TSTP Solution File: SYN052^7 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN052^7 : 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 : n010.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 08:23:01 EDT 2022
% Result : Theorem 21.62s 21.83s
% Output : CNFRefutation 21.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 96
% Syntax : Number of formulae : 329 ( 66 unt; 59 typ; 32 def)
% Number of atoms : 2919 ( 684 equ; 0 cnn)
% Maximal formula atoms : 35 ( 10 avg)
% Number of connectives : 4998 ( 881 ~;1150 |; 9 &;2948 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 58 usr; 18 con; 0-3 aty)
% Number of variables : 956 ( 61 ^ 888 !; 7 ?; 956 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_big_f,type,
big_f: mu > $i > $o ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia_s4,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK10_SY66,type,
sK10_SY66: $i ).
thf(tp_sK11_SY38,type,
sK11_SY38: $i > $i ).
thf(tp_sK12_SY38,type,
sK12_SY38: $i ).
thf(tp_sK13_SY74,type,
sK13_SY74: $i ).
thf(tp_sK14_SY38,type,
sK14_SY38: $i ).
thf(tp_sK15_SY80,type,
sK15_SY80: $i > $i ).
thf(tp_sK16_SY38,type,
sK16_SY38: $i ).
thf(tp_sK17_SY67,type,
sK17_SY67: $i > mu > $i > $i ).
thf(tp_sK18_SY69,type,
sK18_SY69: $i > mu > $i > $i ).
thf(tp_sK19_SY84,type,
sK19_SY84: $i ).
thf(tp_sK1_X,type,
sK1_X: $i > mu ).
thf(tp_sK20_SY88,type,
sK20_SY88: $i ).
thf(tp_sK21_SY95,type,
sK21_SY95: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY5,type,
sK3_SY5: $i ).
thf(tp_sK4_SY33,type,
sK4_SY33: $i ).
thf(tp_sK5_SY51,type,
sK5_SY51: $i ).
thf(tp_sK6_SY38,type,
sK6_SY38: $i ).
thf(tp_sK7_SY60,type,
sK7_SY60: mu ).
thf(tp_sK8_SY65,type,
sK8_SY65: $i ).
thf(tp_sK9_SY38,type,
sK9_SY38: $i ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax) ).
thf(2,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(3,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(4,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(5,conjecture,
( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel22) ).
thf(6,negated_conjecture,
( ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ) )
= $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
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_f @ X ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_f @ X ) ) @ ( mbox_s4 @ p ) ) ) ) ) )
@ ( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ p )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_f @ X1 ) ) ) )
@ ( mbox_s4 @ p ) ) ) ) ) ) ) )
= $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 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) ) )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $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 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) ) )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $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 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) ) )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SX2 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( rel_s4 @ SY5 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX2 @ SX3 )
| ( p @ SX3 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[20]) ).
thf(25,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY24: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV3 @ SV6 )
| ~ ( rel_s4 @ SV6 @ SY24 ) )
| ( rel_s4 @ SV3 @ SY24 ) ) )
= $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,
( ( ~ ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
| ~ ! [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 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) ) )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY25 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
| ~ ( ~ ! [SY33: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY33 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
| ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[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,
( ( ~ ( rel_s4 @ sK2_SX0 @ sK3_SY5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,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 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) ) )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY25 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
| ~ ( ~ ! [SY33: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY33 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
| ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,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(33,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(34,plain,
( ( rel_s4 @ sK2_SX0 @ sK3_SY5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,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 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) ) )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY25 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( ~ ! [SY33: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY33 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
| ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,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)],[32]) ).
thf(38,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)],[33]) ).
thf(39,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 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) ) )
| ~ ! [SX4: $i] :
( ~ ( rel_s4 @ SY25 @ SX4 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( big_f @ SX3 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX4 @ SX5 )
| ( p @ SX5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ! [SY33: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY33 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
| ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,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)],[37]) ).
thf(42,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)],[38]) ).
thf(43,plain,
! [SV9: $i] :
( ( ~ ( rel_s4 @ sK3_SY5 @ SV9 )
| ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV9 )
| ~ ( ~ ! [SY44: $i] :
( ~ ( rel_s4 @ SV9 @ SY44 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY44 @ SX5 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY44 @ SX5 )
| ( big_f @ SY43 @ SX5 ) ) )
| ~ ! [SY47: $i] :
( ~ ( rel_s4 @ SV9 @ SY47 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY47 @ SX5 )
| ( big_f @ SY43 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY47 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ( ~ ! [SY33: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY33 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,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)],[41]) ).
thf(46,plain,
! [SV9: $i] :
( ( ( ~ ( rel_s4 @ sK3_SY5 @ SV9 ) )
= $true )
| ( ( ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV9 )
| ~ ( ~ ! [SY44: $i] :
( ~ ( rel_s4 @ SV9 @ SY44 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY44 @ SX5 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY44 @ SX5 )
| ( big_f @ SY43 @ SX5 ) ) )
| ~ ! [SY47: $i] :
( ~ ( rel_s4 @ SV9 @ SY47 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY47 @ SX5 )
| ( big_f @ SY43 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY47 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(47,plain,
( ( ( ! [SY33: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY33 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ( p @ SX3 ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY33 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,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)],[45]) ).
thf(49,plain,
! [SV9: $i] :
( ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false )
| ( ( ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV9 )
| ~ ( ~ ! [SY44: $i] :
( ~ ( rel_s4 @ SV9 @ SY44 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY44 @ SX5 )
| ( p @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY44 @ SX5 )
| ( big_f @ SY43 @ SX5 ) ) )
| ~ ! [SY47: $i] :
( ~ ( rel_s4 @ SV9 @ SY47 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY47 @ SX5 )
| ( big_f @ SY43 @ SX5 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY47 @ SX5 )
| ( p @ SX5 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
| ~ ! [SY50: $i] :
( ~ ( rel_s4 @ sK4_SY33 @ SY50 )
| ( p @ SY50 ) )
| ! [SY51: $i] :
( ~ ( rel_s4 @ sK4_SY33 @ SY51 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY51 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY51 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(51,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)],[48]) ).
thf(52,plain,
! [SV9: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV9 )
| ~ ( ~ ! [SY54: $i] :
( ~ ( rel_s4 @ SV9 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( p @ SX5 ) )
| ! [SY56: $i] :
( ~ ( rel_s4 @ SY54 @ SY56 )
| ( big_f @ SV10 @ SY56 ) ) )
| ~ ! [SY57: $i] :
( ~ ( rel_s4 @ SV9 @ SY57 )
| ~ ! [SY58: $i] :
( ~ ( rel_s4 @ SY57 @ SY58 )
| ( big_f @ SV10 @ SY58 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY57 @ SX5 )
| ( p @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(53,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK4_SY33 ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
( ( ( ~ ! [SY50: $i] :
( ~ ( rel_s4 @ sK4_SY33 @ SY50 )
| ( p @ SY50 ) )
| ! [SY51: $i] :
( ~ ( rel_s4 @ sK4_SY33 @ SY51 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY51 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY51 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV9: $i,SV10: mu] :
( ( ( ~ ( exists_in_world @ SV10 @ SV9 ) )
= $true )
| ( ( ~ ( ~ ! [SY54: $i] :
( ~ ( rel_s4 @ SV9 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( p @ SX5 ) )
| ! [SY56: $i] :
( ~ ( rel_s4 @ SY54 @ SY56 )
| ( big_f @ SV10 @ SY56 ) ) )
| ~ ! [SY57: $i] :
( ~ ( rel_s4 @ SV9 @ SY57 )
| ~ ! [SY58: $i] :
( ~ ( rel_s4 @ SY57 @ SY58 )
| ( big_f @ SV10 @ SY58 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY57 @ SX5 )
| ( p @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(56,plain,
( ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(57,plain,
( ( ( ~ ! [SY50: $i] :
( ~ ( rel_s4 @ sK4_SY33 @ SY50 )
| ( p @ SY50 ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(58,plain,
( ( ( ! [SY51: $i] :
( ~ ( rel_s4 @ sK4_SY33 @ SY51 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY51 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY51 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV9: $i,SV10: mu] :
( ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( ~ ( ~ ! [SY54: $i] :
( ~ ( rel_s4 @ SV9 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( p @ SX5 ) )
| ! [SY56: $i] :
( ~ ( rel_s4 @ SY54 @ SY56 )
| ( big_f @ SV10 @ SY56 ) ) )
| ~ ! [SY57: $i] :
( ~ ( rel_s4 @ SV9 @ SY57 )
| ~ ! [SY58: $i] :
( ~ ( rel_s4 @ SY57 @ SY58 )
| ( big_f @ SV10 @ SY58 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY57 @ SX5 )
| ( p @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(60,plain,
( ( ( ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
( ( ( ! [SY50: $i] :
( ~ ( rel_s4 @ sK4_SY33 @ SY50 )
| ( p @ SY50 ) ) )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(62,plain,
( ( ( ~ ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
| ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ sK5_SY51 )
| ! [SY61: $i] :
( ~ ( rel_s4 @ sK5_SY51 @ SY61 )
| ( big_f @ SY60 @ SY61 ) ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[58]) ).
thf(63,plain,
! [SV10: mu,SV9: $i] :
( ( ( ~ ! [SY54: $i] :
( ~ ( rel_s4 @ SV9 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( p @ SX5 ) )
| ! [SY56: $i] :
( ~ ( rel_s4 @ SY54 @ SY56 )
| ( big_f @ SV10 @ SY56 ) ) )
| ~ ! [SY57: $i] :
( ~ ( rel_s4 @ SV9 @ SY57 )
| ~ ! [SY58: $i] :
( ~ ( rel_s4 @ SY57 @ SY58 )
| ( big_f @ SV10 @ SY58 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY57 @ SX5 )
| ( p @ SX5 ) ) ) )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK6_SY38 )
| ~ ! [SY62: $i] :
( ~ ( rel_s4 @ sK6_SY38 @ SY62 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY62 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY62 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY65: $i] :
( ~ ( rel_s4 @ sK6_SY38 @ SY65 )
| ( p @ SY65 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(65,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s4 @ sK4_SY33 @ SV11 )
| ( p @ SV11 ) )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(66,plain,
( ( ( ~ ( rel_s4 @ sK4_SY33 @ sK5_SY51 ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(67,plain,
( ( ( ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ sK5_SY51 )
| ! [SY61: $i] :
( ~ ( rel_s4 @ sK5_SY51 @ SY61 )
| ( big_f @ SY60 @ SY61 ) ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(68,plain,
! [SV10: mu,SV9: $i] :
( ( ( ~ ! [SY54: $i] :
( ~ ( rel_s4 @ SV9 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( p @ SX5 ) )
| ! [SY56: $i] :
( ~ ( rel_s4 @ SY54 @ SY56 )
| ( big_f @ SV10 @ SY56 ) ) ) )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV10: mu,SV9: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( rel_s4 @ SV9 @ SY57 )
| ~ ! [SY58: $i] :
( ~ ( rel_s4 @ SY57 @ SY58 )
| ( big_f @ SV10 @ SY58 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY57 @ SX5 )
| ( p @ SX5 ) ) ) )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(70,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK6_SY38 ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(71,plain,
( ( ( ~ ! [SY62: $i] :
( ~ ( rel_s4 @ sK6_SY38 @ SY62 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY62 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY62 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY65: $i] :
( ~ ( rel_s4 @ sK6_SY38 @ SY65 )
| ( p @ SY65 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s4 @ sK4_SY33 @ SV11 ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(73,plain,
( ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(74,plain,
( ( ( ~ ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
| ! [SY66: $i] :
( ~ ( rel_s4 @ sK5_SY51 @ SY66 )
| ( big_f @ sK7_SY60 @ SY66 ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(75,plain,
! [SV10: mu,SV9: $i] :
( ( ( ! [SY54: $i] :
( ~ ( rel_s4 @ SV9 @ SY54 )
| ~ ! [SX5: $i] :
( ~ ( rel_s4 @ SY54 @ SX5 )
| ( p @ SX5 ) )
| ! [SY56: $i] :
( ~ ( rel_s4 @ SY54 @ SY56 )
| ( big_f @ SV10 @ SY56 ) ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(76,plain,
! [SV10: mu,SV9: $i] :
( ( ( ! [SY57: $i] :
( ~ ( rel_s4 @ SV9 @ SY57 )
| ~ ! [SY58: $i] :
( ~ ( rel_s4 @ SY57 @ SY58 )
| ( big_f @ SV10 @ SY58 ) )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY57 @ SX5 )
| ( p @ SX5 ) ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(77,plain,
( ( ( rel_s4 @ sK3_SY5 @ sK6_SY38 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(78,plain,
( ( ( ~ ! [SY62: $i] :
( ~ ( rel_s4 @ sK6_SY38 @ SY62 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY62 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY62 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(79,plain,
( ( ( ! [SY65: $i] :
( ~ ( rel_s4 @ sK6_SY38 @ SY65 )
| ( p @ SY65 ) ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV11: $i] :
( ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
( ( ( ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(82,plain,
( ( ( ~ ( exists_in_world @ sK7_SY60 @ sK5_SY51 ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(83,plain,
( ( ( ! [SY66: $i] :
( ~ ( rel_s4 @ sK5_SY51 @ SY66 )
| ( big_f @ sK7_SY60 @ SY66 ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(84,plain,
! [SV10: mu,SV12: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV12 )
| ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SV12 @ SY67 )
| ( p @ SY67 ) )
| ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV10: mu,SV13: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV13 )
| ~ ! [SY69: $i] :
( ~ ( rel_s4 @ SV13 @ SY69 )
| ( big_f @ SV10 @ SY69 ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(86,plain,
( ( ( ! [SY62: $i] :
( ~ ( rel_s4 @ sK6_SY38 @ SY62 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY62 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY62 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(87,plain,
( ( ( ~ ( rel_s4 @ sK6_SY38 @ sK8_SY65 )
| ( p @ sK8_SY65 ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(88,plain,
! [SV11: $i] :
( ( ( ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(89,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK9_SY38 )
| ~ ! [SY71: $i] :
( ~ ( rel_s4 @ sK9_SY38 @ SY71 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY71 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY71 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY74: $i] :
( ~ ( rel_s4 @ sK9_SY38 @ SY74 )
| ( p @ SY74 ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[81]) ).
thf(90,plain,
( ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(91,plain,
( ( ( ~ ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
| ( big_f @ sK7_SY60 @ sK10_SY66 ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(92,plain,
! [SV10: mu,SV12: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV12 ) )
= $true )
| ( ( ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SV12 @ SY67 )
| ( p @ SY67 ) )
| ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV10: mu,SV13: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV13 ) )
= $true )
| ( ( ~ ! [SY69: $i] :
( ~ ( rel_s4 @ SV13 @ SY69 )
| ( big_f @ SV10 @ SY69 ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV14: $i] :
( ( ( ~ ( rel_s4 @ sK6_SY38 @ SV14 )
| ! [SY75: mu] :
( ~ ( exists_in_world @ SY75 @ SV14 )
| ! [SY76: $i] :
( ~ ( rel_s4 @ SV14 @ SY76 )
| ( big_f @ SY75 @ SY76 ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(95,plain,
( ( ( ~ ( rel_s4 @ sK6_SY38 @ sK8_SY65 ) )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(96,plain,
( ( ( p @ sK8_SY65 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s4 @ sK3_SY5 @ ( sK11_SY38 @ SV11 ) )
| ~ ! [SY77: $i] :
( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SY77 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY77 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY77 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY80: $i] :
( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SY80 )
| ( p @ SY80 ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(98,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK9_SY38 ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(99,plain,
( ( ( ~ ! [SY71: $i] :
( ~ ( rel_s4 @ sK9_SY38 @ SY71 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY71 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY71 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY74: $i] :
( ~ ( rel_s4 @ sK9_SY38 @ SY74 )
| ( p @ SY74 ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(100,plain,
( ( ( ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(101,plain,
( ( ( ~ ( rel_s4 @ sK5_SY51 @ sK10_SY66 ) )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(102,plain,
( ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(103,plain,
! [SV10: mu,SV12: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SV12 @ SY67 )
| ( p @ SY67 ) )
| ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV10: mu,SV13: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( ~ ! [SY69: $i] :
( ~ ( rel_s4 @ SV13 @ SY69 )
| ( big_f @ SV10 @ SY69 ) )
| ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV14: $i] :
( ( ( ~ ( rel_s4 @ sK6_SY38 @ SV14 ) )
= $true )
| ( ( ! [SY75: mu] :
( ~ ( exists_in_world @ SY75 @ SV14 )
| ! [SY76: $i] :
( ~ ( rel_s4 @ SV14 @ SY76 )
| ( big_f @ SY75 @ SY76 ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(106,plain,
( ( ( rel_s4 @ sK6_SY38 @ sK8_SY65 )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(107,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s4 @ sK3_SY5 @ ( sK11_SY38 @ SV11 ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(108,plain,
! [SV11: $i] :
( ( ( ~ ! [SY77: $i] :
( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SY77 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY77 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY77 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY80: $i] :
( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SY80 )
| ( p @ SY80 ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(109,plain,
( ( ( rel_s4 @ sK3_SY5 @ sK9_SY38 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(110,plain,
( ( ( ~ ! [SY71: $i] :
( ~ ( rel_s4 @ sK9_SY38 @ SY71 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY71 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY71 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(111,plain,
( ( ( ! [SY74: $i] :
( ~ ( rel_s4 @ sK9_SY38 @ SY74 )
| ( p @ SY74 ) ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[99]) ).
thf(112,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK12_SY38 )
| ~ ! [SY81: $i] :
( ~ ( rel_s4 @ sK12_SY38 @ SY81 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY81 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY81 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY84: $i] :
( ~ ( rel_s4 @ sK12_SY38 @ SY84 )
| ( p @ SY84 ) ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[100]) ).
thf(113,plain,
( ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true )
| ( ( ~ ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(114,plain,
( ( ( ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( ~ ! [SY67: $i] :
( ~ ( rel_s4 @ SV12 @ SY67 )
| ( p @ SY67 ) ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV9: $i,SV10: mu,SV13: $i] :
( ( ( ~ ! [SY69: $i] :
( ~ ( rel_s4 @ SV13 @ SY69 )
| ( big_f @ SV10 @ SY69 ) ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV14: $i] :
( ( ( rel_s4 @ sK6_SY38 @ SV14 )
= $false )
| ( ( ! [SY75: mu] :
( ~ ( exists_in_world @ SY75 @ SV14 )
| ! [SY76: $i] :
( ~ ( rel_s4 @ SV14 @ SY76 )
| ( big_f @ SY75 @ SY76 ) ) ) )
= $true )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV11: $i] :
( ( ( rel_s4 @ sK3_SY5 @ ( sK11_SY38 @ SV11 ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV11: $i] :
( ( ( ~ ! [SY77: $i] :
( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SY77 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY77 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY77 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(120,plain,
! [SV11: $i] :
( ( ( ! [SY80: $i] :
( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SY80 )
| ( p @ SY80 ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(121,plain,
( ( ( ! [SY71: $i] :
( ~ ( rel_s4 @ sK9_SY38 @ SY71 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY71 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY71 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(122,plain,
( ( ( ~ ( rel_s4 @ sK9_SY38 @ sK13_SY74 )
| ( p @ sK13_SY74 ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(123,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK12_SY38 ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(124,plain,
( ( ( ~ ! [SY81: $i] :
( ~ ( rel_s4 @ sK12_SY38 @ SY81 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY81 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY81 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY84: $i] :
( ~ ( rel_s4 @ sK12_SY38 @ SY84 )
| ( p @ SY84 ) ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(125,plain,
( ( ( ! [SY38: $i] :
( ~ ( rel_s4 @ sK3_SY5 @ SY38 )
| ~ ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SY38 @ SX3 )
| ( p @ SX3 ) ) ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(126,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK14_SY38 )
| ~ ! [SY85: $i] :
( ~ ( rel_s4 @ sK14_SY38 @ SY85 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY85 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY85 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY88: $i] :
( ~ ( rel_s4 @ sK14_SY38 @ SY88 )
| ( p @ SY88 ) ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(127,plain,
! [SV9: $i,SV10: mu,SV12: $i] :
( ( ( ! [SY67: $i] :
( ~ ( rel_s4 @ SV12 @ SY67 )
| ( p @ SY67 ) ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV9: $i,SV10: mu,SV13: $i] :
( ( ( ! [SY69: $i] :
( ~ ( rel_s4 @ SV13 @ SY69 )
| ( big_f @ SV10 @ SY69 ) ) )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV14: $i,SV15: mu] :
( ( ( ~ ( exists_in_world @ SV15 @ SV14 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SV14 @ SY89 )
| ( big_f @ SV15 @ SY89 ) ) )
= $true )
| ( ( rel_s4 @ sK6_SY38 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV11: $i] :
( ( ( ! [SY77: $i] :
( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SY77 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY77 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY77 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(131,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ ( sK15_SY80 @ SV11 ) )
| ( p @ ( sK15_SY80 @ SV11 ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[120]) ).
thf(132,plain,
! [SV16: $i] :
( ( ( ~ ( rel_s4 @ sK9_SY38 @ SV16 )
| ! [SY90: mu] :
( ~ ( exists_in_world @ SY90 @ SV16 )
| ! [SY91: $i] :
( ~ ( rel_s4 @ SV16 @ SY91 )
| ( big_f @ SY90 @ SY91 ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(133,plain,
( ( ( ~ ( rel_s4 @ sK9_SY38 @ sK13_SY74 ) )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(134,plain,
( ( ( p @ sK13_SY74 )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(135,plain,
( ( ( rel_s4 @ sK3_SY5 @ sK12_SY38 )
= $true )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(136,plain,
( ( ( ~ ! [SY81: $i] :
( ~ ( rel_s4 @ sK12_SY38 @ SY81 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY81 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY81 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(137,plain,
( ( ( ! [SY84: $i] :
( ~ ( rel_s4 @ sK12_SY38 @ SY84 )
| ( p @ SY84 ) ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(138,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK16_SY38 )
| ~ ! [SY92: $i] :
( ~ ( rel_s4 @ sK16_SY38 @ SY92 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY92 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY92 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY95: $i] :
( ~ ( rel_s4 @ sK16_SY38 @ SY95 )
| ( p @ SY95 ) ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(139,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK14_SY38 ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(140,plain,
( ( ( ~ ! [SY85: $i] :
( ~ ( rel_s4 @ sK14_SY38 @ SY85 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY85 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY85 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY88: $i] :
( ~ ( rel_s4 @ sK14_SY38 @ SY88 )
| ( p @ SY88 ) ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(141,plain,
! [SV10: mu,SV9: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
| ( p @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[127]) ).
thf(142,plain,
! [SV10: mu,SV9: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
| ( big_f @ SV10 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) ) )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(143,plain,
! [SV14: $i,SV15: mu] :
( ( ( ~ ( exists_in_world @ SV15 @ SV14 ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( rel_s4 @ SV14 @ SY89 )
| ( big_f @ SV15 @ SY89 ) ) )
= $true )
| ( ( rel_s4 @ sK6_SY38 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV17: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
| ! [SY96: mu] :
( ~ ( exists_in_world @ SY96 @ SV17 )
| ! [SY97: $i] :
( ~ ( rel_s4 @ SV17 @ SY97 )
| ( big_f @ SY96 @ SY97 ) ) ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV11: $i] :
( ( ( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ ( sK15_SY80 @ SV11 ) ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(146,plain,
! [SV11: $i] :
( ( ( p @ ( sK15_SY80 @ SV11 ) )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(147,plain,
! [SV16: $i] :
( ( ( ~ ( rel_s4 @ sK9_SY38 @ SV16 ) )
= $true )
| ( ( ! [SY90: mu] :
( ~ ( exists_in_world @ SY90 @ SV16 )
| ! [SY91: $i] :
( ~ ( rel_s4 @ SV16 @ SY91 )
| ( big_f @ SY90 @ SY91 ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(148,plain,
( ( ( rel_s4 @ sK9_SY38 @ sK13_SY74 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(149,plain,
( ( ( ! [SY81: $i] :
( ~ ( rel_s4 @ sK12_SY38 @ SY81 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY81 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY81 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $true )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(150,plain,
( ( ( ~ ( rel_s4 @ sK12_SY38 @ sK19_SY84 )
| ( p @ sK19_SY84 ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[137]) ).
thf(151,plain,
( ( ( ~ ( rel_s4 @ sK3_SY5 @ sK16_SY38 ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(152,plain,
( ( ( ~ ! [SY92: $i] :
( ~ ( rel_s4 @ sK16_SY38 @ SY92 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY92 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY92 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) )
| ! [SY95: $i] :
( ~ ( rel_s4 @ sK16_SY38 @ SY95 )
| ( p @ SY95 ) ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(153,plain,
( ( ( rel_s4 @ sK3_SY5 @ sK14_SY38 )
= $true )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(154,plain,
( ( ( ~ ! [SY85: $i] :
( ~ ( rel_s4 @ sK14_SY38 @ SY85 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY85 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY85 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(155,plain,
( ( ( ! [SY88: $i] :
( ~ ( rel_s4 @ sK14_SY38 @ SY88 )
| ( p @ SY88 ) ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(156,plain,
! [SV10: mu,SV9: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(157,plain,
! [SV12: $i,SV10: mu,SV9: $i] :
( ( ( p @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $false )
| ( ( ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(158,plain,
! [SV10: mu,SV9: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) ) )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(159,plain,
! [SV13: $i,SV9: $i,SV10: mu] :
( ( ( big_f @ SV10 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(160,plain,
! [SV14: $i,SV15: mu] :
( ( ( exists_in_world @ SV15 @ SV14 )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( rel_s4 @ SV14 @ SY89 )
| ( big_f @ SV15 @ SY89 ) ) )
= $true )
| ( ( rel_s4 @ sK6_SY38 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(161,plain,
! [SV17: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 ) )
= $true )
| ( ( ! [SY96: mu] :
( ~ ( exists_in_world @ SY96 @ SV17 )
| ! [SY97: $i] :
( ~ ( rel_s4 @ SV17 @ SY97 )
| ( big_f @ SY96 @ SY97 ) ) ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(162,plain,
! [SV11: $i] :
( ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ ( sK15_SY80 @ SV11 ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(163,plain,
! [SV16: $i] :
( ( ( rel_s4 @ sK9_SY38 @ SV16 )
= $false )
| ( ( ! [SY90: mu] :
( ~ ( exists_in_world @ SY90 @ SV16 )
| ! [SY91: $i] :
( ~ ( rel_s4 @ SV16 @ SY91 )
| ( big_f @ SY90 @ SY91 ) ) ) )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV18: $i] :
( ( ( ~ ( rel_s4 @ sK12_SY38 @ SV18 )
| ! [SY98: mu] :
( ~ ( exists_in_world @ SY98 @ SV18 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SV18 @ SY99 )
| ( big_f @ SY98 @ SY99 ) ) ) )
= $true )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(165,plain,
( ( ( ~ ( rel_s4 @ sK12_SY38 @ sK19_SY84 ) )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(166,plain,
( ( ( p @ sK19_SY84 )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(167,plain,
( ( ( rel_s4 @ sK3_SY5 @ sK16_SY38 )
= $true )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(168,plain,
( ( ( ~ ! [SY92: $i] :
( ~ ( rel_s4 @ sK16_SY38 @ SY92 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY92 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY92 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(169,plain,
( ( ( ! [SY95: $i] :
( ~ ( rel_s4 @ sK16_SY38 @ SY95 )
| ( p @ SY95 ) ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(170,plain,
( ( ( ! [SY85: $i] :
( ~ ( rel_s4 @ sK14_SY38 @ SY85 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY85 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY85 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $true )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(171,plain,
( ( ( ~ ( rel_s4 @ sK14_SY38 @ sK20_SY88 )
| ( p @ sK20_SY88 ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[155]) ).
thf(172,plain,
! [SV10: mu,SV9: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $true )
| ( ( ! [SY68: $i] :
( ~ ( rel_s4 @ SV12 @ SY68 )
| ( big_f @ SV10 @ SY68 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(173,plain,
! [SV9: $i,SV10: mu,SV19: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV19 )
| ( big_f @ SV10 @ SV19 ) )
= $true )
| ( ( p @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(174,plain,
! [SV10: mu,SV9: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( rel_s4 @ SV13 @ SY70 )
| ( p @ SY70 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(175,plain,
! [SV9: $i,SV10: mu,SV20: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV20 )
| ( p @ SV20 ) )
= $true )
| ( ( big_f @ SV10 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(176,plain,
! [SV15: mu,SV21: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV21 )
| ( big_f @ SV15 @ SV21 ) )
= $true )
| ( ( exists_in_world @ SV15 @ SV14 )
= $false )
| ( ( rel_s4 @ sK6_SY38 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(177,plain,
! [SV17: $i,SV11: $i] :
( ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
= $false )
| ( ( ! [SY96: mu] :
( ~ ( exists_in_world @ SY96 @ SV17 )
| ! [SY97: $i] :
( ~ ( rel_s4 @ SV17 @ SY97 )
| ( big_f @ SY96 @ SY97 ) ) ) )
= $true )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(178,plain,
! [SV16: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV16 )
| ! [SY100: $i] :
( ~ ( rel_s4 @ SV16 @ SY100 )
| ( big_f @ SV22 @ SY100 ) ) )
= $true )
| ( ( rel_s4 @ sK9_SY38 @ SV16 )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV18: $i] :
( ( ( ~ ( rel_s4 @ sK12_SY38 @ SV18 ) )
= $true )
| ( ( ! [SY98: mu] :
( ~ ( exists_in_world @ SY98 @ SV18 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SV18 @ SY99 )
| ( big_f @ SY98 @ SY99 ) ) ) )
= $true )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(180,plain,
( ( ( rel_s4 @ sK12_SY38 @ sK19_SY84 )
= $true )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(181,plain,
( ( ( ! [SY92: $i] :
( ~ ( rel_s4 @ sK16_SY38 @ SY92 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SY92 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SY92 @ SX5 )
| ( big_f @ SX4 @ SX5 ) ) ) ) )
= $true )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(182,plain,
( ( ( ~ ( rel_s4 @ sK16_SY38 @ sK21_SY95 )
| ( p @ sK21_SY95 ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[169]) ).
thf(183,plain,
! [SV23: $i] :
( ( ( ~ ( rel_s4 @ sK14_SY38 @ SV23 )
| ! [SY101: mu] :
( ~ ( exists_in_world @ SY101 @ SV23 )
| ! [SY102: $i] :
( ~ ( rel_s4 @ SV23 @ SY102 )
| ( big_f @ SY101 @ SY102 ) ) ) )
= $true )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(184,plain,
( ( ( ~ ( rel_s4 @ sK14_SY38 @ sK20_SY88 ) )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(185,plain,
( ( ( p @ sK20_SY88 )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(186,plain,
! [SV9: $i,SV10: mu,SV24: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV24 )
| ( big_f @ SV10 @ SV24 ) )
= $true )
| ( ( rel_s4 @ SV12 @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(187,plain,
! [SV9: $i,SV10: mu,SV19: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV19 ) )
= $true )
| ( ( big_f @ SV10 @ SV19 )
= $true )
| ( ( p @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(188,plain,
! [SV10: mu,SV9: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV25 )
| ( p @ SV25 ) )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(189,plain,
! [SV9: $i,SV10: mu,SV20: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV20 ) )
= $true )
| ( ( p @ SV20 )
= $true )
| ( ( big_f @ SV10 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(190,plain,
! [SV15: mu,SV21: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV21 ) )
= $true )
| ( ( big_f @ SV15 @ SV21 )
= $true )
| ( ( exists_in_world @ SV15 @ SV14 )
= $false )
| ( ( rel_s4 @ sK6_SY38 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(191,plain,
! [SV11: $i,SV17: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV17 )
| ! [SY103: $i] :
( ~ ( rel_s4 @ SV17 @ SY103 )
| ( big_f @ SV26 @ SY103 ) ) )
= $true )
| ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(192,plain,
! [SV16: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV16 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( rel_s4 @ SV16 @ SY100 )
| ( big_f @ SV22 @ SY100 ) ) )
= $true )
| ( ( rel_s4 @ sK9_SY38 @ SV16 )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(193,plain,
! [SV18: $i] :
( ( ( rel_s4 @ sK12_SY38 @ SV18 )
= $false )
| ( ( ! [SY98: mu] :
( ~ ( exists_in_world @ SY98 @ SV18 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SV18 @ SY99 )
| ( big_f @ SY98 @ SY99 ) ) ) )
= $true )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(194,plain,
! [SV27: $i] :
( ( ( ~ ( rel_s4 @ sK16_SY38 @ SV27 )
| ! [SY104: mu] :
( ~ ( exists_in_world @ SY104 @ SV27 )
| ! [SY105: $i] :
( ~ ( rel_s4 @ SV27 @ SY105 )
| ( big_f @ SY104 @ SY105 ) ) ) )
= $true )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(195,plain,
( ( ( ~ ( rel_s4 @ sK16_SY38 @ sK21_SY95 ) )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(196,plain,
( ( ( p @ sK21_SY95 )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(197,plain,
! [SV23: $i] :
( ( ( ~ ( rel_s4 @ sK14_SY38 @ SV23 ) )
= $true )
| ( ( ! [SY101: mu] :
( ~ ( exists_in_world @ SY101 @ SV23 )
| ! [SY102: $i] :
( ~ ( rel_s4 @ SV23 @ SY102 )
| ( big_f @ SY101 @ SY102 ) ) ) )
= $true )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(198,plain,
( ( ( rel_s4 @ sK14_SY38 @ sK20_SY88 )
= $true )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(199,plain,
! [SV9: $i,SV10: mu,SV24: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV24 ) )
= $true )
| ( ( big_f @ SV10 @ SV24 )
= $true )
| ( ( rel_s4 @ SV12 @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(200,plain,
! [SV9: $i,SV10: mu,SV19: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV19 )
= $false )
| ( ( big_f @ SV10 @ SV19 )
= $true )
| ( ( p @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(201,plain,
! [SV10: mu,SV9: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV25 ) )
= $true )
| ( ( p @ SV25 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(202,plain,
! [SV9: $i,SV10: mu,SV20: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV20 )
= $false )
| ( ( p @ SV20 )
= $true )
| ( ( big_f @ SV10 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $false )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(203,plain,
! [SV15: mu,SV21: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV21 )
= $false )
| ( ( big_f @ SV15 @ SV21 )
= $true )
| ( ( exists_in_world @ SV15 @ SV14 )
= $false )
| ( ( rel_s4 @ sK6_SY38 @ SV14 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ sK4_SY33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(204,plain,
! [SV11: $i,SV17: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV17 ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( rel_s4 @ SV17 @ SY103 )
| ( big_f @ SV26 @ SY103 ) ) )
= $true )
| ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV16: $i,SV22: mu] :
( ( ( exists_in_world @ SV22 @ SV16 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( rel_s4 @ SV16 @ SY100 )
| ( big_f @ SV22 @ SY100 ) ) )
= $true )
| ( ( rel_s4 @ sK9_SY38 @ SV16 )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(206,plain,
! [SV18: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV18 )
| ! [SY106: $i] :
( ~ ( rel_s4 @ SV18 @ SY106 )
| ( big_f @ SV28 @ SY106 ) ) )
= $true )
| ( ( rel_s4 @ sK12_SY38 @ SV18 )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV27: $i] :
( ( ( ~ ( rel_s4 @ sK16_SY38 @ SV27 ) )
= $true )
| ( ( ! [SY104: mu] :
( ~ ( exists_in_world @ SY104 @ SV27 )
| ! [SY105: $i] :
( ~ ( rel_s4 @ SV27 @ SY105 )
| ( big_f @ SY104 @ SY105 ) ) ) )
= $true )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(208,plain,
( ( ( rel_s4 @ sK16_SY38 @ sK21_SY95 )
= $true )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(209,plain,
! [SV23: $i] :
( ( ( rel_s4 @ sK14_SY38 @ SV23 )
= $false )
| ( ( ! [SY101: mu] :
( ~ ( exists_in_world @ SY101 @ SV23 )
| ! [SY102: $i] :
( ~ ( rel_s4 @ SV23 @ SY102 )
| ( big_f @ SY101 @ SY102 ) ) ) )
= $true )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV9: $i,SV10: mu,SV24: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV24 )
= $false )
| ( ( big_f @ SV10 @ SV24 )
= $true )
| ( ( rel_s4 @ SV12 @ ( sK17_SY67 @ SV9 @ SV10 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV12 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV10: mu,SV9: $i,SV25: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV25 )
= $false )
| ( ( p @ SV25 )
= $true )
| ( ( rel_s4 @ SV13 @ ( sK18_SY69 @ SV9 @ SV10 @ SV13 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV13 )
= $false )
| ( ( exists_in_world @ SV10 @ SV9 )
= $false )
| ( ( rel_s4 @ sK3_SY5 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV11: $i,SV17: $i,SV26: mu] :
( ( ( exists_in_world @ SV26 @ SV17 )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( rel_s4 @ SV17 @ SY103 )
| ( big_f @ SV26 @ SY103 ) ) )
= $true )
| ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV22: mu,SV29: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ SV29 )
| ( big_f @ SV22 @ SV29 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV16 )
= $false )
| ( ( rel_s4 @ sK9_SY38 @ SV16 )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(214,plain,
! [SV18: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV18 ) )
= $true )
| ( ( ! [SY106: $i] :
( ~ ( rel_s4 @ SV18 @ SY106 )
| ( big_f @ SV28 @ SY106 ) ) )
= $true )
| ( ( rel_s4 @ sK12_SY38 @ SV18 )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(215,plain,
! [SV27: $i] :
( ( ( rel_s4 @ sK16_SY38 @ SV27 )
= $false )
| ( ( ! [SY104: mu] :
( ~ ( exists_in_world @ SY104 @ SV27 )
| ! [SY105: $i] :
( ~ ( rel_s4 @ SV27 @ SY105 )
| ( big_f @ SY104 @ SY105 ) ) ) )
= $true )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(216,plain,
! [SV23: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV23 )
| ! [SY107: $i] :
( ~ ( rel_s4 @ SV23 @ SY107 )
| ( big_f @ SV30 @ SY107 ) ) )
= $true )
| ( ( rel_s4 @ sK14_SY38 @ SV23 )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(217,plain,
! [SV11: $i,SV26: mu,SV31: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV31 )
| ( big_f @ SV26 @ SV31 ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV17 )
= $false )
| ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(218,plain,
! [SV22: mu,SV29: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ SV29 ) )
= $true )
| ( ( big_f @ SV22 @ SV29 )
= $true )
| ( ( exists_in_world @ SV22 @ SV16 )
= $false )
| ( ( rel_s4 @ sK9_SY38 @ SV16 )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(219,plain,
! [SV18: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV18 )
= $false )
| ( ( ! [SY106: $i] :
( ~ ( rel_s4 @ SV18 @ SY106 )
| ( big_f @ SV28 @ SY106 ) ) )
= $true )
| ( ( rel_s4 @ sK12_SY38 @ SV18 )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(220,plain,
! [SV27: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV27 )
| ! [SY108: $i] :
( ~ ( rel_s4 @ SV27 @ SY108 )
| ( big_f @ SV32 @ SY108 ) ) )
= $true )
| ( ( rel_s4 @ sK16_SY38 @ SV27 )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(221,plain,
! [SV23: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV23 ) )
= $true )
| ( ( ! [SY107: $i] :
( ~ ( rel_s4 @ SV23 @ SY107 )
| ( big_f @ SV30 @ SY107 ) ) )
= $true )
| ( ( rel_s4 @ sK14_SY38 @ SV23 )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(222,plain,
! [SV11: $i,SV26: mu,SV31: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV31 ) )
= $true )
| ( ( big_f @ SV26 @ SV31 )
= $true )
| ( ( exists_in_world @ SV26 @ SV17 )
= $false )
| ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(223,plain,
! [SV22: mu,SV29: $i,SV16: $i] :
( ( ( rel_s4 @ SV16 @ SV29 )
= $false )
| ( ( big_f @ SV22 @ SV29 )
= $true )
| ( ( exists_in_world @ SV22 @ SV16 )
= $false )
| ( ( rel_s4 @ sK9_SY38 @ SV16 )
= $false )
| ( ( rel_s4 @ sK4_SY33 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(224,plain,
! [SV28: mu,SV33: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV33 )
| ( big_f @ SV28 @ SV33 ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV18 )
= $false )
| ( ( rel_s4 @ sK12_SY38 @ SV18 )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(225,plain,
! [SV27: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV27 ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( rel_s4 @ SV27 @ SY108 )
| ( big_f @ SV32 @ SY108 ) ) )
= $true )
| ( ( rel_s4 @ sK16_SY38 @ SV27 )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV23: $i,SV30: mu] :
( ( ( exists_in_world @ SV30 @ SV23 )
= $false )
| ( ( ! [SY107: $i] :
( ~ ( rel_s4 @ SV23 @ SY107 )
| ( big_f @ SV30 @ SY107 ) ) )
= $true )
| ( ( rel_s4 @ sK14_SY38 @ SV23 )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV11: $i,SV26: mu,SV31: $i,SV17: $i] :
( ( ( rel_s4 @ SV17 @ SV31 )
= $false )
| ( ( big_f @ SV26 @ SV31 )
= $true )
| ( ( exists_in_world @ SV26 @ SV17 )
= $false )
| ( ( rel_s4 @ ( sK11_SY38 @ SV11 ) @ SV17 )
= $false )
| ( ( p @ SV11 )
= $true )
| ( ( rel_s4 @ sK4_SY33 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(228,plain,
! [SV28: mu,SV33: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV33 ) )
= $true )
| ( ( big_f @ SV28 @ SV33 )
= $true )
| ( ( exists_in_world @ SV28 @ SV18 )
= $false )
| ( ( rel_s4 @ sK12_SY38 @ SV18 )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV27: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( rel_s4 @ SV27 @ SY108 )
| ( big_f @ SV32 @ SY108 ) ) )
= $true )
| ( ( rel_s4 @ sK16_SY38 @ SV27 )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(230,plain,
! [SV30: mu,SV34: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV34 )
| ( big_f @ SV30 @ SV34 ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV23 )
= $false )
| ( ( rel_s4 @ sK14_SY38 @ SV23 )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(231,plain,
! [SV28: mu,SV33: $i,SV18: $i] :
( ( ( rel_s4 @ SV18 @ SV33 )
= $false )
| ( ( big_f @ SV28 @ SV33 )
= $true )
| ( ( exists_in_world @ SV28 @ SV18 )
= $false )
| ( ( rel_s4 @ sK12_SY38 @ SV18 )
= $false )
| ( ( exists_in_world @ sK7_SY60 @ sK5_SY51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(232,plain,
! [SV32: mu,SV35: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV35 )
| ( big_f @ SV32 @ SV35 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ sK16_SY38 @ SV27 )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(233,plain,
! [SV30: mu,SV34: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV34 ) )
= $true )
| ( ( big_f @ SV30 @ SV34 )
= $true )
| ( ( exists_in_world @ SV30 @ SV23 )
= $false )
| ( ( rel_s4 @ sK14_SY38 @ SV23 )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(234,plain,
! [SV32: mu,SV35: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV35 ) )
= $true )
| ( ( big_f @ SV32 @ SV35 )
= $true )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ sK16_SY38 @ SV27 )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(235,plain,
! [SV30: mu,SV34: $i,SV23: $i] :
( ( ( rel_s4 @ SV23 @ SV34 )
= $false )
| ( ( big_f @ SV30 @ SV34 )
= $true )
| ( ( exists_in_world @ SV30 @ SV23 )
= $false )
| ( ( rel_s4 @ sK14_SY38 @ SV23 )
= $false )
| ( ( big_f @ sK7_SY60 @ sK10_SY66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(236,plain,
! [SV32: mu,SV35: $i,SV27: $i] :
( ( ( rel_s4 @ SV27 @ SV35 )
= $false )
| ( ( big_f @ SV32 @ SV35 )
= $true )
| ( ( exists_in_world @ SV32 @ SV27 )
= $false )
| ( ( rel_s4 @ sK16_SY38 @ SV27 )
= $false )
| ( ( rel_s4 @ sK5_SY51 @ sK10_SY66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(237,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,236,235,231,227,223,211,210,208,203,202,200,198,196,185,180,167,166,162,153,148,146,135,134,118,109,106,96,77,51,42,34,22]) ).
thf(238,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN052^7 : TPTP v8.1.0. Released v5.5.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jul 11 20:20:45 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.38
% 0.15/0.38 No.of.Axioms: 4
% 0.15/0.38
% 0.15/0.38 Length.of.Defs: 5540
% 0.15/0.38
% 0.15/0.38 Contains.Choice.Funs: false
% 0.15/0.39 (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)....................
% 21.62/21.83
% 21.62/21.83 ********************************
% 21.62/21.83 * All subproblems solved! *
% 21.62/21.83 ********************************
% 21.62/21.83 % 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:237,loop_count:0,foatp_calls:1,translation:fof_full)
% 21.62/21.88
% 21.62/21.88 %**** Beginning of derivation protocol ****
% 21.62/21.88 % SZS output start CNFRefutation
% See solution above
% 21.62/21.88
% 21.62/21.88 %**** End of derivation protocol ****
% 21.62/21.88 %**** no. of clauses in derivation: 238 ****
% 21.62/21.88 %**** clause counter: 237 ****
% 21.62/21.88
% 21.62/21.88 % 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:237,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------