @ SY130 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(240,plain,
! [SV27: $i,SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 ) )
= $true )
| ( ( ! [SY131: mu] :
( ~ ( exists_in_world @ SY131 @ SV27 )
| ! [SY132: $i] :
( ~ ( rel_s4 @ SV27 @ SY132 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY132 @ SX5 )
| ( f @ SY131 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV9: $i,SV11: mu] :
( ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ ( sK25_SY104 @ SV9 @ SV11 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(242,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ! [SY126: mu] :
( ~ ( exists_in_world @ SY126 @ ( sK25_SY104 @ SV9 @ SV11 ) )
| ~ ! [SY127: $i] :
( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SY127 )
| ( f @ SY126 @ SY127 ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(243,plain,
! [SV18: mu,SV14: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ ( sK27_SY117 @ SV14 @ SV18 @ SV21 ) )
| ( f @ SV18 @ ( sK27_SY117 @ SV14 @ SV18 @ SV21 ) ) )
= $false )
| ( ( rel_s4 @ SV14 @ SV21 )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[229]) ).
thf(244,plain,
! [SV20: mu,SV25: $i,SV15: $i] :
( ( ( rel_s4 @ SV15 @ SV25 )
= $false )
| ( ( ~ ! [SY128: $i] :
( ~ ( rel_s4 @ SV25 @ SY128 )
| ( f @ SV20 @ SY128 ) ) )
= $true )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(245,plain,
! [SV26: $i] :
( ( ( rel_s4 @ sK14_SY61 @ SV26 )
= $false )
| ( ( f @ sK20_SY79 @ SV26 )
= $true )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(246,plain,
! [SV23: mu,SV29: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV29 )
| ~ ! [SY137: $i] :
( ~ ( rel_s4 @ SV29 @ SY137 )
| ( f @ SV23 @ SY137 ) ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(247,plain,
! [SV30: $i] :
( ( ( ~ ( rel_s4 @ sK17_SY76 @ SV30 )
| ( f @ sK24_SY88 @ SV30 ) )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(248,plain,
! [SV12: $i,SV24: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV24 )
| ! [SY138: $i] :
( ~ ( rel_s4 @ SV24 @ SY138 )
| ~ ! [SY139: $i] :
( ~ ( rel_s4 @ SY138 @ SY139 )
| ( f @ SV31 @ SY139 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(249,plain,
! [SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK28_SY118 @ SV12 ) @ ( sK22_SY94 @ SV12 ) )
| ~ ! [SY140: $i] :
( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SY140 )
| ( f @ ( sK28_SY118 @ SV12 ) @ SY140 ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[236]) ).
thf(250,plain,
! [SV28: $i,SV9: $i,SV11: mu] :
( ( ( ~ ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 ) )
= $true )
| ( ( ! [SY134: mu] :
( ~ ( exists_in_world @ SY134 @ SV28 )
| ! [SY135: $i] :
( ~ ( rel_s4 @ SV28 @ SY135 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY135 @ SX5 )
| ( f @ SY134 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(251,plain,
! [SV9: $i,SV11: mu] :
( ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ ( sK26_SY114 @ SV9 @ SV11 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(252,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ! [SY129: mu] :
( ~ ( exists_in_world @ SY129 @ ( sK26_SY114 @ SV9 @ SV11 ) )
| ~ ! [SY130: $i] :
( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SY130 )
| ( f @ SY129 @ SY130 ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(253,plain,
! [SV27: $i,SV9: $i,SV11: mu] :
( ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( ! [SY131: mu] :
( ~ ( exists_in_world @ SY131 @ SV27 )
| ! [SY132: $i] :
( ~ ( rel_s4 @ SV27 @ SY132 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY132 @ SX5 )
| ( f @ SY131 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(254,plain,
! [SV11: mu,SV9: $i] :
( ( ( ! [SY126: mu] :
( ~ ( exists_in_world @ SY126 @ ( sK25_SY104 @ SV9 @ SV11 ) )
| ~ ! [SY127: $i] :
( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SY127 )
| ( f @ SY126 @ SY127 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(255,plain,
! [SV18: mu,SV14: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ ( sK27_SY117 @ SV14 @ SV18 @ SV21 ) ) )
= $false )
| ( ( rel_s4 @ SV14 @ SV21 )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(256,plain,
! [SV21: $i,SV14: $i,SV18: mu] :
( ( ( f @ SV18 @ ( sK27_SY117 @ SV14 @ SV18 @ SV21 ) )
= $false )
| ( ( rel_s4 @ SV14 @ SV21 )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(257,plain,
! [SV15: $i,SV20: mu,SV25: $i] :
( ( ( ! [SY128: $i] :
( ~ ( rel_s4 @ SV25 @ SY128 )
| ( f @ SV20 @ SY128 ) ) )
= $false )
| ( ( rel_s4 @ SV15 @ SV25 )
= $false )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(258,plain,
! [SV23: mu,SV29: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV29 ) )
= $true )
| ( ( ~ ! [SY137: $i] :
( ~ ( rel_s4 @ SV29 @ SY137 )
| ( f @ SV23 @ SY137 ) ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(259,plain,
! [SV30: $i] :
( ( ( ~ ( rel_s4 @ sK17_SY76 @ SV30 ) )
= $true )
| ( ( f @ sK24_SY88 @ SV30 )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(260,plain,
! [SV12: $i,SV24: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV24 ) )
= $true )
| ( ( ! [SY138: $i] :
( ~ ( rel_s4 @ SV24 @ SY138 )
| ~ ! [SY139: $i] :
( ~ ( rel_s4 @ SY138 @ SY139 )
| ( f @ SV31 @ SY139 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV12: $i] :
( ( ( ~ ( exists_in_world @ ( sK28_SY118 @ SV12 ) @ ( sK22_SY94 @ SV12 ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(262,plain,
! [SV12: $i] :
( ( ( ~ ! [SY140: $i] :
( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SY140 )
| ( f @ ( sK28_SY118 @ SV12 ) @ SY140 ) ) )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(263,plain,
! [SV28: $i,SV9: $i,SV11: mu] :
( ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( ! [SY134: mu] :
( ~ ( exists_in_world @ SY134 @ SV28 )
| ! [SY135: $i] :
( ~ ( rel_s4 @ SV28 @ SY135 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY135 @ SX5 )
| ( f @ SY134 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(264,plain,
! [SV11: mu,SV9: $i] :
( ( ( ! [SY129: mu] :
( ~ ( exists_in_world @ SY129 @ ( sK26_SY114 @ SV9 @ SV11 ) )
| ~ ! [SY130: $i] :
( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SY130 )
| ( f @ SY129 @ SY130 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(265,plain,
! [SV9: $i,SV11: mu,SV27: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV27 )
| ! [SY141: $i] :
( ~ ( rel_s4 @ SV27 @ SY141 )
| ~ ! [SY142: $i] :
( ~ ( rel_s4 @ SY141 @ SY142 )
| ( f @ SV32 @ SY142 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(266,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ ( sK29_SY126 @ SV11 @ SV9 ) @ ( sK25_SY104 @ SV9 @ SV11 ) )
| ~ ! [SY143: $i] :
( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SY143 )
| ( f @ ( sK29_SY126 @ SV11 @ SV9 ) @ SY143 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[254]) ).
thf(267,plain,
! [SV18: mu,SV14: $i,SV21: $i] :
( ( ( rel_s4 @ SV21 @ ( sK27_SY117 @ SV14 @ SV18 @ SV21 ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV21 )
= $false )
| ( ( exists_in_world @ SV18 @ SV14 )
= $false )
| ( ( rel_s4 @ sK8_SY13 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(268,plain,
! [SV20: mu,SV15: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ ( sK30_SY128 @ SV15 @ SV20 @ SV25 ) )
| ( f @ SV20 @ ( sK30_SY128 @ SV15 @ SV20 @ SV25 ) ) )
= $false )
| ( ( rel_s4 @ SV15 @ SV25 )
= $false )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[257]) ).
thf(269,plain,
! [SV23: mu,SV29: $i,SV19: $i] :
( ( ( rel_s4 @ SV19 @ SV29 )
= $false )
| ( ( ~ ! [SY137: $i] :
( ~ ( rel_s4 @ SV29 @ SY137 )
| ( f @ SV23 @ SY137 ) ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV30: $i] :
( ( ( rel_s4 @ sK17_SY76 @ SV30 )
= $false )
| ( ( f @ sK24_SY88 @ SV30 )
= $true )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV12: $i,SV24: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( ! [SY138: $i] :
( ~ ( rel_s4 @ SV24 @ SY138 )
| ~ ! [SY139: $i] :
( ~ ( rel_s4 @ SY138 @ SY139 )
| ( f @ SV31 @ SY139 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV12: $i] :
( ( ( exists_in_world @ ( sK28_SY118 @ SV12 ) @ ( sK22_SY94 @ SV12 ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(273,plain,
! [SV12: $i] :
( ( ( ! [SY140: $i] :
( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SY140 )
| ( f @ ( sK28_SY118 @ SV12 ) @ SY140 ) ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(274,plain,
! [SV9: $i,SV11: mu,SV28: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV28 )
| ! [SY144: $i] :
( ~ ( rel_s4 @ SV28 @ SY144 )
| ~ ! [SY145: $i] :
( ~ ( rel_s4 @ SY144 @ SY145 )
| ( f @ SV33 @ SY145 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(275,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ ( sK31_SY129 @ SV11 @ SV9 ) @ ( sK26_SY114 @ SV9 @ SV11 ) )
| ~ ! [SY146: $i] :
( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SY146 )
| ( f @ ( sK31_SY129 @ SV11 @ SV9 ) @ SY146 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[264]) ).
thf(276,plain,
! [SV9: $i,SV11: mu,SV27: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV27 ) )
= $true )
| ( ( ! [SY141: $i] :
( ~ ( rel_s4 @ SV27 @ SY141 )
| ~ ! [SY142: $i] :
( ~ ( rel_s4 @ SY141 @ SY142 )
| ( f @ SV32 @ SY142 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ ( sK29_SY126 @ SV11 @ SV9 ) @ ( sK25_SY104 @ SV9 @ SV11 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(278,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ! [SY143: $i] :
( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SY143 )
| ( f @ ( sK29_SY126 @ SV11 @ SV9 ) @ SY143 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(279,plain,
! [SV20: mu,SV15: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ ( sK30_SY128 @ SV15 @ SV20 @ SV25 ) ) )
= $false )
| ( ( rel_s4 @ SV15 @ SV25 )
= $false )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(280,plain,
! [SV25: $i,SV15: $i,SV20: mu] :
( ( ( f @ SV20 @ ( sK30_SY128 @ SV15 @ SV20 @ SV25 ) )
= $false )
| ( ( rel_s4 @ SV15 @ SV25 )
= $false )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(281,plain,
! [SV19: $i,SV23: mu,SV29: $i] :
( ( ( ! [SY137: $i] :
( ~ ( rel_s4 @ SV29 @ SY137 )
| ( f @ SV23 @ SY137 ) ) )
= $false )
| ( ( rel_s4 @ SV19 @ SV29 )
= $false )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(282,plain,
! [SV12: $i,SV31: mu,SV34: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV34 )
| ~ ! [SY147: $i] :
( ~ ( rel_s4 @ SV34 @ SY147 )
| ( f @ SV31 @ SY147 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(283,plain,
! [SV35: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SV35 )
| ( f @ ( sK28_SY118 @ SV12 ) @ SV35 ) )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(284,plain,
! [SV9: $i,SV11: mu,SV28: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV28 ) )
= $true )
| ( ( ! [SY144: $i] :
( ~ ( rel_s4 @ SV28 @ SY144 )
| ~ ! [SY145: $i] :
( ~ ( rel_s4 @ SY144 @ SY145 )
| ( f @ SV33 @ SY145 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(285,plain,
! [SV9: $i,SV11: mu] :
( ( ( ~ ( exists_in_world @ ( sK31_SY129 @ SV11 @ SV9 ) @ ( sK26_SY114 @ SV9 @ SV11 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(286,plain,
! [SV11: mu,SV9: $i] :
( ( ( ~ ! [SY146: $i] :
( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SY146 )
| ( f @ ( sK31_SY129 @ SV11 @ SV9 ) @ SY146 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(287,plain,
! [SV9: $i,SV11: mu,SV27: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( ! [SY141: $i] :
( ~ ( rel_s4 @ SV27 @ SY141 )
| ~ ! [SY142: $i] :
( ~ ( rel_s4 @ SY141 @ SY142 )
| ( f @ SV32 @ SY142 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(288,plain,
! [SV9: $i,SV11: mu] :
( ( ( exists_in_world @ ( sK29_SY126 @ SV11 @ SV9 ) @ ( sK25_SY104 @ SV9 @ SV11 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(289,plain,
! [SV11: mu,SV9: $i] :
( ( ( ! [SY143: $i] :
( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SY143 )
| ( f @ ( sK29_SY126 @ SV11 @ SV9 ) @ SY143 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(290,plain,
! [SV20: mu,SV15: $i,SV25: $i] :
( ( ( rel_s4 @ SV25 @ ( sK30_SY128 @ SV15 @ SV20 @ SV25 ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV25 )
= $false )
| ( ( exists_in_world @ SV20 @ SV15 )
= $false )
| ( ( rel_s4 @ sK10_SY13 @ SV15 )
= $false )
| ( ( exists_in_world @ sK6_SY29 @ sK4_SY25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(291,plain,
! [SV23: mu,SV19: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ ( sK32_SY137 @ SV19 @ SV23 @ SV29 ) )
| ( f @ SV23 @ ( sK32_SY137 @ SV19 @ SV23 @ SV29 ) ) )
= $false )
| ( ( rel_s4 @ SV19 @ SV29 )
= $false )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[281]) ).
thf(292,plain,
! [SV12: $i,SV31: mu,SV34: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV34 ) )
= $true )
| ( ( ~ ! [SY147: $i] :
( ~ ( rel_s4 @ SV34 @ SY147 )
| ( f @ SV31 @ SY147 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(293,plain,
! [SV35: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SV35 ) )
= $true )
| ( ( f @ ( sK28_SY118 @ SV12 ) @ SV35 )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(294,plain,
! [SV9: $i,SV11: mu,SV28: $i,SV33: mu] :
( ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( ! [SY144: $i] :
( ~ ( rel_s4 @ SV28 @ SY144 )
| ~ ! [SY145: $i] :
( ~ ( rel_s4 @ SY144 @ SY145 )
| ( f @ SV33 @ SY145 ) ) ) )
= $true )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(295,plain,
! [SV9: $i,SV11: mu] :
( ( ( exists_in_world @ ( sK31_SY129 @ SV11 @ SV9 ) @ ( sK26_SY114 @ SV9 @ SV11 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(296,plain,
! [SV11: mu,SV9: $i] :
( ( ( ! [SY146: $i] :
( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SY146 )
| ( f @ ( sK31_SY129 @ SV11 @ SV9 ) @ SY146 ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(297,plain,
! [SV9: $i,SV11: mu,SV32: mu,SV36: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV36 )
| ~ ! [SY148: $i] :
( ~ ( rel_s4 @ SV36 @ SY148 )
| ( f @ SV32 @ SY148 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(298,plain,
! [SV37: $i,SV11: mu,SV9: $i] :
( ( ( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SV37 )
| ( f @ ( sK29_SY126 @ SV11 @ SV9 ) @ SV37 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(299,plain,
! [SV23: mu,SV19: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ ( sK32_SY137 @ SV19 @ SV23 @ SV29 ) ) )
= $false )
| ( ( rel_s4 @ SV19 @ SV29 )
= $false )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(300,plain,
! [SV29: $i,SV19: $i,SV23: mu] :
( ( ( f @ SV23 @ ( sK32_SY137 @ SV19 @ SV23 @ SV29 ) )
= $false )
| ( ( rel_s4 @ SV19 @ SV29 )
= $false )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(301,plain,
! [SV12: $i,SV31: mu,SV34: $i,SV24: $i] :
( ( ( rel_s4 @ SV24 @ SV34 )
= $false )
| ( ( ~ ! [SY147: $i] :
( ~ ( rel_s4 @ SV34 @ SY147 )
| ( f @ SV31 @ SY147 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(302,plain,
! [SV35: $i,SV12: $i] :
( ( ( rel_s4 @ ( sK22_SY94 @ SV12 ) @ SV35 )
= $false )
| ( ( f @ ( sK28_SY118 @ SV12 ) @ SV35 )
= $true )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(303,plain,
! [SV9: $i,SV11: mu,SV33: mu,SV38: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV38 )
| ~ ! [SY149: $i] :
( ~ ( rel_s4 @ SV38 @ SY149 )
| ( f @ SV33 @ SY149 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(304,plain,
! [SV39: $i,SV11: mu,SV9: $i] :
( ( ( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SV39 )
| ( f @ ( sK31_SY129 @ SV11 @ SV9 ) @ SV39 ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(305,plain,
! [SV9: $i,SV11: mu,SV32: mu,SV36: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV36 ) )
= $true )
| ( ( ~ ! [SY148: $i] :
( ~ ( rel_s4 @ SV36 @ SY148 )
| ( f @ SV32 @ SY148 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(306,plain,
! [SV37: $i,SV11: mu,SV9: $i] :
( ( ( ~ ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SV37 ) )
= $true )
| ( ( f @ ( sK29_SY126 @ SV11 @ SV9 ) @ SV37 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(307,plain,
! [SV23: mu,SV19: $i,SV29: $i] :
( ( ( rel_s4 @ SV29 @ ( sK32_SY137 @ SV19 @ SV23 @ SV29 ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV29 )
= $false )
| ( ( exists_in_world @ SV23 @ SV19 )
= $false )
| ( ( rel_s4 @ sK13_SY13 @ SV19 )
= $false )
| ( ( rel_s4 @ sK4_SY25 @ sK9_SY41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(308,plain,
! [SV12: $i,SV24: $i,SV31: mu,SV34: $i] :
( ( ( ! [SY147: $i] :
( ~ ( rel_s4 @ SV34 @ SY147 )
| ( f @ SV31 @ SY147 ) ) )
= $false )
| ( ( rel_s4 @ SV24 @ SV34 )
= $false )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(309,plain,
! [SV9: $i,SV11: mu,SV33: mu,SV38: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV38 ) )
= $true )
| ( ( ~ ! [SY149: $i] :
( ~ ( rel_s4 @ SV38 @ SY149 )
| ( f @ SV33 @ SY149 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(310,plain,
! [SV39: $i,SV11: mu,SV9: $i] :
( ( ( ~ ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SV39 ) )
= $true )
| ( ( f @ ( sK31_SY129 @ SV11 @ SV9 ) @ SV39 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(311,plain,
! [SV9: $i,SV11: mu,SV32: mu,SV36: $i,SV27: $i] :
( ( ( rel_s4 @ SV27 @ SV36 )
= $false )
| ( ( ~ ! [SY148: $i] :
( ~ ( rel_s4 @ SV36 @ SY148 )
| ( f @ SV32 @ SY148 ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(312,plain,
! [SV37: $i,SV11: mu,SV9: $i] :
( ( ( rel_s4 @ ( sK25_SY104 @ SV9 @ SV11 ) @ SV37 )
= $false )
| ( ( f @ ( sK29_SY126 @ SV11 @ SV9 ) @ SV37 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(313,plain,
! [SV31: mu,SV24: $i,SV12: $i,SV34: $i] :
( ( ( ~ ( rel_s4 @ SV34 @ ( sK33_SY147 @ SV12 @ SV24 @ SV31 @ SV34 ) )
| ( f @ SV31 @ ( sK33_SY147 @ SV12 @ SV24 @ SV31 @ SV34 ) ) )
= $false )
| ( ( rel_s4 @ SV24 @ SV34 )
= $false )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[308]) ).
thf(314,plain,
! [SV9: $i,SV11: mu,SV33: mu,SV38: $i,SV28: $i] :
( ( ( rel_s4 @ SV28 @ SV38 )
= $false )
| ( ( ~ ! [SY149: $i] :
( ~ ( rel_s4 @ SV38 @ SY149 )
| ( f @ SV33 @ SY149 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(315,plain,
! [SV39: $i,SV11: mu,SV9: $i] :
( ( ( rel_s4 @ ( sK26_SY114 @ SV9 @ SV11 ) @ SV39 )
= $false )
| ( ( f @ ( sK31_SY129 @ SV11 @ SV9 ) @ SV39 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(316,plain,
! [SV9: $i,SV11: mu,SV27: $i,SV32: mu,SV36: $i] :
( ( ( ! [SY148: $i] :
( ~ ( rel_s4 @ SV36 @ SY148 )
| ( f @ SV32 @ SY148 ) ) )
= $false )
| ( ( rel_s4 @ SV27 @ SV36 )
= $false )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(317,plain,
! [SV31: mu,SV24: $i,SV12: $i,SV34: $i] :
( ( ( ~ ( rel_s4 @ SV34 @ ( sK33_SY147 @ SV12 @ SV24 @ SV31 @ SV34 ) ) )
= $false )
| ( ( rel_s4 @ SV24 @ SV34 )
= $false )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(318,plain,
! [SV34: $i,SV24: $i,SV12: $i,SV31: mu] :
( ( ( f @ SV31 @ ( sK33_SY147 @ SV12 @ SV24 @ SV31 @ SV34 ) )
= $false )
| ( ( rel_s4 @ SV24 @ SV34 )
= $false )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(319,plain,
! [SV9: $i,SV11: mu,SV28: $i,SV33: mu,SV38: $i] :
( ( ( ! [SY149: $i] :
( ~ ( rel_s4 @ SV38 @ SY149 )
| ( f @ SV33 @ SY149 ) ) )
= $false )
| ( ( rel_s4 @ SV28 @ SV38 )
= $false )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(320,plain,
! [SV32: mu,SV27: $i,SV11: mu,SV9: $i,SV36: $i] :
( ( ( ~ ( rel_s4 @ SV36 @ ( sK34_SY148 @ SV9 @ SV11 @ SV27 @ SV32 @ SV36 ) )
| ( f @ SV32 @ ( sK34_SY148 @ SV9 @ SV11 @ SV27 @ SV32 @ SV36 ) ) )
= $false )
| ( ( rel_s4 @ SV27 @ SV36 )
= $false )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[316]) ).
thf(321,plain,
! [SV31: mu,SV24: $i,SV12: $i,SV34: $i] :
( ( ( rel_s4 @ SV34 @ ( sK33_SY147 @ SV12 @ SV24 @ SV31 @ SV34 ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV34 )
= $false )
| ( ( exists_in_world @ SV31 @ SV24 )
= $false )
| ( ( rel_s4 @ ( sK18_SY13 @ SV12 ) @ SV24 )
= $false )
| ( ( f @ sK6_SY29 @ SV12 )
= $true )
| ( ( rel_s4 @ sK9_SY41 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(322,plain,
! [SV33: mu,SV28: $i,SV11: mu,SV9: $i,SV38: $i] :
( ( ( ~ ( rel_s4 @ SV38 @ ( sK35_SY149 @ SV9 @ SV11 @ SV28 @ SV33 @ SV38 ) )
| ( f @ SV33 @ ( sK35_SY149 @ SV9 @ SV11 @ SV28 @ SV33 @ SV38 ) ) )
= $false )
| ( ( rel_s4 @ SV28 @ SV38 )
= $false )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[319]) ).
thf(323,plain,
! [SV32: mu,SV27: $i,SV11: mu,SV9: $i,SV36: $i] :
( ( ( ~ ( rel_s4 @ SV36 @ ( sK34_SY148 @ SV9 @ SV11 @ SV27 @ SV32 @ SV36 ) ) )
= $false )
| ( ( rel_s4 @ SV27 @ SV36 )
= $false )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(324,plain,
! [SV36: $i,SV27: $i,SV11: mu,SV9: $i,SV32: mu] :
( ( ( f @ SV32 @ ( sK34_SY148 @ SV9 @ SV11 @ SV27 @ SV32 @ SV36 ) )
= $false )
| ( ( rel_s4 @ SV27 @ SV36 )
= $false )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(325,plain,
! [SV33: mu,SV28: $i,SV11: mu,SV9: $i,SV38: $i] :
( ( ( ~ ( rel_s4 @ SV38 @ ( sK35_SY149 @ SV9 @ SV11 @ SV28 @ SV33 @ SV38 ) ) )
= $false )
| ( ( rel_s4 @ SV28 @ SV38 )
= $false )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(326,plain,
! [SV38: $i,SV28: $i,SV11: mu,SV9: $i,SV33: mu] :
( ( ( f @ SV33 @ ( sK35_SY149 @ SV9 @ SV11 @ SV28 @ SV33 @ SV38 ) )
= $false )
| ( ( rel_s4 @ SV28 @ SV38 )
= $false )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(327,plain,
! [SV32: mu,SV27: $i,SV11: mu,SV9: $i,SV36: $i] :
( ( ( rel_s4 @ SV36 @ ( sK34_SY148 @ SV9 @ SV11 @ SV27 @ SV32 @ SV36 ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV36 )
= $false )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ ( sK19_SY13 @ SV11 @ SV9 ) @ SV27 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( f @ SV11 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(328,plain,
! [SV33: mu,SV28: $i,SV11: mu,SV9: $i,SV38: $i] :
( ( ( rel_s4 @ SV38 @ ( sK35_SY149 @ SV9 @ SV11 @ SV28 @ SV33 @ SV38 ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV38 )
= $false )
| ( ( exists_in_world @ SV33 @ SV28 )
= $false )
| ( ( rel_s4 @ ( sK21_SY13 @ SV11 @ SV9 ) @ SV28 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( exists_in_world @ SV11 @ SV9 )
= $false )
| ( ( rel_s4 @ SV9 @ ( sK15_SY56 @ SV11 @ SV9 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(329,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,328,327,326,324,321,318,315,312,307,302,300,295,290,288,280,272,270,267,256,251,245,241,233,223,221,214,208,207,199,193,174,172,167,163,143,132,124,116,106,85,82,59,49,38,22]) ).
thf(330,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN397^7 : TPTP v8.1.0. Released v5.5.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 12 00:03:44 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35
% 0.19/0.35 No.of.Axioms: 4
% 0.19/0.35
% 0.19/0.35 Length.of.Defs: 5540
% 0.19/0.35
% 0.19/0.35 Contains.Choice.Funs: false
% 0.19/0.36 (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6,loop_count:0,foatp_calls:0,translation:fof_full)...........................
% 1.29/1.50
% 1.29/1.50 ********************************
% 1.29/1.50 * All subproblems solved! *
% 1.29/1.50 ********************************
% 1.29/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:329,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.35/1.60
% 1.35/1.60 %**** Beginning of derivation protocol ****
% 1.35/1.60 % SZS output start CNFRefutation
% See solution above
% 1.35/1.60
% 1.35/1.60 %**** End of derivation protocol ****
% 1.35/1.60 %**** no. of clauses in derivation: 330 ****
% 1.35/1.60 %**** clause counter: 329 ****
% 1.35/1.60
% 1.35/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:329,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------