%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:06:58 AM UTC 2026
% Result : Theorem 20.64s 3.66s
% Output : CNFRefutation 20.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 68
% Syntax : Number of formulae : 740 ( 161 unt; 0 typ; 32 def)
% Number of atoms : 12100 (3177 equ; 0 cnn)
% Maximal formula atoms : 16 ( 16 avg)
% Number of connectives : 15840 (2654 ~;4599 |; 13 &;8560 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 3 con; 0-3 aty)
% Number of variables : 3494 ( 49 ^;3436 !; 9 ?;3494 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
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_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK1_SY1,type,
sK1_SY1: $i ).
thf(tp_sK2_SY1522,type,
sK2_SY1522: $i > $i ).
thf(tp_sK3_SY1523,type,
sK3_SY1523: $i > mu ).
thf(tp_v1,type,
v1: $i > $o ).
thf(tp_v2,type,
v2: $i > $o ).
thf(tp_v3,type,
v3: $i > $o ).
thf(tp_v4,type,
v4: $i > $o ).
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,
mvalid @ ( mdia_s4 @ mtrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',deontic1) ).
thf(2,axiom,
mvalid @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat30) ).
thf(3,axiom,
mvalid @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat29) ).
thf(4,axiom,
mvalid @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat28) ).
thf(5,axiom,
mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat27) ).
thf(6,axiom,
mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat26) ).
thf(7,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat25) ).
thf(8,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat24) ).
thf(9,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat23) ).
thf(10,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat22) ).
thf(11,axiom,
mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat21) ).
thf(12,axiom,
mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat20) ).
thf(13,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat19) ).
thf(14,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat18) ).
thf(15,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat17) ).
thf(16,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat16) ).
thf(17,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat15) ).
thf(18,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat14) ).
thf(19,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat13) ).
thf(20,axiom,
mvalid @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat12) ).
thf(21,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat11) ).
thf(22,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat10) ).
thf(23,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat9) ).
thf(24,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat8) ).
thf(25,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat7) ).
thf(26,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat6) ).
thf(27,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat5) ).
thf(28,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat4) ).
thf(29,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat3) ).
thf(30,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat2) ).
thf(31,axiom,
mvalid @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',persat1) ).
thf(32,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(33,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(35,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(36,conjecture,
mvalid @ mfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',result1) ).
thf(37,negated_conjecture,
( ( mvalid @ mfalse )
= $false ),
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,plain,
( ( ! [SY1: $i] : ~ $true )
= $false ),
inference(unfold_def,[status(thm)],[37,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(39,plain,
( ( ! [SY9: $i] :
~ ! [SY10: $i] :
( ~ ( rel_s4 @ SY9 @ SY10 )
| ~ $true ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(40,plain,
( ( ! [SY59: $i] :
( ~ ( v4 @ SY59 )
| ! [SY60: $i] :
( ~ ( rel_s4 @ SY59 @ SY60 )
| ! [SY20: $i] :
( ~ ( rel_s4 @ SY60 @ SY20 )
| ( v2 @ SY20 ) ) )
| ! [SY62: $i] :
( ~ ( rel_s4 @ SY59 @ SY62 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY62 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY64: $i] :
( ~ ( rel_s4 @ SY59 @ SY64 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY64 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(41,plain,
( ( ! [SY119: $i] :
( ~ ( v4 @ SY119 )
| ! [SY120: $i] :
( ~ ( rel_s4 @ SY119 @ SY120 )
| ! [SY80: $i] :
( ~ ( rel_s4 @ SY120 @ SY80 )
| ( v1 @ SY80 ) ) )
| ! [SY122: $i] :
( ~ ( rel_s4 @ SY119 @ SY122 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY122 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY124: $i] :
( ~ ( rel_s4 @ SY119 @ SY124 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY124 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(42,plain,
( ( ! [SY174: $i] :
( ~ ( v4 @ SY174 )
| ! [SY175: $i] :
( ~ ( rel_s4 @ SY174 @ SY175 )
| ( v3 @ SY175 ) )
| ! [SY176: $i] :
( ~ ( rel_s4 @ SY174 @ SY176 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY176 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY178: $i] :
( ~ ( rel_s4 @ SY174 @ SY178 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY178 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(43,plain,
( ( ! [SY232: $i] :
( ~ ( v3 @ SY232 )
| ! [SY233: $i] :
( ~ ( rel_s4 @ SY232 @ SY233 )
| ! [SY193: $i] :
( ~ ( rel_s4 @ SY233 @ SY193 )
| ( v2 @ SY193 ) ) )
| ! [SY235: $i] :
( ~ ( rel_s4 @ SY232 @ SY235 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY235 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY237: $i] :
( ~ ( rel_s4 @ SY232 @ SY237 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY237 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(44,plain,
( ( ! [SY281: $i] :
( ~ ( v3 @ SY281 )
| ! [SY282: $i] :
( ~ ( rel_s4 @ SY281 @ SY282 )
| ~ ( v2 @ SY282 ) )
| ! [SY283: $i] :
( ~ ( rel_s4 @ SY281 @ SY283 )
| ~ ( v4 @ SY283 ) )
| ! [SY284: $i] :
( ~ ( rel_s4 @ SY281 @ SY284 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY284 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(45,plain,
( ( ! [SY326: $i] :
( ~ ( v1 @ SY326 )
| ! [SY327: $i] :
( ~ ( rel_s4 @ SY326 @ SY327 )
| ~ ( v1 @ SY327 ) )
| ! [SY328: $i] :
( ~ ( rel_s4 @ SY326 @ SY328 )
| ~ ( v3 @ SY328 ) )
| ! [SY329: $i] :
( ~ ( rel_s4 @ SY326 @ SY329 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY329 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(46,plain,
( ( ! [SY372: $i] :
( ~ ( v1 @ SY372 )
| ~ ( v4 @ SY372 )
| ! [SY373: $i] :
( ~ ( rel_s4 @ SY372 @ SY373 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY373 @ SY346 )
| ( v3 @ SY346 ) ) )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SY372 @ SY375 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY375 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(47,plain,
( ( ! [SY417: $i] :
( ~ ( v1 @ SY417 )
| ~ ( v4 @ SY417 )
| ! [SY418: $i] :
( ~ ( rel_s4 @ SY417 @ SY418 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY418 @ SY392 )
| ( v1 @ SY392 ) ) )
| ! [SY420: $i] :
( ~ ( rel_s4 @ SY417 @ SY420 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY420 @ SY401 )
| ( v4 @ SY401 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(48,plain,
( ( ! [SY462: $i] :
( ~ ( v1 @ SY462 )
| ~ ( v3 @ SY462 )
| ! [SY463: $i] :
( ~ ( rel_s4 @ SY462 @ SY463 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY463 @ SY437 )
| ( v2 @ SY437 ) ) )
| ! [SY465: $i] :
( ~ ( rel_s4 @ SY462 @ SY465 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY465 @ SY446 )
| ( v3 @ SY446 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(49,plain,
( ( ! [SY507: $i] :
( ( v4 @ SY507 )
| ~ ( v2 @ SY507 )
| ! [SY508: $i] :
( ~ ( rel_s4 @ SY507 @ SY508 )
| ! [SY481: $i] :
( ~ ( rel_s4 @ SY508 @ SY481 )
| ( v3 @ SY481 ) ) )
| ! [SY510: $i] :
( ~ ( rel_s4 @ SY507 @ SY510 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY510 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) ) )
= $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(50,plain,
( ( ! [SY545: $i] :
( ( v4 @ SY545 )
| ~ ( v2 @ SY545 )
| ! [SY546: $i] :
( ~ ( rel_s4 @ SY545 @ SY546 )
| ~ ( v1 @ SY546 ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY545 @ SY547 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY547 @ SY532 )
| ( v2 @ SY532 ) ) ) ) )
= $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(51,plain,
( ( ! [SY599: $i] :
( ( v3 @ SY599 )
| ! [SY600: $i] :
( ~ ( rel_s4 @ SY599 @ SY600 )
| ! [SY559: $i] :
( ~ ( rel_s4 @ SY600 @ SY559 )
| ( v3 @ SY559 ) ) )
| ! [SY602: $i] :
( ~ ( rel_s4 @ SY599 @ SY602 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY602 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY604: $i] :
( ~ ( rel_s4 @ SY599 @ SY604 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY604 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,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(52,plain,
( ( ! [SY652: $i] :
( ( v3 @ SY652 )
| ! [SY653: $i] :
( ~ ( rel_s4 @ SY652 @ SY653 )
| ~ ( v3 @ SY653 ) )
| ! [SY654: $i] :
( ~ ( rel_s4 @ SY652 @ SY654 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY654 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY656: $i] :
( ~ ( rel_s4 @ SY652 @ SY656 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY656 @ SY634 )
| ( v3 @ SY634 ) ) ) ) )
= $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(53,plain,
( ( ! [SY698: $i] :
( ( v3 @ SY698 )
| ! [SY699: $i] :
( ~ ( rel_s4 @ SY698 @ SY699 )
| ~ ( v2 @ SY699 ) )
| ! [SY700: $i] :
( ~ ( rel_s4 @ SY698 @ SY700 )
| ~ ( v3 @ SY700 ) )
| ! [SY701: $i] :
( ~ ( rel_s4 @ SY698 @ SY701 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY701 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,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(54,plain,
( ( ! [SY746: $i] :
( ( v3 @ SY746 )
| ! [SY747: $i] :
( ~ ( rel_s4 @ SY746 @ SY747 )
| ( v4 @ SY747 ) )
| ! [SY748: $i] :
( ~ ( rel_s4 @ SY746 @ SY748 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY748 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY750: $i] :
( ~ ( rel_s4 @ SY746 @ SY750 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY750 @ SY728 )
| ( v3 @ SY728 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,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(55,plain,
( ( ! [SY794: $i] :
( ( v3 @ SY794 )
| ~ ( v2 @ SY794 )
| ! [SY795: $i] :
( ~ ( rel_s4 @ SY794 @ SY795 )
| ! [SY768: $i] :
( ~ ( rel_s4 @ SY795 @ SY768 )
| ~ ( v2 @ SY768 ) ) )
| ! [SY797: $i] :
( ~ ( rel_s4 @ SY794 @ SY797 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY797 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,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(56,plain,
( ( ! [SY832: $i] :
( ( v3 @ SY832 )
| ~ ( v1 @ SY832 )
| ! [SY833: $i] :
( ~ ( rel_s4 @ SY832 @ SY833 )
| ~ ( v3 @ SY833 ) )
| ! [SY834: $i] :
( ~ ( rel_s4 @ SY832 @ SY834 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY834 @ SY819 )
| ( v4 @ SY819 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(57,plain,
( ( ! [SY862: $i] :
( ( v3 @ SY862 )
| ~ ( v1 @ SY862 )
| ~ ( v4 @ SY862 )
| ! [SY863: $i] :
( ~ ( rel_s4 @ SY862 @ SY863 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY863 @ SY852 )
| ( v2 @ SY852 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(58,plain,
( ( ! [SY895: $i] :
( ( v3 @ SY895 )
| ( v4 @ SY895 )
| ! [SY896: $i] :
( ~ ( rel_s4 @ SY895 @ SY896 )
| ~ ( v4 @ SY896 ) )
| ! [SY897: $i] :
( ~ ( rel_s4 @ SY895 @ SY897 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY897 @ SY882 )
| ( v1 @ SY882 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(59,plain,
( ( ! [SY936: $i] :
( ( v2 @ SY936 )
| ! [SY937: $i] :
( ~ ( rel_s4 @ SY936 @ SY937 )
| ( v4 @ SY937 ) )
| ! [SY938: $i] :
( ~ ( rel_s4 @ SY936 @ SY938 )
| ~ ( v4 @ SY938 ) )
| ! [SY939: $i] :
( ~ ( rel_s4 @ SY936 @ SY939 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY939 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,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(60,plain,
( ( ! [SY975: $i] :
( ( v2 @ SY975 )
| ~ ( v4 @ SY975 )
| ! [SY976: $i] :
( ~ ( rel_s4 @ SY975 @ SY976 )
| ~ ( v4 @ SY976 ) )
| ! [SY977: $i] :
( ~ ( rel_s4 @ SY975 @ SY977 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY977 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22,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(61,plain,
( ( ! [SY1012: $i] :
( ( v2 @ SY1012 )
| ~ ( v3 @ SY1012 )
| ! [SY1013: $i] :
( ~ ( rel_s4 @ SY1012 @ SY1013 )
| ~ ( v3 @ SY1013 ) )
| ! [SY1014: $i] :
( ~ ( rel_s4 @ SY1012 @ SY1014 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1014 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(62,plain,
( ( ! [SY1049: $i] :
( ( v2 @ SY1049 )
| ~ ( v1 @ SY1049 )
| ! [SY1050: $i] :
( ~ ( rel_s4 @ SY1049 @ SY1050 )
| ~ ( v3 @ SY1050 ) )
| ! [SY1051: $i] :
( ~ ( rel_s4 @ SY1049 @ SY1051 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1051 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24,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(63,plain,
( ( ! [SY1098: $i] :
( ( v1 @ SY1098 )
| ! [SY1099: $i] :
( ~ ( rel_s4 @ SY1098 @ SY1099 )
| ~ ( v3 @ SY1099 ) )
| ! [SY1100: $i] :
( ~ ( rel_s4 @ SY1098 @ SY1100 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1100 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1102: $i] :
( ~ ( rel_s4 @ SY1098 @ SY1102 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1102 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25,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(64,plain,
( ( ! [SY1150: $i] :
( ( v1 @ SY1150 )
| ! [SY1151: $i] :
( ~ ( rel_s4 @ SY1150 @ SY1151 )
| ~ ( v2 @ SY1151 ) )
| ! [SY1152: $i] :
( ~ ( rel_s4 @ SY1150 @ SY1152 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1152 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1154: $i] :
( ~ ( rel_s4 @ SY1150 @ SY1154 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1154 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26,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(65,plain,
( ( ! [SY1201: $i] :
( ( v1 @ SY1201 )
| ! [SY1202: $i] :
( ~ ( rel_s4 @ SY1201 @ SY1202 )
| ( v1 @ SY1202 ) )
| ! [SY1203: $i] :
( ~ ( rel_s4 @ SY1201 @ SY1203 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1203 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1205: $i] :
( ~ ( rel_s4 @ SY1201 @ SY1205 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1205 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27,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(66,plain,
( ( ! [SY1248: $i] :
( ( v1 @ SY1248 )
| ~ ( v3 @ SY1248 )
| ! [SY1249: $i] :
( ~ ( rel_s4 @ SY1248 @ SY1249 )
| ! [SY1222: $i] :
( ~ ( rel_s4 @ SY1249 @ SY1222 )
| ( v2 @ SY1222 ) ) )
| ! [SY1251: $i] :
( ~ ( rel_s4 @ SY1248 @ SY1251 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1251 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28,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(67,plain,
( ( ! [SY1286: $i] :
( ( v1 @ SY1286 )
| ~ ( v3 @ SY1286 )
| ! [SY1287: $i] :
( ~ ( rel_s4 @ SY1286 @ SY1287 )
| ~ ( v4 @ SY1287 ) )
| ! [SY1288: $i] :
( ~ ( rel_s4 @ SY1286 @ SY1288 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1288 @ SY1273 )
| ( v1 @ SY1273 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29,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(68,plain,
( ( ! [SY1329: $i] :
( ( v1 @ SY1329 )
| ~ ( v2 @ SY1329 )
| ! [SY1330: $i] :
( ~ ( rel_s4 @ SY1329 @ SY1330 )
| ! [SY1303: $i] :
( ~ ( rel_s4 @ SY1330 @ SY1303 )
| ( v4 @ SY1303 ) ) )
| ! [SY1332: $i] :
( ~ ( rel_s4 @ SY1329 @ SY1332 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1332 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,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(69,plain,
( ( ! [SY1374: $i] :
( ( v1 @ SY1374 )
| ( v3 @ SY1374 )
| ! [SY1375: $i] :
( ~ ( rel_s4 @ SY1374 @ SY1375 )
| ! [SY1348: $i] :
( ~ ( rel_s4 @ SY1375 @ SY1348 )
| ~ ( v1 @ SY1348 ) ) )
| ! [SY1377: $i] :
( ~ ( rel_s4 @ SY1374 @ SY1377 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1377 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(70,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32,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(71,plain,
( ( ! [SY1387: $i,SY1388: $i,SY1389: $i] :
( ( ( rel_s4 @ SY1387 @ SY1388 )
& ( rel_s4 @ SY1388 @ SY1389 ) )
=> ( rel_s4 @ SY1387 @ SY1389 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(72,plain,
( ( ! [SY1393: $i] : ( rel_s4 @ SY1393 @ SY1393 ) )
= $true ),
inference(unfold_def,[status(thm)],[34,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(73,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[35,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(74,plain,
( ( ~ $true ) = $false ),
inference(extcnf_forall_neg,[status(esa)],[38]) ).
thf(75,plain,
$true = $true,
inference(polarity_switch,[status(thm)],[74]) ).
thf(76,plain,
( ( ! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [SY1393: $i] : ( rel_s4 @ SY1393 @ SY1393 ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(78,plain,
( ( ! [SY1387: $i,SY1388: $i,SY1389: $i] :
( ( ( rel_s4 @ SY1387 @ SY1388 )
& ( rel_s4 @ SY1388 @ SY1389 ) )
=> ( rel_s4 @ SY1387 @ SY1389 ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(79,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)],[70]) ).
thf(80,plain,
( ( ! [SY1374: $i] :
( ( v1 @ SY1374 )
| ( v3 @ SY1374 )
| ! [SY1375: $i] :
( ~ ( rel_s4 @ SY1374 @ SY1375 )
| ! [SY1348: $i] :
( ~ ( rel_s4 @ SY1375 @ SY1348 )
| ~ ( v1 @ SY1348 ) ) )
| ! [SY1377: $i] :
( ~ ( rel_s4 @ SY1374 @ SY1377 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1377 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(81,plain,
( ( ! [SY1329: $i] :
( ( v1 @ SY1329 )
| ~ ( v2 @ SY1329 )
| ! [SY1330: $i] :
( ~ ( rel_s4 @ SY1329 @ SY1330 )
| ! [SY1303: $i] :
( ~ ( rel_s4 @ SY1330 @ SY1303 )
| ( v4 @ SY1303 ) ) )
| ! [SY1332: $i] :
( ~ ( rel_s4 @ SY1329 @ SY1332 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1332 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(82,plain,
( ( ! [SY1286: $i] :
( ( v1 @ SY1286 )
| ~ ( v3 @ SY1286 )
| ! [SY1287: $i] :
( ~ ( rel_s4 @ SY1286 @ SY1287 )
| ~ ( v4 @ SY1287 ) )
| ! [SY1288: $i] :
( ~ ( rel_s4 @ SY1286 @ SY1288 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1288 @ SY1273 )
| ( v1 @ SY1273 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(83,plain,
( ( ! [SY1248: $i] :
( ( v1 @ SY1248 )
| ~ ( v3 @ SY1248 )
| ! [SY1249: $i] :
( ~ ( rel_s4 @ SY1248 @ SY1249 )
| ! [SY1222: $i] :
( ~ ( rel_s4 @ SY1249 @ SY1222 )
| ( v2 @ SY1222 ) ) )
| ! [SY1251: $i] :
( ~ ( rel_s4 @ SY1248 @ SY1251 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1251 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(84,plain,
( ( ! [SY1201: $i] :
( ( v1 @ SY1201 )
| ! [SY1202: $i] :
( ~ ( rel_s4 @ SY1201 @ SY1202 )
| ( v1 @ SY1202 ) )
| ! [SY1203: $i] :
( ~ ( rel_s4 @ SY1201 @ SY1203 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1203 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1205: $i] :
( ~ ( rel_s4 @ SY1201 @ SY1205 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1205 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(85,plain,
( ( ! [SY1150: $i] :
( ( v1 @ SY1150 )
| ! [SY1151: $i] :
( ~ ( rel_s4 @ SY1150 @ SY1151 )
| ~ ( v2 @ SY1151 ) )
| ! [SY1152: $i] :
( ~ ( rel_s4 @ SY1150 @ SY1152 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1152 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1154: $i] :
( ~ ( rel_s4 @ SY1150 @ SY1154 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1154 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(86,plain,
( ( ! [SY1098: $i] :
( ( v1 @ SY1098 )
| ! [SY1099: $i] :
( ~ ( rel_s4 @ SY1098 @ SY1099 )
| ~ ( v3 @ SY1099 ) )
| ! [SY1100: $i] :
( ~ ( rel_s4 @ SY1098 @ SY1100 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1100 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1102: $i] :
( ~ ( rel_s4 @ SY1098 @ SY1102 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1102 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(87,plain,
( ( ! [SY1049: $i] :
( ( v2 @ SY1049 )
| ~ ( v1 @ SY1049 )
| ! [SY1050: $i] :
( ~ ( rel_s4 @ SY1049 @ SY1050 )
| ~ ( v3 @ SY1050 ) )
| ! [SY1051: $i] :
( ~ ( rel_s4 @ SY1049 @ SY1051 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1051 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(88,plain,
( ( ! [SY1012: $i] :
( ( v2 @ SY1012 )
| ~ ( v3 @ SY1012 )
| ! [SY1013: $i] :
( ~ ( rel_s4 @ SY1012 @ SY1013 )
| ~ ( v3 @ SY1013 ) )
| ! [SY1014: $i] :
( ~ ( rel_s4 @ SY1012 @ SY1014 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1014 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(89,plain,
( ( ! [SY975: $i] :
( ( v2 @ SY975 )
| ~ ( v4 @ SY975 )
| ! [SY976: $i] :
( ~ ( rel_s4 @ SY975 @ SY976 )
| ~ ( v4 @ SY976 ) )
| ! [SY977: $i] :
( ~ ( rel_s4 @ SY975 @ SY977 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY977 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(90,plain,
( ( ! [SY936: $i] :
( ( v2 @ SY936 )
| ! [SY937: $i] :
( ~ ( rel_s4 @ SY936 @ SY937 )
| ( v4 @ SY937 ) )
| ! [SY938: $i] :
( ~ ( rel_s4 @ SY936 @ SY938 )
| ~ ( v4 @ SY938 ) )
| ! [SY939: $i] :
( ~ ( rel_s4 @ SY936 @ SY939 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY939 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(91,plain,
( ( ! [SY895: $i] :
( ( v3 @ SY895 )
| ( v4 @ SY895 )
| ! [SY896: $i] :
( ~ ( rel_s4 @ SY895 @ SY896 )
| ~ ( v4 @ SY896 ) )
| ! [SY897: $i] :
( ~ ( rel_s4 @ SY895 @ SY897 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY897 @ SY882 )
| ( v1 @ SY882 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(92,plain,
( ( ! [SY862: $i] :
( ( v3 @ SY862 )
| ~ ( v1 @ SY862 )
| ~ ( v4 @ SY862 )
| ! [SY863: $i] :
( ~ ( rel_s4 @ SY862 @ SY863 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY863 @ SY852 )
| ( v2 @ SY852 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(93,plain,
( ( ! [SY832: $i] :
( ( v3 @ SY832 )
| ~ ( v1 @ SY832 )
| ! [SY833: $i] :
( ~ ( rel_s4 @ SY832 @ SY833 )
| ~ ( v3 @ SY833 ) )
| ! [SY834: $i] :
( ~ ( rel_s4 @ SY832 @ SY834 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY834 @ SY819 )
| ( v4 @ SY819 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(94,plain,
( ( ! [SY794: $i] :
( ( v3 @ SY794 )
| ~ ( v2 @ SY794 )
| ! [SY795: $i] :
( ~ ( rel_s4 @ SY794 @ SY795 )
| ! [SY768: $i] :
( ~ ( rel_s4 @ SY795 @ SY768 )
| ~ ( v2 @ SY768 ) ) )
| ! [SY797: $i] :
( ~ ( rel_s4 @ SY794 @ SY797 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY797 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(95,plain,
( ( ! [SY746: $i] :
( ( v3 @ SY746 )
| ! [SY747: $i] :
( ~ ( rel_s4 @ SY746 @ SY747 )
| ( v4 @ SY747 ) )
| ! [SY748: $i] :
( ~ ( rel_s4 @ SY746 @ SY748 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY748 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY750: $i] :
( ~ ( rel_s4 @ SY746 @ SY750 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY750 @ SY728 )
| ( v3 @ SY728 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(96,plain,
( ( ! [SY698: $i] :
( ( v3 @ SY698 )
| ! [SY699: $i] :
( ~ ( rel_s4 @ SY698 @ SY699 )
| ~ ( v2 @ SY699 ) )
| ! [SY700: $i] :
( ~ ( rel_s4 @ SY698 @ SY700 )
| ~ ( v3 @ SY700 ) )
| ! [SY701: $i] :
( ~ ( rel_s4 @ SY698 @ SY701 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY701 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(97,plain,
( ( ! [SY652: $i] :
( ( v3 @ SY652 )
| ! [SY653: $i] :
( ~ ( rel_s4 @ SY652 @ SY653 )
| ~ ( v3 @ SY653 ) )
| ! [SY654: $i] :
( ~ ( rel_s4 @ SY652 @ SY654 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY654 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY656: $i] :
( ~ ( rel_s4 @ SY652 @ SY656 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY656 @ SY634 )
| ( v3 @ SY634 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(98,plain,
( ( ! [SY599: $i] :
( ( v3 @ SY599 )
| ! [SY600: $i] :
( ~ ( rel_s4 @ SY599 @ SY600 )
| ! [SY559: $i] :
( ~ ( rel_s4 @ SY600 @ SY559 )
| ( v3 @ SY559 ) ) )
| ! [SY602: $i] :
( ~ ( rel_s4 @ SY599 @ SY602 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY602 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY604: $i] :
( ~ ( rel_s4 @ SY599 @ SY604 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY604 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(99,plain,
( ( ! [SY545: $i] :
( ( v4 @ SY545 )
| ~ ( v2 @ SY545 )
| ! [SY546: $i] :
( ~ ( rel_s4 @ SY545 @ SY546 )
| ~ ( v1 @ SY546 ) )
| ! [SY547: $i] :
( ~ ( rel_s4 @ SY545 @ SY547 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY547 @ SY532 )
| ( v2 @ SY532 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(100,plain,
( ( ! [SY507: $i] :
( ( v4 @ SY507 )
| ~ ( v2 @ SY507 )
| ! [SY508: $i] :
( ~ ( rel_s4 @ SY507 @ SY508 )
| ! [SY481: $i] :
( ~ ( rel_s4 @ SY508 @ SY481 )
| ( v3 @ SY481 ) ) )
| ! [SY510: $i] :
( ~ ( rel_s4 @ SY507 @ SY510 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY510 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(101,plain,
( ( ! [SY462: $i] :
( ~ ( v1 @ SY462 )
| ~ ( v3 @ SY462 )
| ! [SY463: $i] :
( ~ ( rel_s4 @ SY462 @ SY463 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY463 @ SY437 )
| ( v2 @ SY437 ) ) )
| ! [SY465: $i] :
( ~ ( rel_s4 @ SY462 @ SY465 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY465 @ SY446 )
| ( v3 @ SY446 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(102,plain,
( ( ! [SY417: $i] :
( ~ ( v1 @ SY417 )
| ~ ( v4 @ SY417 )
| ! [SY418: $i] :
( ~ ( rel_s4 @ SY417 @ SY418 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY418 @ SY392 )
| ( v1 @ SY392 ) ) )
| ! [SY420: $i] :
( ~ ( rel_s4 @ SY417 @ SY420 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY420 @ SY401 )
| ( v4 @ SY401 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(103,plain,
( ( ! [SY372: $i] :
( ~ ( v1 @ SY372 )
| ~ ( v4 @ SY372 )
| ! [SY373: $i] :
( ~ ( rel_s4 @ SY372 @ SY373 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY373 @ SY346 )
| ( v3 @ SY346 ) ) )
| ! [SY375: $i] :
( ~ ( rel_s4 @ SY372 @ SY375 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY375 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(104,plain,
( ( ! [SY326: $i] :
( ~ ( v1 @ SY326 )
| ! [SY327: $i] :
( ~ ( rel_s4 @ SY326 @ SY327 )
| ~ ( v1 @ SY327 ) )
| ! [SY328: $i] :
( ~ ( rel_s4 @ SY326 @ SY328 )
| ~ ( v3 @ SY328 ) )
| ! [SY329: $i] :
( ~ ( rel_s4 @ SY326 @ SY329 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY329 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(105,plain,
( ( ! [SY281: $i] :
( ~ ( v3 @ SY281 )
| ! [SY282: $i] :
( ~ ( rel_s4 @ SY281 @ SY282 )
| ~ ( v2 @ SY282 ) )
| ! [SY283: $i] :
( ~ ( rel_s4 @ SY281 @ SY283 )
| ~ ( v4 @ SY283 ) )
| ! [SY284: $i] :
( ~ ( rel_s4 @ SY281 @ SY284 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY284 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(106,plain,
( ( ! [SY232: $i] :
( ~ ( v3 @ SY232 )
| ! [SY233: $i] :
( ~ ( rel_s4 @ SY232 @ SY233 )
| ! [SY193: $i] :
( ~ ( rel_s4 @ SY233 @ SY193 )
| ( v2 @ SY193 ) ) )
| ! [SY235: $i] :
( ~ ( rel_s4 @ SY232 @ SY235 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY235 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY237: $i] :
( ~ ( rel_s4 @ SY232 @ SY237 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY237 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(107,plain,
( ( ! [SY174: $i] :
( ~ ( v4 @ SY174 )
| ! [SY175: $i] :
( ~ ( rel_s4 @ SY174 @ SY175 )
| ( v3 @ SY175 ) )
| ! [SY176: $i] :
( ~ ( rel_s4 @ SY174 @ SY176 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY176 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY178: $i] :
( ~ ( rel_s4 @ SY174 @ SY178 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY178 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(108,plain,
( ( ! [SY119: $i] :
( ~ ( v4 @ SY119 )
| ! [SY120: $i] :
( ~ ( rel_s4 @ SY119 @ SY120 )
| ! [SY80: $i] :
( ~ ( rel_s4 @ SY120 @ SY80 )
| ( v1 @ SY80 ) ) )
| ! [SY122: $i] :
( ~ ( rel_s4 @ SY119 @ SY122 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY122 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY124: $i] :
( ~ ( rel_s4 @ SY119 @ SY124 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY124 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(109,plain,
( ( ! [SY59: $i] :
( ~ ( v4 @ SY59 )
| ! [SY60: $i] :
( ~ ( rel_s4 @ SY59 @ SY60 )
| ! [SY20: $i] :
( ~ ( rel_s4 @ SY60 @ SY20 )
| ( v2 @ SY20 ) ) )
| ! [SY62: $i] :
( ~ ( rel_s4 @ SY59 @ SY62 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY62 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY64: $i] :
( ~ ( rel_s4 @ SY59 @ SY64 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY64 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(110,plain,
( ( ! [SY9: $i] :
~ ! [SY10: $i] :
( ~ ( rel_s4 @ SY9 @ SY10 )
| ~ $true ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(111,plain,
$true = $true,
inference(copy,[status(thm)],[75]) ).
thf(112,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
~ ( exists_in_world @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[76,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(113,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)],[78,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(114,plain,
( ( ! [SX0: mu,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( exists_in_world @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( exists_in_world @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,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(115,plain,
! [SV1: $i] :
( ( rel_s4 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(116,plain,
! [SV2: $i] :
( ( ( v1 @ SV2 )
| ( v3 @ SV2 )
| ! [SY1397: $i] :
( ~ ( rel_s4 @ SV2 @ SY1397 )
| ! [SY1348: $i] :
( ~ ( rel_s4 @ SY1397 @ SY1348 )
| ~ ( v1 @ SY1348 ) ) )
| ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(117,plain,
! [SV3: $i] :
( ( ( v1 @ SV3 )
| ~ ( v2 @ SV3 )
| ! [SY1401: $i] :
( ~ ( rel_s4 @ SV3 @ SY1401 )
| ! [SY1303: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1303 )
| ( v4 @ SY1303 ) ) )
| ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(118,plain,
! [SV4: $i] :
( ( ( v1 @ SV4 )
| ~ ( v3 @ SV4 )
| ! [SY1405: $i] :
( ~ ( rel_s4 @ SV4 @ SY1405 )
| ~ ( v4 @ SY1405 ) )
| ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(119,plain,
! [SV5: $i] :
( ( ( v1 @ SV5 )
| ~ ( v3 @ SV5 )
| ! [SY1408: $i] :
( ~ ( rel_s4 @ SV5 @ SY1408 )
| ! [SY1222: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1222 )
| ( v2 @ SY1222 ) ) )
| ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(120,plain,
! [SV6: $i] :
( ( ( v1 @ SV6 )
| ! [SY1412: $i] :
( ~ ( rel_s4 @ SV6 @ SY1412 )
| ( v1 @ SY1412 ) )
| ! [SY1413: $i] :
( ~ ( rel_s4 @ SV6 @ SY1413 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(121,plain,
! [SV7: $i] :
( ( ( v1 @ SV7 )
| ! [SY1417: $i] :
( ~ ( rel_s4 @ SV7 @ SY1417 )
| ~ ( v2 @ SY1417 ) )
| ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(122,plain,
! [SV8: $i] :
( ( ( v1 @ SV8 )
| ! [SY1422: $i] :
( ~ ( rel_s4 @ SV8 @ SY1422 )
| ~ ( v3 @ SY1422 ) )
| ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(123,plain,
! [SV9: $i] :
( ( ( v2 @ SV9 )
| ~ ( v1 @ SV9 )
| ! [SY1427: $i] :
( ~ ( rel_s4 @ SV9 @ SY1427 )
| ~ ( v3 @ SY1427 ) )
| ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(124,plain,
! [SV10: $i] :
( ( ( v2 @ SV10 )
| ~ ( v3 @ SV10 )
| ! [SY1430: $i] :
( ~ ( rel_s4 @ SV10 @ SY1430 )
| ~ ( v3 @ SY1430 ) )
| ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(125,plain,
! [SV11: $i] :
( ( ( v2 @ SV11 )
| ~ ( v4 @ SV11 )
| ! [SY1433: $i] :
( ~ ( rel_s4 @ SV11 @ SY1433 )
| ~ ( v4 @ SY1433 ) )
| ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(126,plain,
! [SV12: $i] :
( ( ( v2 @ SV12 )
| ! [SY1436: $i] :
( ~ ( rel_s4 @ SV12 @ SY1436 )
| ( v4 @ SY1436 ) )
| ! [SY1437: $i] :
( ~ ( rel_s4 @ SV12 @ SY1437 )
| ~ ( v4 @ SY1437 ) )
| ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(127,plain,
! [SV13: $i] :
( ( ( v3 @ SV13 )
| ( v4 @ SV13 )
| ! [SY1440: $i] :
( ~ ( rel_s4 @ SV13 @ SY1440 )
| ~ ( v4 @ SY1440 ) )
| ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(128,plain,
! [SV14: $i] :
( ( ( v3 @ SV14 )
| ~ ( v1 @ SV14 )
| ~ ( v4 @ SV14 )
| ! [SY1443: $i] :
( ~ ( rel_s4 @ SV14 @ SY1443 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY1443 @ SY852 )
| ( v2 @ SY852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(129,plain,
! [SV15: $i] :
( ( ( v3 @ SV15 )
| ~ ( v1 @ SV15 )
| ! [SY1445: $i] :
( ~ ( rel_s4 @ SV15 @ SY1445 )
| ~ ( v3 @ SY1445 ) )
| ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(130,plain,
! [SV16: $i] :
( ( ( v3 @ SV16 )
| ~ ( v2 @ SV16 )
| ! [SY1448: $i] :
( ~ ( rel_s4 @ SV16 @ SY1448 )
| ! [SY768: $i] :
( ~ ( rel_s4 @ SY1448 @ SY768 )
| ~ ( v2 @ SY768 ) ) )
| ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(131,plain,
! [SV17: $i] :
( ( ( v3 @ SV17 )
| ! [SY1452: $i] :
( ~ ( rel_s4 @ SV17 @ SY1452 )
| ( v4 @ SY1452 ) )
| ! [SY1453: $i] :
( ~ ( rel_s4 @ SV17 @ SY1453 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY1453 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(132,plain,
! [SV18: $i] :
( ( ( v3 @ SV18 )
| ! [SY1457: $i] :
( ~ ( rel_s4 @ SV18 @ SY1457 )
| ~ ( v2 @ SY1457 ) )
| ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(133,plain,
! [SV19: $i] :
( ( ( v3 @ SV19 )
| ! [SY1461: $i] :
( ~ ( rel_s4 @ SV19 @ SY1461 )
| ~ ( v3 @ SY1461 ) )
| ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(134,plain,
! [SV20: $i] :
( ( ( v3 @ SV20 )
| ! [SY1466: $i] :
( ~ ( rel_s4 @ SV20 @ SY1466 )
| ! [SY559: $i] :
( ~ ( rel_s4 @ SY1466 @ SY559 )
| ( v3 @ SY559 ) ) )
| ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(135,plain,
! [SV21: $i] :
( ( ( v4 @ SV21 )
| ~ ( v2 @ SV21 )
| ! [SY1472: $i] :
( ~ ( rel_s4 @ SV21 @ SY1472 )
| ~ ( v1 @ SY1472 ) )
| ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(136,plain,
! [SV22: $i] :
( ( ( v4 @ SV22 )
| ~ ( v2 @ SV22 )
| ! [SY1475: $i] :
( ~ ( rel_s4 @ SV22 @ SY1475 )
| ! [SY481: $i] :
( ~ ( rel_s4 @ SY1475 @ SY481 )
| ( v3 @ SY481 ) ) )
| ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(137,plain,
! [SV23: $i] :
( ( ~ ( v1 @ SV23 )
| ~ ( v3 @ SV23 )
| ! [SY1479: $i] :
( ~ ( rel_s4 @ SV23 @ SY1479 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY1479 @ SY437 )
| ( v2 @ SY437 ) ) )
| ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(138,plain,
! [SV24: $i] :
( ( ~ ( v1 @ SV24 )
| ~ ( v4 @ SV24 )
| ! [SY1483: $i] :
( ~ ( rel_s4 @ SV24 @ SY1483 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY1483 @ SY392 )
| ( v1 @ SY392 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(139,plain,
! [SV25: $i] :
( ( ~ ( v1 @ SV25 )
| ~ ( v4 @ SV25 )
| ! [SY1487: $i] :
( ~ ( rel_s4 @ SV25 @ SY1487 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY1487 @ SY346 )
| ( v3 @ SY346 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(140,plain,
! [SV26: $i] :
( ( ~ ( v1 @ SV26 )
| ! [SY1491: $i] :
( ~ ( rel_s4 @ SV26 @ SY1491 )
| ~ ( v1 @ SY1491 ) )
| ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(141,plain,
! [SV27: $i] :
( ( ~ ( v3 @ SV27 )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SV27 @ SY1495 )
| ~ ( v2 @ SY1495 ) )
| ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(142,plain,
! [SV28: $i] :
( ( ~ ( v3 @ SV28 )
| ! [SY1499: $i] :
( ~ ( rel_s4 @ SV28 @ SY1499 )
| ! [SY193: $i] :
( ~ ( rel_s4 @ SY1499 @ SY193 )
| ( v2 @ SY193 ) ) )
| ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(143,plain,
! [SV29: $i] :
( ( ~ ( v4 @ SV29 )
| ! [SY1505: $i] :
( ~ ( rel_s4 @ SV29 @ SY1505 )
| ( v3 @ SY1505 ) )
| ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(144,plain,
! [SV30: $i] :
( ( ~ ( v4 @ SV30 )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SV30 @ SY1510 )
| ! [SY80: $i] :
( ~ ( rel_s4 @ SY1510 @ SY80 )
| ( v1 @ SY80 ) ) )
| ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(145,plain,
! [SV31: $i] :
( ( ~ ( v4 @ SV31 )
| ! [SY1516: $i] :
( ~ ( rel_s4 @ SV31 @ SY1516 )
| ! [SY20: $i] :
( ~ ( rel_s4 @ SY1516 @ SY20 )
| ( v2 @ SY20 ) ) )
| ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(146,plain,
! [SV32: $i] :
( ( ~ ! [SY1522: $i] :
( ~ ( rel_s4 @ SV32 @ SY1522 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(147,plain,
! [SV33: $i] :
( ( ~ ! [SY1523: mu] :
~ ( exists_in_world @ SY1523 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(148,plain,
! [SV34: $i] :
( ( ! [SY1524: $i,SY1525: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV34 @ SY1524 )
| ~ ( rel_s4 @ SY1524 @ SY1525 ) )
| ( rel_s4 @ SV34 @ SY1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(149,plain,
! [SV35: mu] :
( ( ! [SY1526: $i,SY1527: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV35 @ SY1526 )
| ~ ( rel_s4 @ SY1526 @ SY1527 ) )
| ( exists_in_world @ SV35 @ SY1527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(150,plain,
! [SV2: $i] :
( ( ( v1 @ SV2 )
= $true )
| ( ( ( v3 @ SV2 )
| ! [SY1397: $i] :
( ~ ( rel_s4 @ SV2 @ SY1397 )
| ! [SY1348: $i] :
( ~ ( rel_s4 @ SY1397 @ SY1348 )
| ~ ( v1 @ SY1348 ) ) )
| ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(151,plain,
! [SV3: $i] :
( ( ( v1 @ SV3 )
= $true )
| ( ( ~ ( v2 @ SV3 )
| ! [SY1401: $i] :
( ~ ( rel_s4 @ SV3 @ SY1401 )
| ! [SY1303: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1303 )
| ( v4 @ SY1303 ) ) )
| ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(152,plain,
! [SV4: $i] :
( ( ( v1 @ SV4 )
= $true )
| ( ( ~ ( v3 @ SV4 )
| ! [SY1405: $i] :
( ~ ( rel_s4 @ SV4 @ SY1405 )
| ~ ( v4 @ SY1405 ) )
| ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(153,plain,
! [SV5: $i] :
( ( ( v1 @ SV5 )
= $true )
| ( ( ~ ( v3 @ SV5 )
| ! [SY1408: $i] :
( ~ ( rel_s4 @ SV5 @ SY1408 )
| ! [SY1222: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1222 )
| ( v2 @ SY1222 ) ) )
| ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(154,plain,
! [SV6: $i] :
( ( ( v1 @ SV6 )
= $true )
| ( ( ! [SY1412: $i] :
( ~ ( rel_s4 @ SV6 @ SY1412 )
| ( v1 @ SY1412 ) )
| ! [SY1413: $i] :
( ~ ( rel_s4 @ SV6 @ SY1413 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(155,plain,
! [SV7: $i] :
( ( ( v1 @ SV7 )
= $true )
| ( ( ! [SY1417: $i] :
( ~ ( rel_s4 @ SV7 @ SY1417 )
| ~ ( v2 @ SY1417 ) )
| ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(156,plain,
! [SV8: $i] :
( ( ( v1 @ SV8 )
= $true )
| ( ( ! [SY1422: $i] :
( ~ ( rel_s4 @ SV8 @ SY1422 )
| ~ ( v3 @ SY1422 ) )
| ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(157,plain,
! [SV9: $i] :
( ( ( v2 @ SV9 )
= $true )
| ( ( ~ ( v1 @ SV9 )
| ! [SY1427: $i] :
( ~ ( rel_s4 @ SV9 @ SY1427 )
| ~ ( v3 @ SY1427 ) )
| ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(158,plain,
! [SV10: $i] :
( ( ( v2 @ SV10 )
= $true )
| ( ( ~ ( v3 @ SV10 )
| ! [SY1430: $i] :
( ~ ( rel_s4 @ SV10 @ SY1430 )
| ~ ( v3 @ SY1430 ) )
| ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(159,plain,
! [SV11: $i] :
( ( ( v2 @ SV11 )
= $true )
| ( ( ~ ( v4 @ SV11 )
| ! [SY1433: $i] :
( ~ ( rel_s4 @ SV11 @ SY1433 )
| ~ ( v4 @ SY1433 ) )
| ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(160,plain,
! [SV12: $i] :
( ( ( v2 @ SV12 )
= $true )
| ( ( ! [SY1436: $i] :
( ~ ( rel_s4 @ SV12 @ SY1436 )
| ( v4 @ SY1436 ) )
| ! [SY1437: $i] :
( ~ ( rel_s4 @ SV12 @ SY1437 )
| ~ ( v4 @ SY1437 ) )
| ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(161,plain,
! [SV13: $i] :
( ( ( v3 @ SV13 )
= $true )
| ( ( ( v4 @ SV13 )
| ! [SY1440: $i] :
( ~ ( rel_s4 @ SV13 @ SY1440 )
| ~ ( v4 @ SY1440 ) )
| ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(162,plain,
! [SV14: $i] :
( ( ( v3 @ SV14 )
= $true )
| ( ( ~ ( v1 @ SV14 )
| ~ ( v4 @ SV14 )
| ! [SY1443: $i] :
( ~ ( rel_s4 @ SV14 @ SY1443 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY1443 @ SY852 )
| ( v2 @ SY852 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(163,plain,
! [SV15: $i] :
( ( ( v3 @ SV15 )
= $true )
| ( ( ~ ( v1 @ SV15 )
| ! [SY1445: $i] :
( ~ ( rel_s4 @ SV15 @ SY1445 )
| ~ ( v3 @ SY1445 ) )
| ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(164,plain,
! [SV16: $i] :
( ( ( v3 @ SV16 )
= $true )
| ( ( ~ ( v2 @ SV16 )
| ! [SY1448: $i] :
( ~ ( rel_s4 @ SV16 @ SY1448 )
| ! [SY768: $i] :
( ~ ( rel_s4 @ SY1448 @ SY768 )
| ~ ( v2 @ SY768 ) ) )
| ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(165,plain,
! [SV17: $i] :
( ( ( v3 @ SV17 )
= $true )
| ( ( ! [SY1452: $i] :
( ~ ( rel_s4 @ SV17 @ SY1452 )
| ( v4 @ SY1452 ) )
| ! [SY1453: $i] :
( ~ ( rel_s4 @ SV17 @ SY1453 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY1453 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(166,plain,
! [SV18: $i] :
( ( ( v3 @ SV18 )
= $true )
| ( ( ! [SY1457: $i] :
( ~ ( rel_s4 @ SV18 @ SY1457 )
| ~ ( v2 @ SY1457 ) )
| ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(167,plain,
! [SV19: $i] :
( ( ( v3 @ SV19 )
= $true )
| ( ( ! [SY1461: $i] :
( ~ ( rel_s4 @ SV19 @ SY1461 )
| ~ ( v3 @ SY1461 ) )
| ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(168,plain,
! [SV20: $i] :
( ( ( v3 @ SV20 )
= $true )
| ( ( ! [SY1466: $i] :
( ~ ( rel_s4 @ SV20 @ SY1466 )
| ! [SY559: $i] :
( ~ ( rel_s4 @ SY1466 @ SY559 )
| ( v3 @ SY559 ) ) )
| ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(169,plain,
! [SV21: $i] :
( ( ( v4 @ SV21 )
= $true )
| ( ( ~ ( v2 @ SV21 )
| ! [SY1472: $i] :
( ~ ( rel_s4 @ SV21 @ SY1472 )
| ~ ( v1 @ SY1472 ) )
| ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(170,plain,
! [SV22: $i] :
( ( ( v4 @ SV22 )
= $true )
| ( ( ~ ( v2 @ SV22 )
| ! [SY1475: $i] :
( ~ ( rel_s4 @ SV22 @ SY1475 )
| ! [SY481: $i] :
( ~ ( rel_s4 @ SY1475 @ SY481 )
| ( v3 @ SY481 ) ) )
| ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(171,plain,
! [SV23: $i] :
( ( ( ~ ( v1 @ SV23 ) )
= $true )
| ( ( ~ ( v3 @ SV23 )
| ! [SY1479: $i] :
( ~ ( rel_s4 @ SV23 @ SY1479 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY1479 @ SY437 )
| ( v2 @ SY437 ) ) )
| ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(172,plain,
! [SV24: $i] :
( ( ( ~ ( v1 @ SV24 ) )
= $true )
| ( ( ~ ( v4 @ SV24 )
| ! [SY1483: $i] :
( ~ ( rel_s4 @ SV24 @ SY1483 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY1483 @ SY392 )
| ( v1 @ SY392 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(173,plain,
! [SV25: $i] :
( ( ( ~ ( v1 @ SV25 ) )
= $true )
| ( ( ~ ( v4 @ SV25 )
| ! [SY1487: $i] :
( ~ ( rel_s4 @ SV25 @ SY1487 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY1487 @ SY346 )
| ( v3 @ SY346 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(174,plain,
! [SV26: $i] :
( ( ( ~ ( v1 @ SV26 ) )
= $true )
| ( ( ! [SY1491: $i] :
( ~ ( rel_s4 @ SV26 @ SY1491 )
| ~ ( v1 @ SY1491 ) )
| ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(175,plain,
! [SV27: $i] :
( ( ( ~ ( v3 @ SV27 ) )
= $true )
| ( ( ! [SY1495: $i] :
( ~ ( rel_s4 @ SV27 @ SY1495 )
| ~ ( v2 @ SY1495 ) )
| ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(176,plain,
! [SV28: $i] :
( ( ( ~ ( v3 @ SV28 ) )
= $true )
| ( ( ! [SY1499: $i] :
( ~ ( rel_s4 @ SV28 @ SY1499 )
| ! [SY193: $i] :
( ~ ( rel_s4 @ SY1499 @ SY193 )
| ( v2 @ SY193 ) ) )
| ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(177,plain,
! [SV29: $i] :
( ( ( ~ ( v4 @ SV29 ) )
= $true )
| ( ( ! [SY1505: $i] :
( ~ ( rel_s4 @ SV29 @ SY1505 )
| ( v3 @ SY1505 ) )
| ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(178,plain,
! [SV30: $i] :
( ( ( ~ ( v4 @ SV30 ) )
= $true )
| ( ( ! [SY1510: $i] :
( ~ ( rel_s4 @ SV30 @ SY1510 )
| ! [SY80: $i] :
( ~ ( rel_s4 @ SY1510 @ SY80 )
| ( v1 @ SY80 ) ) )
| ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(179,plain,
! [SV31: $i] :
( ( ( ~ ( v4 @ SV31 ) )
= $true )
| ( ( ! [SY1516: $i] :
( ~ ( rel_s4 @ SV31 @ SY1516 )
| ! [SY20: $i] :
( ~ ( rel_s4 @ SY1516 @ SY20 )
| ( v2 @ SY20 ) ) )
| ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(180,plain,
! [SV32: $i] :
( ( ! [SY1522: $i] :
( ~ ( rel_s4 @ SV32 @ SY1522 )
| ~ $true ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(181,plain,
! [SV33: $i] :
( ( ! [SY1523: mu] :
~ ( exists_in_world @ SY1523 @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(182,plain,
! [SV36: $i,SV34: $i] :
( ( ! [SY1528: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV34 @ SV36 )
| ~ ( rel_s4 @ SV36 @ SY1528 ) )
| ( rel_s4 @ SV34 @ SY1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(183,plain,
! [SV37: $i,SV35: mu] :
( ( ! [SY1529: $i] :
( ~ ~ ( ~ ( exists_in_world @ SV35 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SY1529 ) )
| ( exists_in_world @ SV35 @ SY1529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(184,plain,
! [SV2: $i] :
( ( ( v3 @ SV2 )
= $true )
| ( ( ! [SY1397: $i] :
( ~ ( rel_s4 @ SV2 @ SY1397 )
| ! [SY1348: $i] :
( ~ ( rel_s4 @ SY1397 @ SY1348 )
| ~ ( v1 @ SY1348 ) ) )
| ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(185,plain,
! [SV3: $i] :
( ( ( ~ ( v2 @ SV3 ) )
= $true )
| ( ( ! [SY1401: $i] :
( ~ ( rel_s4 @ SV3 @ SY1401 )
| ! [SY1303: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1303 )
| ( v4 @ SY1303 ) ) )
| ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(186,plain,
! [SV4: $i] :
( ( ( ~ ( v3 @ SV4 ) )
= $true )
| ( ( ! [SY1405: $i] :
( ~ ( rel_s4 @ SV4 @ SY1405 )
| ~ ( v4 @ SY1405 ) )
| ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(187,plain,
! [SV5: $i] :
( ( ( ~ ( v3 @ SV5 ) )
= $true )
| ( ( ! [SY1408: $i] :
( ~ ( rel_s4 @ SV5 @ SY1408 )
| ! [SY1222: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1222 )
| ( v2 @ SY1222 ) ) )
| ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(188,plain,
! [SV6: $i] :
( ( ( ! [SY1412: $i] :
( ~ ( rel_s4 @ SV6 @ SY1412 )
| ( v1 @ SY1412 ) ) )
= $true )
| ( ( ! [SY1413: $i] :
( ~ ( rel_s4 @ SV6 @ SY1413 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(189,plain,
! [SV7: $i] :
( ( ( ! [SY1417: $i] :
( ~ ( rel_s4 @ SV7 @ SY1417 )
| ~ ( v2 @ SY1417 ) ) )
= $true )
| ( ( ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(190,plain,
! [SV8: $i] :
( ( ( ! [SY1422: $i] :
( ~ ( rel_s4 @ SV8 @ SY1422 )
| ~ ( v3 @ SY1422 ) ) )
= $true )
| ( ( ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(191,plain,
! [SV9: $i] :
( ( ( ~ ( v1 @ SV9 ) )
= $true )
| ( ( ! [SY1427: $i] :
( ~ ( rel_s4 @ SV9 @ SY1427 )
| ~ ( v3 @ SY1427 ) )
| ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(192,plain,
! [SV10: $i] :
( ( ( ~ ( v3 @ SV10 ) )
= $true )
| ( ( ! [SY1430: $i] :
( ~ ( rel_s4 @ SV10 @ SY1430 )
| ~ ( v3 @ SY1430 ) )
| ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(193,plain,
! [SV11: $i] :
( ( ( ~ ( v4 @ SV11 ) )
= $true )
| ( ( ! [SY1433: $i] :
( ~ ( rel_s4 @ SV11 @ SY1433 )
| ~ ( v4 @ SY1433 ) )
| ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(194,plain,
! [SV12: $i] :
( ( ( ! [SY1436: $i] :
( ~ ( rel_s4 @ SV12 @ SY1436 )
| ( v4 @ SY1436 ) ) )
= $true )
| ( ( ! [SY1437: $i] :
( ~ ( rel_s4 @ SV12 @ SY1437 )
| ~ ( v4 @ SY1437 ) )
| ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(195,plain,
! [SV13: $i] :
( ( ( v4 @ SV13 )
= $true )
| ( ( ! [SY1440: $i] :
( ~ ( rel_s4 @ SV13 @ SY1440 )
| ~ ( v4 @ SY1440 ) )
| ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(196,plain,
! [SV14: $i] :
( ( ( ~ ( v1 @ SV14 ) )
= $true )
| ( ( ~ ( v4 @ SV14 )
| ! [SY1443: $i] :
( ~ ( rel_s4 @ SV14 @ SY1443 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY1443 @ SY852 )
| ( v2 @ SY852 ) ) ) )
= $true )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(197,plain,
! [SV15: $i] :
( ( ( ~ ( v1 @ SV15 ) )
= $true )
| ( ( ! [SY1445: $i] :
( ~ ( rel_s4 @ SV15 @ SY1445 )
| ~ ( v3 @ SY1445 ) )
| ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(198,plain,
! [SV16: $i] :
( ( ( ~ ( v2 @ SV16 ) )
= $true )
| ( ( ! [SY1448: $i] :
( ~ ( rel_s4 @ SV16 @ SY1448 )
| ! [SY768: $i] :
( ~ ( rel_s4 @ SY1448 @ SY768 )
| ~ ( v2 @ SY768 ) ) )
| ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(199,plain,
! [SV17: $i] :
( ( ( ! [SY1452: $i] :
( ~ ( rel_s4 @ SV17 @ SY1452 )
| ( v4 @ SY1452 ) ) )
= $true )
| ( ( ! [SY1453: $i] :
( ~ ( rel_s4 @ SV17 @ SY1453 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY1453 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(200,plain,
! [SV18: $i] :
( ( ( ! [SY1457: $i] :
( ~ ( rel_s4 @ SV18 @ SY1457 )
| ~ ( v2 @ SY1457 ) ) )
= $true )
| ( ( ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(201,plain,
! [SV19: $i] :
( ( ( ! [SY1461: $i] :
( ~ ( rel_s4 @ SV19 @ SY1461 )
| ~ ( v3 @ SY1461 ) ) )
= $true )
| ( ( ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(202,plain,
! [SV20: $i] :
( ( ( ! [SY1466: $i] :
( ~ ( rel_s4 @ SV20 @ SY1466 )
| ! [SY559: $i] :
( ~ ( rel_s4 @ SY1466 @ SY559 )
| ( v3 @ SY559 ) ) ) )
= $true )
| ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(203,plain,
! [SV21: $i] :
( ( ( ~ ( v2 @ SV21 ) )
= $true )
| ( ( ! [SY1472: $i] :
( ~ ( rel_s4 @ SV21 @ SY1472 )
| ~ ( v1 @ SY1472 ) )
| ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(204,plain,
! [SV22: $i] :
( ( ( ~ ( v2 @ SV22 ) )
= $true )
| ( ( ! [SY1475: $i] :
( ~ ( rel_s4 @ SV22 @ SY1475 )
| ! [SY481: $i] :
( ~ ( rel_s4 @ SY1475 @ SY481 )
| ( v3 @ SY481 ) ) )
| ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(205,plain,
! [SV23: $i] :
( ( ( v1 @ SV23 )
= $false )
| ( ( ~ ( v3 @ SV23 )
| ! [SY1479: $i] :
( ~ ( rel_s4 @ SV23 @ SY1479 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY1479 @ SY437 )
| ( v2 @ SY437 ) ) )
| ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(206,plain,
! [SV24: $i] :
( ( ( v1 @ SV24 )
= $false )
| ( ( ~ ( v4 @ SV24 )
| ! [SY1483: $i] :
( ~ ( rel_s4 @ SV24 @ SY1483 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY1483 @ SY392 )
| ( v1 @ SY392 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(207,plain,
! [SV25: $i] :
( ( ( v1 @ SV25 )
= $false )
| ( ( ~ ( v4 @ SV25 )
| ! [SY1487: $i] :
( ~ ( rel_s4 @ SV25 @ SY1487 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY1487 @ SY346 )
| ( v3 @ SY346 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(208,plain,
! [SV26: $i] :
( ( ( v1 @ SV26 )
= $false )
| ( ( ! [SY1491: $i] :
( ~ ( rel_s4 @ SV26 @ SY1491 )
| ~ ( v1 @ SY1491 ) )
| ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(209,plain,
! [SV27: $i] :
( ( ( v3 @ SV27 )
= $false )
| ( ( ! [SY1495: $i] :
( ~ ( rel_s4 @ SV27 @ SY1495 )
| ~ ( v2 @ SY1495 ) )
| ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(210,plain,
! [SV28: $i] :
( ( ( v3 @ SV28 )
= $false )
| ( ( ! [SY1499: $i] :
( ~ ( rel_s4 @ SV28 @ SY1499 )
| ! [SY193: $i] :
( ~ ( rel_s4 @ SY1499 @ SY193 )
| ( v2 @ SY193 ) ) )
| ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(211,plain,
! [SV29: $i] :
( ( ( v4 @ SV29 )
= $false )
| ( ( ! [SY1505: $i] :
( ~ ( rel_s4 @ SV29 @ SY1505 )
| ( v3 @ SY1505 ) )
| ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(212,plain,
! [SV30: $i] :
( ( ( v4 @ SV30 )
= $false )
| ( ( ! [SY1510: $i] :
( ~ ( rel_s4 @ SV30 @ SY1510 )
| ! [SY80: $i] :
( ~ ( rel_s4 @ SY1510 @ SY80 )
| ( v1 @ SY80 ) ) )
| ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(213,plain,
! [SV31: $i] :
( ( ( v4 @ SV31 )
= $false )
| ( ( ! [SY1516: $i] :
( ~ ( rel_s4 @ SV31 @ SY1516 )
| ! [SY20: $i] :
( ~ ( rel_s4 @ SY1516 @ SY20 )
| ( v2 @ SY20 ) ) )
| ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(214,plain,
! [SV32: $i] :
( ( ~ ( rel_s4 @ SV32 @ ( sK2_SY1522 @ SV32 ) )
| ~ $true )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[180]) ).
thf(215,plain,
! [SV33: $i] :
( ( ~ ( exists_in_world @ ( sK3_SY1523 @ SV33 ) @ SV33 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[181]) ).
thf(216,plain,
! [SV38: $i,SV36: $i,SV34: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV34 @ SV36 )
| ~ ( rel_s4 @ SV36 @ SV38 ) )
| ( rel_s4 @ SV34 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(217,plain,
! [SV39: $i,SV37: $i,SV35: mu] :
( ( ~ ~ ( ~ ( exists_in_world @ SV35 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV39 ) )
| ( exists_in_world @ SV35 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(218,plain,
! [SV2: $i] :
( ( ( ! [SY1397: $i] :
( ~ ( rel_s4 @ SV2 @ SY1397 )
| ! [SY1348: $i] :
( ~ ( rel_s4 @ SY1397 @ SY1348 )
| ~ ( v1 @ SY1348 ) ) ) )
= $true )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(219,plain,
! [SV3: $i] :
( ( ( v2 @ SV3 )
= $false )
| ( ( ! [SY1401: $i] :
( ~ ( rel_s4 @ SV3 @ SY1401 )
| ! [SY1303: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1303 )
| ( v4 @ SY1303 ) ) )
| ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(220,plain,
! [SV4: $i] :
( ( ( v3 @ SV4 )
= $false )
| ( ( ! [SY1405: $i] :
( ~ ( rel_s4 @ SV4 @ SY1405 )
| ~ ( v4 @ SY1405 ) )
| ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(221,plain,
! [SV5: $i] :
( ( ( v3 @ SV5 )
= $false )
| ( ( ! [SY1408: $i] :
( ~ ( rel_s4 @ SV5 @ SY1408 )
| ! [SY1222: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1222 )
| ( v2 @ SY1222 ) ) )
| ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(222,plain,
! [SV40: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV40 )
| ( v1 @ SV40 ) )
= $true )
| ( ( ! [SY1413: $i] :
( ~ ( rel_s4 @ SV6 @ SY1413 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(223,plain,
! [SV41: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV41 )
| ~ ( v2 @ SV41 ) )
= $true )
| ( ( ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(224,plain,
! [SV42: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV42 )
| ~ ( v3 @ SV42 ) )
= $true )
| ( ( ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(225,plain,
! [SV9: $i] :
( ( ( v1 @ SV9 )
= $false )
| ( ( ! [SY1427: $i] :
( ~ ( rel_s4 @ SV9 @ SY1427 )
| ~ ( v3 @ SY1427 ) )
| ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(226,plain,
! [SV10: $i] :
( ( ( v3 @ SV10 )
= $false )
| ( ( ! [SY1430: $i] :
( ~ ( rel_s4 @ SV10 @ SY1430 )
| ~ ( v3 @ SY1430 ) )
| ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(227,plain,
! [SV11: $i] :
( ( ( v4 @ SV11 )
= $false )
| ( ( ! [SY1433: $i] :
( ~ ( rel_s4 @ SV11 @ SY1433 )
| ~ ( v4 @ SY1433 ) )
| ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(228,plain,
! [SV43: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV43 )
| ( v4 @ SV43 ) )
= $true )
| ( ( ! [SY1437: $i] :
( ~ ( rel_s4 @ SV12 @ SY1437 )
| ~ ( v4 @ SY1437 ) )
| ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(229,plain,
! [SV13: $i] :
( ( ( ! [SY1440: $i] :
( ~ ( rel_s4 @ SV13 @ SY1440 )
| ~ ( v4 @ SY1440 ) ) )
= $true )
| ( ( ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(230,plain,
! [SV14: $i] :
( ( ( v1 @ SV14 )
= $false )
| ( ( ~ ( v4 @ SV14 )
| ! [SY1443: $i] :
( ~ ( rel_s4 @ SV14 @ SY1443 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY1443 @ SY852 )
| ( v2 @ SY852 ) ) ) )
= $true )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(231,plain,
! [SV15: $i] :
( ( ( v1 @ SV15 )
= $false )
| ( ( ! [SY1445: $i] :
( ~ ( rel_s4 @ SV15 @ SY1445 )
| ~ ( v3 @ SY1445 ) )
| ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(232,plain,
! [SV16: $i] :
( ( ( v2 @ SV16 )
= $false )
| ( ( ! [SY1448: $i] :
( ~ ( rel_s4 @ SV16 @ SY1448 )
| ! [SY768: $i] :
( ~ ( rel_s4 @ SY1448 @ SY768 )
| ~ ( v2 @ SY768 ) ) )
| ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(233,plain,
! [SV44: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV44 )
| ( v4 @ SV44 ) )
= $true )
| ( ( ! [SY1453: $i] :
( ~ ( rel_s4 @ SV17 @ SY1453 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY1453 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(234,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV45 )
| ~ ( v2 @ SV45 ) )
= $true )
| ( ( ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(235,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV46 )
| ~ ( v3 @ SV46 ) )
= $true )
| ( ( ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(236,plain,
! [SV47: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV47 )
| ! [SY1530: $i] :
( ~ ( rel_s4 @ SV47 @ SY1530 )
| ( v3 @ SY1530 ) ) )
= $true )
| ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV21: $i] :
( ( ( v2 @ SV21 )
= $false )
| ( ( ! [SY1472: $i] :
( ~ ( rel_s4 @ SV21 @ SY1472 )
| ~ ( v1 @ SY1472 ) )
| ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(238,plain,
! [SV22: $i] :
( ( ( v2 @ SV22 )
= $false )
| ( ( ! [SY1475: $i] :
( ~ ( rel_s4 @ SV22 @ SY1475 )
| ! [SY481: $i] :
( ~ ( rel_s4 @ SY1475 @ SY481 )
| ( v3 @ SY481 ) ) )
| ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(239,plain,
! [SV23: $i] :
( ( ( ~ ( v3 @ SV23 ) )
= $true )
| ( ( ! [SY1479: $i] :
( ~ ( rel_s4 @ SV23 @ SY1479 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY1479 @ SY437 )
| ( v2 @ SY437 ) ) )
| ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(240,plain,
! [SV24: $i] :
( ( ( ~ ( v4 @ SV24 ) )
= $true )
| ( ( ! [SY1483: $i] :
( ~ ( rel_s4 @ SV24 @ SY1483 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY1483 @ SY392 )
| ( v1 @ SY392 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(241,plain,
! [SV25: $i] :
( ( ( ~ ( v4 @ SV25 ) )
= $true )
| ( ( ! [SY1487: $i] :
( ~ ( rel_s4 @ SV25 @ SY1487 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY1487 @ SY346 )
| ( v3 @ SY346 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(242,plain,
! [SV26: $i] :
( ( ( ! [SY1491: $i] :
( ~ ( rel_s4 @ SV26 @ SY1491 )
| ~ ( v1 @ SY1491 ) ) )
= $true )
| ( ( ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(243,plain,
! [SV27: $i] :
( ( ( ! [SY1495: $i] :
( ~ ( rel_s4 @ SV27 @ SY1495 )
| ~ ( v2 @ SY1495 ) ) )
= $true )
| ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(244,plain,
! [SV28: $i] :
( ( ( ! [SY1499: $i] :
( ~ ( rel_s4 @ SV28 @ SY1499 )
| ! [SY193: $i] :
( ~ ( rel_s4 @ SY1499 @ SY193 )
| ( v2 @ SY193 ) ) ) )
= $true )
| ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(245,plain,
! [SV29: $i] :
( ( ( ! [SY1505: $i] :
( ~ ( rel_s4 @ SV29 @ SY1505 )
| ( v3 @ SY1505 ) ) )
= $true )
| ( ( ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(246,plain,
! [SV30: $i] :
( ( ( ! [SY1510: $i] :
( ~ ( rel_s4 @ SV30 @ SY1510 )
| ! [SY80: $i] :
( ~ ( rel_s4 @ SY1510 @ SY80 )
| ( v1 @ SY80 ) ) ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(247,plain,
! [SV31: $i] :
( ( ( ! [SY1516: $i] :
( ~ ( rel_s4 @ SV31 @ SY1516 )
| ! [SY20: $i] :
( ~ ( rel_s4 @ SY1516 @ SY20 )
| ( v2 @ SY20 ) ) ) )
= $true )
| ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(248,plain,
! [SV32: $i] :
( ( ~ ( rel_s4 @ SV32 @ ( sK2_SY1522 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(249,plain,
( ( ~ $true ) = $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(250,plain,
! [SV33: $i] :
( ( exists_in_world @ ( sK3_SY1523 @ SV33 ) @ SV33 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(251,plain,
! [SV38: $i,SV36: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV34 @ SV36 )
| ~ ( rel_s4 @ SV36 @ SV38 ) ) )
= $true )
| ( ( rel_s4 @ SV34 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(252,plain,
! [SV39: $i,SV37: $i,SV35: mu] :
( ( ( ~ ~ ( ~ ( exists_in_world @ SV35 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV39 ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(253,plain,
! [SV48: $i,SV2: $i] :
( ( ( ~ ( rel_s4 @ SV2 @ SV48 )
| ! [SY1531: $i] :
( ~ ( rel_s4 @ SV48 @ SY1531 )
| ~ ( v1 @ SY1531 ) ) )
= $true )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(254,plain,
! [SV3: $i] :
( ( ( ! [SY1401: $i] :
( ~ ( rel_s4 @ SV3 @ SY1401 )
| ! [SY1303: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1303 )
| ( v4 @ SY1303 ) ) ) )
= $true )
| ( ( ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(255,plain,
! [SV4: $i] :
( ( ( ! [SY1405: $i] :
( ~ ( rel_s4 @ SV4 @ SY1405 )
| ~ ( v4 @ SY1405 ) ) )
= $true )
| ( ( ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(256,plain,
! [SV5: $i] :
( ( ( ! [SY1408: $i] :
( ~ ( rel_s4 @ SV5 @ SY1408 )
| ! [SY1222: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1222 )
| ( v2 @ SY1222 ) ) ) )
= $true )
| ( ( ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(257,plain,
! [SV40: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV40 ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( ! [SY1413: $i] :
( ~ ( rel_s4 @ SV6 @ SY1413 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(258,plain,
! [SV41: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV41 ) )
= $true )
| ( ( ~ ( v2 @ SV41 ) )
= $true )
| ( ( ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(259,plain,
! [SV42: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV42 ) )
= $true )
| ( ( ~ ( v3 @ SV42 ) )
= $true )
| ( ( ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(260,plain,
! [SV9: $i] :
( ( ( ! [SY1427: $i] :
( ~ ( rel_s4 @ SV9 @ SY1427 )
| ~ ( v3 @ SY1427 ) ) )
= $true )
| ( ( ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(261,plain,
! [SV10: $i] :
( ( ( ! [SY1430: $i] :
( ~ ( rel_s4 @ SV10 @ SY1430 )
| ~ ( v3 @ SY1430 ) ) )
= $true )
| ( ( ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(262,plain,
! [SV11: $i] :
( ( ( ! [SY1433: $i] :
( ~ ( rel_s4 @ SV11 @ SY1433 )
| ~ ( v4 @ SY1433 ) ) )
= $true )
| ( ( ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(263,plain,
! [SV43: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV43 ) )
= $true )
| ( ( v4 @ SV43 )
= $true )
| ( ( ! [SY1437: $i] :
( ~ ( rel_s4 @ SV12 @ SY1437 )
| ~ ( v4 @ SY1437 ) )
| ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(264,plain,
! [SV49: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV49 )
| ~ ( v4 @ SV49 ) )
= $true )
| ( ( ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(265,plain,
! [SV14: $i] :
( ( ( ~ ( v4 @ SV14 ) )
= $true )
| ( ( ! [SY1443: $i] :
( ~ ( rel_s4 @ SV14 @ SY1443 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY1443 @ SY852 )
| ( v2 @ SY852 ) ) ) )
= $true )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(266,plain,
! [SV15: $i] :
( ( ( ! [SY1445: $i] :
( ~ ( rel_s4 @ SV15 @ SY1445 )
| ~ ( v3 @ SY1445 ) ) )
= $true )
| ( ( ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(267,plain,
! [SV16: $i] :
( ( ( ! [SY1448: $i] :
( ~ ( rel_s4 @ SV16 @ SY1448 )
| ! [SY768: $i] :
( ~ ( rel_s4 @ SY1448 @ SY768 )
| ~ ( v2 @ SY768 ) ) ) )
= $true )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(268,plain,
! [SV44: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV44 ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( ! [SY1453: $i] :
( ~ ( rel_s4 @ SV17 @ SY1453 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY1453 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(269,plain,
! [SV45: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV45 ) )
= $true )
| ( ( ~ ( v2 @ SV45 ) )
= $true )
| ( ( ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(270,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV46 ) )
= $true )
| ( ( ~ ( v3 @ SV46 ) )
= $true )
| ( ( ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(271,plain,
! [SV47: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV47 ) )
= $true )
| ( ( ! [SY1530: $i] :
( ~ ( rel_s4 @ SV47 @ SY1530 )
| ( v3 @ SY1530 ) ) )
= $true )
| ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(272,plain,
! [SV21: $i] :
( ( ( ! [SY1472: $i] :
( ~ ( rel_s4 @ SV21 @ SY1472 )
| ~ ( v1 @ SY1472 ) ) )
= $true )
| ( ( ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(273,plain,
! [SV22: $i] :
( ( ( ! [SY1475: $i] :
( ~ ( rel_s4 @ SV22 @ SY1475 )
| ! [SY481: $i] :
( ~ ( rel_s4 @ SY1475 @ SY481 )
| ( v3 @ SY481 ) ) ) )
= $true )
| ( ( ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(274,plain,
! [SV23: $i] :
( ( ( v3 @ SV23 )
= $false )
| ( ( ! [SY1479: $i] :
( ~ ( rel_s4 @ SV23 @ SY1479 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY1479 @ SY437 )
| ( v2 @ SY437 ) ) )
| ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(275,plain,
! [SV24: $i] :
( ( ( v4 @ SV24 )
= $false )
| ( ( ! [SY1483: $i] :
( ~ ( rel_s4 @ SV24 @ SY1483 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY1483 @ SY392 )
| ( v1 @ SY392 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(276,plain,
! [SV25: $i] :
( ( ( v4 @ SV25 )
= $false )
| ( ( ! [SY1487: $i] :
( ~ ( rel_s4 @ SV25 @ SY1487 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY1487 @ SY346 )
| ( v3 @ SY346 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(277,plain,
! [SV50: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV50 )
| ~ ( v1 @ SV50 ) )
= $true )
| ( ( ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(278,plain,
! [SV51: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV51 )
| ~ ( v2 @ SV51 ) )
= $true )
| ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(279,plain,
! [SV52: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV52 )
| ! [SY1532: $i] :
( ~ ( rel_s4 @ SV52 @ SY1532 )
| ( v2 @ SY1532 ) ) )
= $true )
| ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(280,plain,
! [SV53: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV53 )
| ( v3 @ SV53 ) )
= $true )
| ( ( ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(281,plain,
! [SV54: $i,SV30: $i] :
( ( ( ~ ( rel_s4 @ SV30 @ SV54 )
| ! [SY1533: $i] :
( ~ ( rel_s4 @ SV54 @ SY1533 )
| ( v1 @ SY1533 ) ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(282,plain,
! [SV55: $i,SV31: $i] :
( ( ( ~ ( rel_s4 @ SV31 @ SV55 )
| ! [SY1534: $i] :
( ~ ( rel_s4 @ SV55 @ SY1534 )
| ( v2 @ SY1534 ) ) )
= $true )
| ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(283,plain,
! [SV32: $i] :
( ( rel_s4 @ SV32 @ ( sK2_SY1522 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(284,plain,
$true = $true,
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(285,plain,
! [SV38: $i,SV36: $i,SV34: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV34 @ SV36 )
| ~ ( rel_s4 @ SV36 @ SV38 ) ) )
= $false )
| ( ( rel_s4 @ SV34 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(286,plain,
! [SV39: $i,SV37: $i,SV35: mu] :
( ( ( ~ ( ~ ( exists_in_world @ SV35 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV39 ) ) )
= $false )
| ( ( exists_in_world @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(287,plain,
! [SV48: $i,SV2: $i] :
( ( ( ~ ( rel_s4 @ SV2 @ SV48 ) )
= $true )
| ( ( ! [SY1531: $i] :
( ~ ( rel_s4 @ SV48 @ SY1531 )
| ~ ( v1 @ SY1531 ) ) )
= $true )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(288,plain,
! [SV56: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV56 )
| ! [SY1535: $i] :
( ~ ( rel_s4 @ SV56 @ SY1535 )
| ( v4 @ SY1535 ) ) )
= $true )
| ( ( ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(289,plain,
! [SV57: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV57 )
| ~ ( v4 @ SV57 ) )
= $true )
| ( ( ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(290,plain,
! [SV58: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV58 )
| ! [SY1536: $i] :
( ~ ( rel_s4 @ SV58 @ SY1536 )
| ( v2 @ SY1536 ) ) )
= $true )
| ( ( ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(291,plain,
! [SV40: $i,SV6: $i] :
( ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( ! [SY1413: $i] :
( ~ ( rel_s4 @ SV6 @ SY1413 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1173 )
| ( v4 @ SY1173 ) ) )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(292,plain,
! [SV41: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( ~ ( v2 @ SV41 ) )
= $true )
| ( ( ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(293,plain,
! [SV42: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( ~ ( v3 @ SV42 ) )
= $true )
| ( ( ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(294,plain,
! [SV59: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV59 )
| ~ ( v3 @ SV59 ) )
= $true )
| ( ( ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(295,plain,
! [SV60: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV60 )
| ~ ( v3 @ SV60 ) )
= $true )
| ( ( ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(296,plain,
! [SV61: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ SV11 @ SV61 )
| ~ ( v4 @ SV61 ) )
= $true )
| ( ( ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(297,plain,
! [SV43: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( ! [SY1437: $i] :
( ~ ( rel_s4 @ SV12 @ SY1437 )
| ~ ( v4 @ SY1437 ) )
| ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(298,plain,
! [SV49: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV49 ) )
= $true )
| ( ( ~ ( v4 @ SV49 ) )
= $true )
| ( ( ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(299,plain,
! [SV14: $i] :
( ( ( v4 @ SV14 )
= $false )
| ( ( ! [SY1443: $i] :
( ~ ( rel_s4 @ SV14 @ SY1443 )
| ! [SY852: $i] :
( ~ ( rel_s4 @ SY1443 @ SY852 )
| ( v2 @ SY852 ) ) ) )
= $true )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(300,plain,
! [SV62: $i,SV15: $i] :
( ( ( ~ ( rel_s4 @ SV15 @ SV62 )
| ~ ( v3 @ SV62 ) )
= $true )
| ( ( ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(301,plain,
! [SV63: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ SV63 )
| ! [SY1537: $i] :
( ~ ( rel_s4 @ SV63 @ SY1537 )
| ~ ( v2 @ SY1537 ) ) )
= $true )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(302,plain,
! [SV44: $i,SV17: $i] :
( ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v4 @ SV44 )
= $true )
| ( ( ! [SY1453: $i] :
( ~ ( rel_s4 @ SV17 @ SY1453 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY1453 @ SY719 )
| ( v2 @ SY719 ) ) )
| ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(303,plain,
! [SV45: $i,SV18: $i] :
( ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( ~ ( v2 @ SV45 ) )
= $true )
| ( ( ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(304,plain,
! [SV46: $i,SV19: $i] :
( ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( ~ ( v3 @ SV46 ) )
= $true )
| ( ( ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(305,plain,
! [SV47: $i,SV20: $i] :
( ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( ! [SY1530: $i] :
( ~ ( rel_s4 @ SV47 @ SY1530 )
| ( v3 @ SY1530 ) ) )
= $true )
| ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(306,plain,
! [SV64: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ SV64 )
| ~ ( v1 @ SV64 ) )
= $true )
| ( ( ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(307,plain,
! [SV65: $i,SV22: $i] :
( ( ( ~ ( rel_s4 @ SV22 @ SV65 )
| ! [SY1538: $i] :
( ~ ( rel_s4 @ SV65 @ SY1538 )
| ( v3 @ SY1538 ) ) )
= $true )
| ( ( ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(308,plain,
! [SV23: $i] :
( ( ( ! [SY1479: $i] :
( ~ ( rel_s4 @ SV23 @ SY1479 )
| ! [SY437: $i] :
( ~ ( rel_s4 @ SY1479 @ SY437 )
| ( v2 @ SY437 ) ) ) )
= $true )
| ( ( ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(309,plain,
! [SV24: $i] :
( ( ( ! [SY1483: $i] :
( ~ ( rel_s4 @ SV24 @ SY1483 )
| ! [SY392: $i] :
( ~ ( rel_s4 @ SY1483 @ SY392 )
| ( v1 @ SY392 ) ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(310,plain,
! [SV25: $i] :
( ( ( ! [SY1487: $i] :
( ~ ( rel_s4 @ SV25 @ SY1487 )
| ! [SY346: $i] :
( ~ ( rel_s4 @ SY1487 @ SY346 )
| ( v3 @ SY346 ) ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(311,plain,
! [SV50: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV50 ) )
= $true )
| ( ( ~ ( v1 @ SV50 ) )
= $true )
| ( ( ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(312,plain,
! [SV51: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV51 ) )
= $true )
| ( ( ~ ( v2 @ SV51 ) )
= $true )
| ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(313,plain,
! [SV52: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV52 ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( rel_s4 @ SV52 @ SY1532 )
| ( v2 @ SY1532 ) ) )
= $true )
| ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(314,plain,
! [SV53: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV53 ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(315,plain,
! [SV54: $i,SV30: $i] :
( ( ( ~ ( rel_s4 @ SV30 @ SV54 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( rel_s4 @ SV54 @ SY1533 )
| ( v1 @ SY1533 ) ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(316,plain,
! [SV55: $i,SV31: $i] :
( ( ( ~ ( rel_s4 @ SV31 @ SV55 ) )
= $true )
| ( ( ! [SY1534: $i] :
( ~ ( rel_s4 @ SV55 @ SY1534 )
| ( v2 @ SY1534 ) ) )
= $true )
| ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(317,plain,
! [SV38: $i,SV36: $i,SV34: $i] :
( ( ( ~ ( rel_s4 @ SV34 @ SV36 )
| ~ ( rel_s4 @ SV36 @ SV38 ) )
= $true )
| ( ( rel_s4 @ SV34 @ SV38 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(318,plain,
! [SV39: $i,SV37: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(319,plain,
! [SV48: $i,SV2: $i] :
( ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( ! [SY1531: $i] :
( ~ ( rel_s4 @ SV48 @ SY1531 )
| ~ ( v1 @ SY1531 ) ) )
= $true )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(320,plain,
! [SV56: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV56 ) )
= $true )
| ( ( ! [SY1535: $i] :
( ~ ( rel_s4 @ SV56 @ SY1535 )
| ( v4 @ SY1535 ) ) )
= $true )
| ( ( ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(321,plain,
! [SV57: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV57 ) )
= $true )
| ( ( ~ ( v4 @ SV57 ) )
= $true )
| ( ( ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(322,plain,
! [SV58: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV58 ) )
= $true )
| ( ( ! [SY1536: $i] :
( ~ ( rel_s4 @ SV58 @ SY1536 )
| ( v2 @ SY1536 ) ) )
= $true )
| ( ( ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(323,plain,
! [SV40: $i,SV6: $i] :
( ( ( ! [SY1413: $i] :
( ~ ( rel_s4 @ SV6 @ SY1413 )
| ! [SY1173: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1173 )
| ( v4 @ SY1173 ) ) ) )
= $true )
| ( ( ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(324,plain,
! [SV7: $i,SV41: $i] :
( ( ( v2 @ SV41 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(325,plain,
! [SV8: $i,SV42: $i] :
( ( ( v3 @ SV42 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) )
| ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(326,plain,
! [SV59: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV59 ) )
= $true )
| ( ( ~ ( v3 @ SV59 ) )
= $true )
| ( ( ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(327,plain,
! [SV60: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV60 ) )
= $true )
| ( ( ~ ( v3 @ SV60 ) )
= $true )
| ( ( ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(328,plain,
! [SV61: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ SV11 @ SV61 ) )
= $true )
| ( ( ~ ( v4 @ SV61 ) )
= $true )
| ( ( ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(329,plain,
! [SV43: $i,SV12: $i] :
( ( ( ! [SY1437: $i] :
( ~ ( rel_s4 @ SV12 @ SY1437 )
| ~ ( v4 @ SY1437 ) ) )
= $true )
| ( ( ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(330,plain,
! [SV49: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( ~ ( v4 @ SV49 ) )
= $true )
| ( ( ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(331,plain,
! [SV66: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV66 )
| ! [SY1539: $i] :
( ~ ( rel_s4 @ SV66 @ SY1539 )
| ( v2 @ SY1539 ) ) )
= $true )
| ( ( v4 @ SV14 )
= $false )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(332,plain,
! [SV62: $i,SV15: $i] :
( ( ( ~ ( rel_s4 @ SV15 @ SV62 ) )
= $true )
| ( ( ~ ( v3 @ SV62 ) )
= $true )
| ( ( ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(333,plain,
! [SV63: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ SV63 ) )
= $true )
| ( ( ! [SY1537: $i] :
( ~ ( rel_s4 @ SV63 @ SY1537 )
| ~ ( v2 @ SY1537 ) ) )
= $true )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(334,plain,
! [SV44: $i,SV17: $i] :
( ( ( ! [SY1453: $i] :
( ~ ( rel_s4 @ SV17 @ SY1453 )
| ! [SY719: $i] :
( ~ ( rel_s4 @ SY1453 @ SY719 )
| ( v2 @ SY719 ) ) ) )
= $true )
| ( ( ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(335,plain,
! [SV18: $i,SV45: $i] :
( ( ( v2 @ SV45 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(336,plain,
! [SV19: $i,SV46: $i] :
( ( ( v3 @ SV46 )
= $false )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(337,plain,
! [SV20: $i,SV67: $i,SV47: $i] :
( ( ( ~ ( rel_s4 @ SV47 @ SV67 )
| ( v3 @ SV67 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(338,plain,
! [SV64: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ SV64 ) )
= $true )
| ( ( ~ ( v1 @ SV64 ) )
= $true )
| ( ( ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(339,plain,
! [SV65: $i,SV22: $i] :
( ( ( ~ ( rel_s4 @ SV22 @ SV65 ) )
= $true )
| ( ( ! [SY1538: $i] :
( ~ ( rel_s4 @ SV65 @ SY1538 )
| ( v3 @ SY1538 ) ) )
= $true )
| ( ( ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(340,plain,
! [SV68: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV68 )
| ! [SY1540: $i] :
( ~ ( rel_s4 @ SV68 @ SY1540 )
| ( v2 @ SY1540 ) ) )
= $true )
| ( ( ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(341,plain,
! [SV69: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV69 )
| ! [SY1541: $i] :
( ~ ( rel_s4 @ SV69 @ SY1541 )
| ( v1 @ SY1541 ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(342,plain,
! [SV70: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV70 )
| ! [SY1542: $i] :
( ~ ( rel_s4 @ SV70 @ SY1542 )
| ( v3 @ SY1542 ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(343,plain,
! [SV50: $i,SV26: $i] :
( ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( ~ ( v1 @ SV50 ) )
= $true )
| ( ( ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(344,plain,
! [SV51: $i,SV27: $i] :
( ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( ~ ( v2 @ SV51 ) )
= $true )
| ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(345,plain,
! [SV52: $i,SV28: $i] :
( ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( rel_s4 @ SV52 @ SY1532 )
| ( v2 @ SY1532 ) ) )
= $true )
| ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(346,plain,
! [SV53: $i,SV29: $i] :
( ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) )
| ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(347,plain,
! [SV54: $i,SV30: $i] :
( ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( ! [SY1533: $i] :
( ~ ( rel_s4 @ SV54 @ SY1533 )
| ( v1 @ SY1533 ) ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(348,plain,
! [SV55: $i,SV31: $i] :
( ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( ! [SY1534: $i] :
( ~ ( rel_s4 @ SV55 @ SY1534 )
| ( v2 @ SY1534 ) ) )
= $true )
| ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(349,plain,
! [SV38: $i,SV36: $i,SV34: $i] :
( ( ( ~ ( rel_s4 @ SV34 @ SV36 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV36 @ SV38 ) )
= $true )
| ( ( rel_s4 @ SV34 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(350,plain,
! [SV39: $i,SV37: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV37 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV37 @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(351,plain,
! [SV2: $i,SV71: $i,SV48: $i] :
( ( ( ~ ( rel_s4 @ SV48 @ SV71 )
| ~ ( v1 @ SV71 ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(352,plain,
! [SV56: $i,SV3: $i] :
( ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( ! [SY1535: $i] :
( ~ ( rel_s4 @ SV56 @ SY1535 )
| ( v4 @ SY1535 ) ) )
= $true )
| ( ( ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(353,plain,
! [SV57: $i,SV4: $i] :
( ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( ~ ( v4 @ SV57 ) )
= $true )
| ( ( ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(354,plain,
! [SV58: $i,SV5: $i] :
( ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( ! [SY1536: $i] :
( ~ ( rel_s4 @ SV58 @ SY1536 )
| ( v2 @ SY1536 ) ) )
= $true )
| ( ( ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(355,plain,
! [SV40: $i,SV72: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV72 )
| ! [SY1543: $i] :
( ~ ( rel_s4 @ SV72 @ SY1543 )
| ( v4 @ SY1543 ) ) )
= $true )
| ( ( ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(356,plain,
! [SV41: $i,SV7: $i] :
( ( ( ! [SY1418: $i] :
( ~ ( rel_s4 @ SV7 @ SY1418 )
| ! [SY1122: $i] :
( ~ ( rel_s4 @ SY1418 @ SY1122 )
| ( v2 @ SY1122 ) ) ) )
= $true )
| ( ( ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(357,plain,
! [SV42: $i,SV8: $i] :
( ( ( ! [SY1423: $i] :
( ~ ( rel_s4 @ SV8 @ SY1423 )
| ! [SY1070: $i] :
( ~ ( rel_s4 @ SY1423 @ SY1070 )
| ~ ( v1 @ SY1070 ) ) ) )
= $true )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(358,plain,
! [SV59: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( ~ ( v3 @ SV59 ) )
= $true )
| ( ( ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(359,plain,
! [SV60: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( ~ ( v3 @ SV60 ) )
= $true )
| ( ( ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(360,plain,
! [SV61: $i,SV11: $i] :
( ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( ~ ( v4 @ SV61 ) )
= $true )
| ( ( ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(361,plain,
! [SV43: $i,SV73: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV73 )
| ~ ( v4 @ SV73 ) )
= $true )
| ( ( ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(362,plain,
! [SV13: $i,SV49: $i] :
( ( ( v4 @ SV49 )
= $false )
| ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( ! [SY1441: $i] :
( ~ ( rel_s4 @ SV13 @ SY1441 )
| ! [SY882: $i] :
( ~ ( rel_s4 @ SY1441 @ SY882 )
| ( v1 @ SY882 ) ) ) )
= $true )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(363,plain,
! [SV66: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV66 ) )
= $true )
| ( ( ! [SY1539: $i] :
( ~ ( rel_s4 @ SV66 @ SY1539 )
| ( v2 @ SY1539 ) ) )
= $true )
| ( ( v4 @ SV14 )
= $false )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(364,plain,
! [SV62: $i,SV15: $i] :
( ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( ~ ( v3 @ SV62 ) )
= $true )
| ( ( ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(365,plain,
! [SV63: $i,SV16: $i] :
( ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( ! [SY1537: $i] :
( ~ ( rel_s4 @ SV63 @ SY1537 )
| ~ ( v2 @ SY1537 ) ) )
= $true )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(366,plain,
! [SV44: $i,SV74: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV74 )
| ! [SY1544: $i] :
( ~ ( rel_s4 @ SV74 @ SY1544 )
| ( v2 @ SY1544 ) ) )
= $true )
| ( ( ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(367,plain,
! [SV45: $i,SV18: $i] :
( ( ( ! [SY1458: $i] :
( ~ ( rel_s4 @ SV18 @ SY1458 )
| ~ ( v3 @ SY1458 ) ) )
= $true )
| ( ( ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(368,plain,
! [SV46: $i,SV19: $i] :
( ( ( ! [SY1462: $i] :
( ~ ( rel_s4 @ SV19 @ SY1462 )
| ! [SY625: $i] :
( ~ ( rel_s4 @ SY1462 @ SY625 )
| ( v2 @ SY625 ) ) ) )
= $true )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(369,plain,
! [SV20: $i,SV67: $i,SV47: $i] :
( ( ( ~ ( rel_s4 @ SV47 @ SV67 ) )
= $true )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(370,plain,
! [SV64: $i,SV21: $i] :
( ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( ~ ( v1 @ SV64 ) )
= $true )
| ( ( ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(371,plain,
! [SV65: $i,SV22: $i] :
( ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( ! [SY1538: $i] :
( ~ ( rel_s4 @ SV65 @ SY1538 )
| ( v3 @ SY1538 ) ) )
= $true )
| ( ( ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(372,plain,
! [SV68: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV68 ) )
= $true )
| ( ( ! [SY1540: $i] :
( ~ ( rel_s4 @ SV68 @ SY1540 )
| ( v2 @ SY1540 ) ) )
= $true )
| ( ( ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(373,plain,
! [SV69: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV69 ) )
= $true )
| ( ( ! [SY1541: $i] :
( ~ ( rel_s4 @ SV69 @ SY1541 )
| ( v1 @ SY1541 ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(374,plain,
! [SV70: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV70 ) )
= $true )
| ( ( ! [SY1542: $i] :
( ~ ( rel_s4 @ SV70 @ SY1542 )
| ( v3 @ SY1542 ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(375,plain,
! [SV26: $i,SV50: $i] :
( ( ( v1 @ SV50 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) )
| ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(376,plain,
! [SV27: $i,SV51: $i] :
( ( ( v2 @ SV51 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) )
| ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(377,plain,
! [SV28: $i,SV75: $i,SV52: $i] :
( ( ( ~ ( rel_s4 @ SV52 @ SV75 )
| ( v2 @ SV75 ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(378,plain,
! [SV53: $i,SV29: $i] :
( ( ( ! [SY1506: $i] :
( ~ ( rel_s4 @ SV29 @ SY1506 )
| ! [SY146: $i] :
( ~ ( rel_s4 @ SY1506 @ SY146 )
| ~ ( v1 @ SY146 ) ) ) )
= $true )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(379,plain,
! [SV30: $i,SV76: $i,SV54: $i] :
( ( ( ~ ( rel_s4 @ SV54 @ SV76 )
| ( v1 @ SV76 ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(380,plain,
! [SV31: $i,SV77: $i,SV55: $i] :
( ( ( ~ ( rel_s4 @ SV55 @ SV77 )
| ( v2 @ SV77 ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(381,plain,
! [SV38: $i,SV36: $i,SV34: $i] :
( ( ( rel_s4 @ SV34 @ SV36 )
= $false )
| ( ( ~ ( rel_s4 @ SV36 @ SV38 ) )
= $true )
| ( ( rel_s4 @ SV34 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(382,plain,
! [SV39: $i,SV37: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV37 )
= $false )
| ( ( ~ ( rel_s4 @ SV37 @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(383,plain,
! [SV2: $i,SV71: $i,SV48: $i] :
( ( ( ~ ( rel_s4 @ SV48 @ SV71 ) )
= $true )
| ( ( ~ ( v1 @ SV71 ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(384,plain,
! [SV3: $i,SV78: $i,SV56: $i] :
( ( ( ~ ( rel_s4 @ SV56 @ SV78 )
| ( v4 @ SV78 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(385,plain,
! [SV4: $i,SV57: $i] :
( ( ( v4 @ SV57 )
= $false )
| ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( ! [SY1406: $i] :
( ~ ( rel_s4 @ SV4 @ SY1406 )
| ! [SY1273: $i] :
( ~ ( rel_s4 @ SY1406 @ SY1273 )
| ( v1 @ SY1273 ) ) ) )
= $true )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(386,plain,
! [SV5: $i,SV79: $i,SV58: $i] :
( ( ( ~ ( rel_s4 @ SV58 @ SV79 )
| ( v2 @ SV79 ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(387,plain,
! [SV40: $i,SV72: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV72 ) )
= $true )
| ( ( ! [SY1543: $i] :
( ~ ( rel_s4 @ SV72 @ SY1543 )
| ( v4 @ SY1543 ) ) )
= $true )
| ( ( ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(388,plain,
! [SV41: $i,SV80: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV80 )
| ! [SY1545: $i] :
( ~ ( rel_s4 @ SV80 @ SY1545 )
| ( v2 @ SY1545 ) ) )
= $true )
| ( ( ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(389,plain,
! [SV42: $i,SV81: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV81 )
| ! [SY1546: $i] :
( ~ ( rel_s4 @ SV81 @ SY1546 )
| ~ ( v1 @ SY1546 ) ) )
= $true )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(390,plain,
! [SV9: $i,SV59: $i] :
( ( ( v3 @ SV59 )
= $false )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( ! [SY1428: $i] :
( ~ ( rel_s4 @ SV9 @ SY1428 )
| ! [SY1036: $i] :
( ~ ( rel_s4 @ SY1428 @ SY1036 )
| ~ ( v3 @ SY1036 ) ) ) )
= $true )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(391,plain,
! [SV10: $i,SV60: $i] :
( ( ( v3 @ SV60 )
= $false )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( ! [SY1431: $i] :
( ~ ( rel_s4 @ SV10 @ SY1431 )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY1431 @ SY999 )
| ~ ( v3 @ SY999 ) ) ) )
= $true )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(392,plain,
! [SV11: $i,SV61: $i] :
( ( ( v4 @ SV61 )
= $false )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( ! [SY1434: $i] :
( ~ ( rel_s4 @ SV11 @ SY1434 )
| ! [SY962: $i] :
( ~ ( rel_s4 @ SY1434 @ SY962 )
| ~ ( v4 @ SY962 ) ) ) )
= $true )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(393,plain,
! [SV43: $i,SV73: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV73 ) )
= $true )
| ( ( ~ ( v4 @ SV73 ) )
= $true )
| ( ( ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(394,plain,
! [SV49: $i,SV82: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV82 )
| ! [SY1547: $i] :
( ~ ( rel_s4 @ SV82 @ SY1547 )
| ( v1 @ SY1547 ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( v4 @ SV49 )
= $false )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(395,plain,
! [SV66: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV66 )
= $false )
| ( ( ! [SY1539: $i] :
( ~ ( rel_s4 @ SV66 @ SY1539 )
| ( v2 @ SY1539 ) ) )
= $true )
| ( ( v4 @ SV14 )
= $false )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(396,plain,
! [SV15: $i,SV62: $i] :
( ( ( v3 @ SV62 )
= $false )
| ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( ! [SY1446: $i] :
( ~ ( rel_s4 @ SV15 @ SY1446 )
| ! [SY819: $i] :
( ~ ( rel_s4 @ SY1446 @ SY819 )
| ( v4 @ SY819 ) ) ) )
= $true )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(397,plain,
! [SV16: $i,SV83: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV83 )
| ~ ( v2 @ SV83 ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(398,plain,
! [SV44: $i,SV74: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV74 ) )
= $true )
| ( ( ! [SY1544: $i] :
( ~ ( rel_s4 @ SV74 @ SY1544 )
| ( v2 @ SY1544 ) ) )
= $true )
| ( ( ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(399,plain,
! [SV45: $i,SV84: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV84 )
| ~ ( v3 @ SV84 ) )
= $true )
| ( ( ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(400,plain,
! [SV46: $i,SV85: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV85 )
| ! [SY1548: $i] :
( ~ ( rel_s4 @ SV85 @ SY1548 )
| ( v2 @ SY1548 ) ) )
= $true )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(401,plain,
! [SV20: $i,SV67: $i,SV47: $i] :
( ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(402,plain,
! [SV21: $i,SV64: $i] :
( ( ( v1 @ SV64 )
= $false )
| ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( ! [SY1473: $i] :
( ~ ( rel_s4 @ SV21 @ SY1473 )
| ! [SY532: $i] :
( ~ ( rel_s4 @ SY1473 @ SY532 )
| ( v2 @ SY532 ) ) ) )
= $true )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(403,plain,
! [SV22: $i,SV86: $i,SV65: $i] :
( ( ( ~ ( rel_s4 @ SV65 @ SV86 )
| ( v3 @ SV86 ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(404,plain,
! [SV68: $i,SV23: $i] :
( ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( ! [SY1540: $i] :
( ~ ( rel_s4 @ SV68 @ SY1540 )
| ( v2 @ SY1540 ) ) )
= $true )
| ( ( ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(405,plain,
! [SV69: $i,SV24: $i] :
( ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( ! [SY1541: $i] :
( ~ ( rel_s4 @ SV69 @ SY1541 )
| ( v1 @ SY1541 ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(406,plain,
! [SV70: $i,SV25: $i] :
( ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( ! [SY1542: $i] :
( ~ ( rel_s4 @ SV70 @ SY1542 )
| ( v3 @ SY1542 ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(407,plain,
! [SV50: $i,SV26: $i] :
( ( ( ! [SY1492: $i] :
( ~ ( rel_s4 @ SV26 @ SY1492 )
| ~ ( v3 @ SY1492 ) ) )
= $true )
| ( ( ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(408,plain,
! [SV51: $i,SV27: $i] :
( ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV27 @ SY1496 )
| ~ ( v4 @ SY1496 ) ) )
= $true )
| ( ( ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(409,plain,
! [SV28: $i,SV75: $i,SV52: $i] :
( ( ( ~ ( rel_s4 @ SV52 @ SV75 ) )
= $true )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(410,plain,
! [SV53: $i,SV87: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV87 )
| ! [SY1549: $i] :
( ~ ( rel_s4 @ SV87 @ SY1549 )
| ~ ( v1 @ SY1549 ) ) )
= $true )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(411,plain,
! [SV30: $i,SV76: $i,SV54: $i] :
( ( ( ~ ( rel_s4 @ SV54 @ SV76 ) )
= $true )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(412,plain,
! [SV31: $i,SV77: $i,SV55: $i] :
( ( ( ~ ( rel_s4 @ SV55 @ SV77 ) )
= $true )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(413,plain,
! [SV34: $i,SV38: $i,SV36: $i] :
( ( ( rel_s4 @ SV36 @ SV38 )
= $false )
| ( ( rel_s4 @ SV34 @ SV36 )
= $false )
| ( ( rel_s4 @ SV34 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(414,plain,
! [SV35: mu,SV39: $i,SV37: $i] :
( ( ( rel_s4 @ SV37 @ SV39 )
= $false )
| ( ( exists_in_world @ SV35 @ SV37 )
= $false )
| ( ( exists_in_world @ SV35 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(415,plain,
! [SV2: $i,SV71: $i,SV48: $i] :
( ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( ~ ( v1 @ SV71 ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(416,plain,
! [SV3: $i,SV78: $i,SV56: $i] :
( ( ( ~ ( rel_s4 @ SV56 @ SV78 ) )
= $true )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(417,plain,
! [SV57: $i,SV88: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV88 )
| ! [SY1550: $i] :
( ~ ( rel_s4 @ SV88 @ SY1550 )
| ( v1 @ SY1550 ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( v4 @ SV57 )
= $false )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(418,plain,
! [SV5: $i,SV79: $i,SV58: $i] :
( ( ( ~ ( rel_s4 @ SV58 @ SV79 ) )
= $true )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(419,plain,
! [SV40: $i,SV72: $i,SV6: $i] :
( ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( ! [SY1543: $i] :
( ~ ( rel_s4 @ SV72 @ SY1543 )
| ( v4 @ SY1543 ) ) )
= $true )
| ( ( ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(420,plain,
! [SV41: $i,SV80: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV80 ) )
= $true )
| ( ( ! [SY1545: $i] :
( ~ ( rel_s4 @ SV80 @ SY1545 )
| ( v2 @ SY1545 ) ) )
= $true )
| ( ( ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(421,plain,
! [SV42: $i,SV81: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV81 ) )
= $true )
| ( ( ! [SY1546: $i] :
( ~ ( rel_s4 @ SV81 @ SY1546 )
| ~ ( v1 @ SY1546 ) ) )
= $true )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(422,plain,
! [SV59: $i,SV89: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV89 )
| ! [SY1551: $i] :
( ~ ( rel_s4 @ SV89 @ SY1551 )
| ~ ( v3 @ SY1551 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( v3 @ SV59 )
= $false )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(423,plain,
! [SV60: $i,SV90: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV90 )
| ! [SY1552: $i] :
( ~ ( rel_s4 @ SV90 @ SY1552 )
| ~ ( v3 @ SY1552 ) ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( v3 @ SV60 )
= $false )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(424,plain,
! [SV61: $i,SV91: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ SV11 @ SV91 )
| ! [SY1553: $i] :
( ~ ( rel_s4 @ SV91 @ SY1553 )
| ~ ( v4 @ SY1553 ) ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( v4 @ SV61 )
= $false )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(425,plain,
! [SV43: $i,SV73: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( ~ ( v4 @ SV73 ) )
= $true )
| ( ( ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(426,plain,
! [SV49: $i,SV82: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV82 ) )
= $true )
| ( ( ! [SY1547: $i] :
( ~ ( rel_s4 @ SV82 @ SY1547 )
| ( v1 @ SY1547 ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( v4 @ SV49 )
= $false )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(427,plain,
! [SV14: $i,SV92: $i,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ SV92 )
| ( v2 @ SV92 ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV66 )
= $false )
| ( ( v4 @ SV14 )
= $false )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(428,plain,
! [SV62: $i,SV93: $i,SV15: $i] :
( ( ( ~ ( rel_s4 @ SV15 @ SV93 )
| ! [SY1554: $i] :
( ~ ( rel_s4 @ SV93 @ SY1554 )
| ( v4 @ SY1554 ) ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( v3 @ SV62 )
= $false )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(429,plain,
! [SV16: $i,SV83: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV83 ) )
= $true )
| ( ( ~ ( v2 @ SV83 ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(430,plain,
! [SV44: $i,SV74: $i,SV17: $i] :
( ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( ! [SY1544: $i] :
( ~ ( rel_s4 @ SV74 @ SY1544 )
| ( v2 @ SY1544 ) ) )
= $true )
| ( ( ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(431,plain,
! [SV45: $i,SV84: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV84 ) )
= $true )
| ( ( ~ ( v3 @ SV84 ) )
= $true )
| ( ( ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(432,plain,
! [SV46: $i,SV85: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV85 ) )
= $true )
| ( ( ! [SY1548: $i] :
( ~ ( rel_s4 @ SV85 @ SY1548 )
| ( v2 @ SY1548 ) ) )
= $true )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(433,plain,
! [SV67: $i,SV47: $i,SV20: $i] :
( ( ( ! [SY1468: $i] :
( ~ ( rel_s4 @ SV20 @ SY1468 )
| ! [SY569: $i] :
( ~ ( rel_s4 @ SY1468 @ SY569 )
| ~ ( v3 @ SY569 ) ) ) )
= $true )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(434,plain,
! [SV64: $i,SV94: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ SV94 )
| ! [SY1555: $i] :
( ~ ( rel_s4 @ SV94 @ SY1555 )
| ( v2 @ SY1555 ) ) )
= $true )
| ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( v1 @ SV64 )
= $false )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(435,plain,
! [SV22: $i,SV86: $i,SV65: $i] :
( ( ( ~ ( rel_s4 @ SV65 @ SV86 ) )
= $true )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(436,plain,
! [SV23: $i,SV95: $i,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ SV95 )
| ( v2 @ SV95 ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(437,plain,
! [SV24: $i,SV96: $i,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ SV96 )
| ( v1 @ SV96 ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(438,plain,
! [SV25: $i,SV97: $i,SV70: $i] :
( ( ( ~ ( rel_s4 @ SV70 @ SV97 )
| ( v3 @ SV97 ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(439,plain,
! [SV50: $i,SV98: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV98 )
| ~ ( v3 @ SV98 ) )
= $true )
| ( ( ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(440,plain,
! [SV51: $i,SV99: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV99 )
| ~ ( v4 @ SV99 ) )
= $true )
| ( ( ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(441,plain,
! [SV28: $i,SV75: $i,SV52: $i] :
( ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(442,plain,
! [SV53: $i,SV87: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV87 ) )
= $true )
| ( ( ! [SY1549: $i] :
( ~ ( rel_s4 @ SV87 @ SY1549 )
| ~ ( v1 @ SY1549 ) ) )
= $true )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(443,plain,
! [SV30: $i,SV76: $i,SV54: $i] :
( ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) )
| ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(444,plain,
! [SV31: $i,SV77: $i,SV55: $i] :
( ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(445,plain,
! [SV2: $i,SV48: $i,SV71: $i] :
( ( ( v1 @ SV71 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( ! [SY1399: $i] :
( ~ ( rel_s4 @ SV2 @ SY1399 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1399 @ SY1358 )
| ~ ( v2 @ SY1358 ) ) ) )
= $true )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(446,plain,
! [SV3: $i,SV78: $i,SV56: $i] :
( ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( ! [SY1403: $i] :
( ~ ( rel_s4 @ SV3 @ SY1403 )
| ! [SY1313: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1313 )
| ~ ( v1 @ SY1313 ) ) ) )
= $true )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(447,plain,
! [SV57: $i,SV88: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV88 ) )
= $true )
| ( ( ! [SY1550: $i] :
( ~ ( rel_s4 @ SV88 @ SY1550 )
| ( v1 @ SY1550 ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( v4 @ SV57 )
= $false )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(448,plain,
! [SV5: $i,SV79: $i,SV58: $i] :
( ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( ! [SY1410: $i] :
( ~ ( rel_s4 @ SV5 @ SY1410 )
| ! [SY1232: $i] :
( ~ ( rel_s4 @ SY1410 @ SY1232 )
| ~ ( v3 @ SY1232 ) ) ) )
= $true )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(449,plain,
! [SV40: $i,SV6: $i,SV100: $i,SV72: $i] :
( ( ( ~ ( rel_s4 @ SV72 @ SV100 )
| ( v4 @ SV100 ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(450,plain,
! [SV41: $i,SV80: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( ! [SY1545: $i] :
( ~ ( rel_s4 @ SV80 @ SY1545 )
| ( v2 @ SY1545 ) ) )
= $true )
| ( ( ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(451,plain,
! [SV42: $i,SV81: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( ! [SY1546: $i] :
( ~ ( rel_s4 @ SV81 @ SY1546 )
| ~ ( v1 @ SY1546 ) ) )
= $true )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(452,plain,
! [SV59: $i,SV89: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV89 ) )
= $true )
| ( ( ! [SY1551: $i] :
( ~ ( rel_s4 @ SV89 @ SY1551 )
| ~ ( v3 @ SY1551 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( v3 @ SV59 )
= $false )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(453,plain,
! [SV60: $i,SV90: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV90 ) )
= $true )
| ( ( ! [SY1552: $i] :
( ~ ( rel_s4 @ SV90 @ SY1552 )
| ~ ( v3 @ SY1552 ) ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( v3 @ SV60 )
= $false )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(454,plain,
! [SV61: $i,SV91: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ SV11 @ SV91 ) )
= $true )
| ( ( ! [SY1553: $i] :
( ~ ( rel_s4 @ SV91 @ SY1553 )
| ~ ( v4 @ SY1553 ) ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( v4 @ SV61 )
= $false )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(455,plain,
! [SV43: $i,SV12: $i,SV73: $i] :
( ( ( v4 @ SV73 )
= $false )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( ! [SY1438: $i] :
( ~ ( rel_s4 @ SV12 @ SY1438 )
| ! [SY921: $i] :
( ~ ( rel_s4 @ SY1438 @ SY921 )
| ~ ( v3 @ SY921 ) ) ) )
= $true )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(456,plain,
! [SV49: $i,SV82: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV82 )
= $false )
| ( ( ! [SY1547: $i] :
( ~ ( rel_s4 @ SV82 @ SY1547 )
| ( v1 @ SY1547 ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( v4 @ SV49 )
= $false )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(457,plain,
! [SV14: $i,SV92: $i,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ SV92 ) )
= $true )
| ( ( v2 @ SV92 )
= $true )
| ( ( rel_s4 @ SV14 @ SV66 )
= $false )
| ( ( v4 @ SV14 )
= $false )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(458,plain,
! [SV62: $i,SV93: $i,SV15: $i] :
( ( ( ~ ( rel_s4 @ SV15 @ SV93 ) )
= $true )
| ( ( ! [SY1554: $i] :
( ~ ( rel_s4 @ SV93 @ SY1554 )
| ( v4 @ SY1554 ) ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( v3 @ SV62 )
= $false )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(459,plain,
! [SV16: $i,SV83: $i,SV63: $i] :
( ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( ~ ( v2 @ SV83 ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(460,plain,
! [SV44: $i,SV17: $i,SV101: $i,SV74: $i] :
( ( ( ~ ( rel_s4 @ SV74 @ SV101 )
| ( v2 @ SV101 ) )
= $true )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(461,plain,
! [SV45: $i,SV84: $i,SV18: $i] :
( ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( ~ ( v3 @ SV84 ) )
= $true )
| ( ( ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(462,plain,
! [SV46: $i,SV85: $i,SV19: $i] :
( ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( ! [SY1548: $i] :
( ~ ( rel_s4 @ SV85 @ SY1548 )
| ( v2 @ SY1548 ) ) )
= $true )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(463,plain,
! [SV67: $i,SV47: $i,SV102: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV102 )
| ! [SY1556: $i] :
( ~ ( rel_s4 @ SV102 @ SY1556 )
| ~ ( v3 @ SY1556 ) ) )
= $true )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(464,plain,
! [SV64: $i,SV94: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ SV94 ) )
= $true )
| ( ( ! [SY1555: $i] :
( ~ ( rel_s4 @ SV94 @ SY1555 )
| ( v2 @ SY1555 ) ) )
= $true )
| ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( v1 @ SV64 )
= $false )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(465,plain,
! [SV22: $i,SV86: $i,SV65: $i] :
( ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( ! [SY1477: $i] :
( ~ ( rel_s4 @ SV22 @ SY1477 )
| ! [SY491: $i] :
( ~ ( rel_s4 @ SY1477 @ SY491 )
| ~ ( v1 @ SY491 ) ) ) )
= $true )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(466,plain,
! [SV23: $i,SV95: $i,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ SV95 ) )
= $true )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(467,plain,
! [SV24: $i,SV96: $i,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ SV96 ) )
= $true )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(468,plain,
! [SV25: $i,SV97: $i,SV70: $i] :
( ( ( ~ ( rel_s4 @ SV70 @ SV97 ) )
= $true )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(469,plain,
! [SV50: $i,SV98: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV98 ) )
= $true )
| ( ( ~ ( v3 @ SV98 ) )
= $true )
| ( ( ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(470,plain,
! [SV51: $i,SV99: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV99 ) )
= $true )
| ( ( ~ ( v4 @ SV99 ) )
= $true )
| ( ( ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(471,plain,
! [SV75: $i,SV52: $i,SV28: $i] :
( ( ( ! [SY1501: $i] :
( ~ ( rel_s4 @ SV28 @ SY1501 )
| ! [SY202: $i] :
( ~ ( rel_s4 @ SY1501 @ SY202 )
| ( v4 @ SY202 ) ) ) )
= $true )
| ( ( ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(472,plain,
! [SV53: $i,SV87: $i,SV29: $i] :
( ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( ! [SY1549: $i] :
( ~ ( rel_s4 @ SV87 @ SY1549 )
| ~ ( v1 @ SY1549 ) ) )
= $true )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(473,plain,
! [SV76: $i,SV54: $i,SV30: $i] :
( ( ( ! [SY1512: $i] :
( ~ ( rel_s4 @ SV30 @ SY1512 )
| ! [SY89: $i] :
( ~ ( rel_s4 @ SY1512 @ SY89 )
| ( v3 @ SY89 ) ) ) )
= $true )
| ( ( ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(474,plain,
! [SV77: $i,SV55: $i,SV31: $i] :
( ( ( ! [SY1518: $i] :
( ~ ( rel_s4 @ SV31 @ SY1518 )
| ! [SY29: $i] :
( ~ ( rel_s4 @ SY1518 @ SY29 )
| ( v3 @ SY29 ) ) ) )
= $true )
| ( ( ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(475,plain,
! [SV71: $i,SV48: $i,SV103: $i,SV2: $i] :
( ( ( ~ ( rel_s4 @ SV2 @ SV103 )
| ! [SY1557: $i] :
( ~ ( rel_s4 @ SV103 @ SY1557 )
| ~ ( v2 @ SY1557 ) ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( v1 @ SV71 )
= $false )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(476,plain,
! [SV78: $i,SV56: $i,SV104: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV104 )
| ! [SY1558: $i] :
( ~ ( rel_s4 @ SV104 @ SY1558 )
| ~ ( v1 @ SY1558 ) ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(477,plain,
! [SV57: $i,SV88: $i,SV4: $i] :
( ( ( rel_s4 @ SV4 @ SV88 )
= $false )
| ( ( ! [SY1550: $i] :
( ~ ( rel_s4 @ SV88 @ SY1550 )
| ( v1 @ SY1550 ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( v4 @ SV57 )
= $false )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(478,plain,
! [SV79: $i,SV58: $i,SV105: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV105 )
| ! [SY1559: $i] :
( ~ ( rel_s4 @ SV105 @ SY1559 )
| ~ ( v3 @ SY1559 ) ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(479,plain,
! [SV40: $i,SV6: $i,SV100: $i,SV72: $i] :
( ( ( ~ ( rel_s4 @ SV72 @ SV100 ) )
= $true )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(480,plain,
! [SV41: $i,SV7: $i,SV106: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV106 )
| ( v2 @ SV106 ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(481,plain,
! [SV42: $i,SV8: $i,SV107: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV107 )
| ~ ( v1 @ SV107 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(482,plain,
! [SV59: $i,SV89: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV89 )
= $false )
| ( ( ! [SY1551: $i] :
( ~ ( rel_s4 @ SV89 @ SY1551 )
| ~ ( v3 @ SY1551 ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( v3 @ SV59 )
= $false )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(483,plain,
! [SV60: $i,SV90: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV90 )
= $false )
| ( ( ! [SY1552: $i] :
( ~ ( rel_s4 @ SV90 @ SY1552 )
| ~ ( v3 @ SY1552 ) ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( v3 @ SV60 )
= $false )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(484,plain,
! [SV61: $i,SV91: $i,SV11: $i] :
( ( ( rel_s4 @ SV11 @ SV91 )
= $false )
| ( ( ! [SY1553: $i] :
( ~ ( rel_s4 @ SV91 @ SY1553 )
| ~ ( v4 @ SY1553 ) ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( v4 @ SV61 )
= $false )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(485,plain,
! [SV43: $i,SV73: $i,SV108: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV108 )
| ! [SY1560: $i] :
( ~ ( rel_s4 @ SV108 @ SY1560 )
| ~ ( v3 @ SY1560 ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( v4 @ SV73 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(486,plain,
! [SV49: $i,SV13: $i,SV109: $i,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ SV109 )
| ( v1 @ SV109 ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV82 )
= $false )
| ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( v4 @ SV49 )
= $false )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(487,plain,
! [SV14: $i,SV92: $i,SV66: $i] :
( ( ( rel_s4 @ SV66 @ SV92 )
= $false )
| ( ( v2 @ SV92 )
= $true )
| ( ( rel_s4 @ SV14 @ SV66 )
= $false )
| ( ( v4 @ SV14 )
= $false )
| ( ( v1 @ SV14 )
= $false )
| ( ( v3 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(488,plain,
! [SV62: $i,SV93: $i,SV15: $i] :
( ( ( rel_s4 @ SV15 @ SV93 )
= $false )
| ( ( ! [SY1554: $i] :
( ~ ( rel_s4 @ SV93 @ SY1554 )
| ( v4 @ SY1554 ) ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( v3 @ SV62 )
= $false )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(489,plain,
! [SV16: $i,SV63: $i,SV83: $i] :
( ( ( v2 @ SV83 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( ! [SY1450: $i] :
( ~ ( rel_s4 @ SV16 @ SY1450 )
| ! [SY778: $i] :
( ~ ( rel_s4 @ SY1450 @ SY778 )
| ~ ( v4 @ SY778 ) ) ) )
= $true )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(490,plain,
! [SV44: $i,SV17: $i,SV101: $i,SV74: $i] :
( ( ( ~ ( rel_s4 @ SV74 @ SV101 ) )
= $true )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(491,plain,
! [SV45: $i,SV18: $i,SV84: $i] :
( ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( ! [SY1459: $i] :
( ~ ( rel_s4 @ SV18 @ SY1459 )
| ! [SY683: $i] :
( ~ ( rel_s4 @ SY1459 @ SY683 )
| ~ ( v3 @ SY683 ) ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(492,plain,
! [SV46: $i,SV19: $i,SV110: $i,SV85: $i] :
( ( ( ~ ( rel_s4 @ SV85 @ SV110 )
| ( v2 @ SV110 ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(493,plain,
! [SV67: $i,SV47: $i,SV102: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV102 ) )
= $true )
| ( ( ! [SY1556: $i] :
( ~ ( rel_s4 @ SV102 @ SY1556 )
| ~ ( v3 @ SY1556 ) ) )
= $true )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(494,plain,
! [SV64: $i,SV94: $i,SV21: $i] :
( ( ( rel_s4 @ SV21 @ SV94 )
= $false )
| ( ( ! [SY1555: $i] :
( ~ ( rel_s4 @ SV94 @ SY1555 )
| ( v2 @ SY1555 ) ) )
= $true )
| ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( v1 @ SV64 )
= $false )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(495,plain,
! [SV86: $i,SV65: $i,SV111: $i,SV22: $i] :
( ( ( ~ ( rel_s4 @ SV22 @ SV111 )
| ! [SY1561: $i] :
( ~ ( rel_s4 @ SV111 @ SY1561 )
| ~ ( v1 @ SY1561 ) ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(496,plain,
! [SV23: $i,SV95: $i,SV68: $i] :
( ( ( rel_s4 @ SV68 @ SV95 )
= $false )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( ! [SY1481: $i] :
( ~ ( rel_s4 @ SV23 @ SY1481 )
| ! [SY446: $i] :
( ~ ( rel_s4 @ SY1481 @ SY446 )
| ( v3 @ SY446 ) ) ) )
= $true )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(497,plain,
! [SV24: $i,SV96: $i,SV69: $i] :
( ( ( rel_s4 @ SV69 @ SV96 )
= $false )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( rel_s4 @ SV24 @ SY1485 )
| ! [SY401: $i] :
( ~ ( rel_s4 @ SY1485 @ SY401 )
| ( v4 @ SY401 ) ) ) )
= $true )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(498,plain,
! [SV25: $i,SV97: $i,SV70: $i] :
( ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( rel_s4 @ SV25 @ SY1489 )
| ! [SY356: $i] :
( ~ ( rel_s4 @ SY1489 @ SY356 )
| ~ ( v2 @ SY356 ) ) ) )
= $true )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(499,plain,
! [SV50: $i,SV98: $i,SV26: $i] :
( ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( ~ ( v3 @ SV98 ) )
= $true )
| ( ( ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(500,plain,
! [SV51: $i,SV99: $i,SV27: $i] :
( ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( ~ ( v4 @ SV99 ) )
= $true )
| ( ( ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(501,plain,
! [SV75: $i,SV52: $i,SV112: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV112 )
| ! [SY1562: $i] :
( ~ ( rel_s4 @ SV112 @ SY1562 )
| ( v4 @ SY1562 ) ) )
= $true )
| ( ( ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(502,plain,
! [SV53: $i,SV29: $i,SV113: $i,SV87: $i] :
( ( ( ~ ( rel_s4 @ SV87 @ SV113 )
| ~ ( v1 @ SV113 ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(503,plain,
! [SV76: $i,SV54: $i,SV114: $i,SV30: $i] :
( ( ( ~ ( rel_s4 @ SV30 @ SV114 )
| ! [SY1563: $i] :
( ~ ( rel_s4 @ SV114 @ SY1563 )
| ( v3 @ SY1563 ) ) )
= $true )
| ( ( ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(504,plain,
! [SV77: $i,SV55: $i,SV115: $i,SV31: $i] :
( ( ( ~ ( rel_s4 @ SV31 @ SV115 )
| ! [SY1564: $i] :
( ~ ( rel_s4 @ SV115 @ SY1564 )
| ( v3 @ SY1564 ) ) )
= $true )
| ( ( ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(505,plain,
! [SV71: $i,SV48: $i,SV103: $i,SV2: $i] :
( ( ( ~ ( rel_s4 @ SV2 @ SV103 ) )
= $true )
| ( ( ! [SY1557: $i] :
( ~ ( rel_s4 @ SV103 @ SY1557 )
| ~ ( v2 @ SY1557 ) ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( v1 @ SV71 )
= $false )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(506,plain,
! [SV78: $i,SV56: $i,SV104: $i,SV3: $i] :
( ( ( ~ ( rel_s4 @ SV3 @ SV104 ) )
= $true )
| ( ( ! [SY1558: $i] :
( ~ ( rel_s4 @ SV104 @ SY1558 )
| ~ ( v1 @ SY1558 ) ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(507,plain,
! [SV57: $i,SV4: $i,SV116: $i,SV88: $i] :
( ( ( ~ ( rel_s4 @ SV88 @ SV116 )
| ( v1 @ SV116 ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV88 )
= $false )
| ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( v4 @ SV57 )
= $false )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(508,plain,
! [SV79: $i,SV58: $i,SV105: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV105 ) )
= $true )
| ( ( ! [SY1559: $i] :
( ~ ( rel_s4 @ SV105 @ SY1559 )
| ~ ( v3 @ SY1559 ) ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(509,plain,
! [SV40: $i,SV6: $i,SV100: $i,SV72: $i] :
( ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( ! [SY1415: $i] :
( ~ ( rel_s4 @ SV6 @ SY1415 )
| ! [SY1183: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1183 )
| ~ ( v2 @ SY1183 ) ) ) )
= $true )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(510,plain,
! [SV41: $i,SV7: $i,SV106: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV106 ) )
= $true )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(511,plain,
! [SV42: $i,SV8: $i,SV107: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV107 ) )
= $true )
| ( ( ~ ( v1 @ SV107 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(512,plain,
! [SV59: $i,SV9: $i,SV117: $i,SV89: $i] :
( ( ( ~ ( rel_s4 @ SV89 @ SV117 )
| ~ ( v3 @ SV117 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV89 )
= $false )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( v3 @ SV59 )
= $false )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(513,plain,
! [SV60: $i,SV10: $i,SV118: $i,SV90: $i] :
( ( ( ~ ( rel_s4 @ SV90 @ SV118 )
| ~ ( v3 @ SV118 ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV90 )
= $false )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( v3 @ SV60 )
= $false )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(514,plain,
! [SV61: $i,SV11: $i,SV119: $i,SV91: $i] :
( ( ( ~ ( rel_s4 @ SV91 @ SV119 )
| ~ ( v4 @ SV119 ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV91 )
= $false )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( v4 @ SV61 )
= $false )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(515,plain,
! [SV43: $i,SV73: $i,SV108: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV108 ) )
= $true )
| ( ( ! [SY1560: $i] :
( ~ ( rel_s4 @ SV108 @ SY1560 )
| ~ ( v3 @ SY1560 ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( v4 @ SV73 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(516,plain,
! [SV49: $i,SV13: $i,SV109: $i,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ SV109 ) )
= $true )
| ( ( v1 @ SV109 )
= $true )
| ( ( rel_s4 @ SV13 @ SV82 )
= $false )
| ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( v4 @ SV49 )
= $false )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(517,plain,
! [SV62: $i,SV15: $i,SV120: $i,SV93: $i] :
( ( ( ~ ( rel_s4 @ SV93 @ SV120 )
| ( v4 @ SV120 ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV93 )
= $false )
| ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( v3 @ SV62 )
= $false )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(518,plain,
! [SV83: $i,SV63: $i,SV121: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ SV121 )
| ! [SY1565: $i] :
( ~ ( rel_s4 @ SV121 @ SY1565 )
| ~ ( v4 @ SY1565 ) ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( v2 @ SV83 )
= $false )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(519,plain,
! [SV44: $i,SV17: $i,SV101: $i,SV74: $i] :
( ( ( rel_s4 @ SV74 @ SV101 )
= $false )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( ! [SY1455: $i] :
( ~ ( rel_s4 @ SV17 @ SY1455 )
| ! [SY728: $i] :
( ~ ( rel_s4 @ SY1455 @ SY728 )
| ( v3 @ SY728 ) ) ) )
= $true )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(520,plain,
! [SV45: $i,SV84: $i,SV122: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV122 )
| ! [SY1566: $i] :
( ~ ( rel_s4 @ SV122 @ SY1566 )
| ~ ( v3 @ SY1566 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(521,plain,
! [SV46: $i,SV19: $i,SV110: $i,SV85: $i] :
( ( ( ~ ( rel_s4 @ SV85 @ SV110 ) )
= $true )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(522,plain,
! [SV67: $i,SV47: $i,SV102: $i,SV20: $i] :
( ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( ! [SY1556: $i] :
( ~ ( rel_s4 @ SV102 @ SY1556 )
| ~ ( v3 @ SY1556 ) ) )
= $true )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(523,plain,
! [SV64: $i,SV21: $i,SV123: $i,SV94: $i] :
( ( ( ~ ( rel_s4 @ SV94 @ SV123 )
| ( v2 @ SV123 ) )
= $true )
| ( ( rel_s4 @ SV21 @ SV94 )
= $false )
| ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( v1 @ SV64 )
= $false )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(524,plain,
! [SV86: $i,SV65: $i,SV111: $i,SV22: $i] :
( ( ( ~ ( rel_s4 @ SV22 @ SV111 ) )
= $true )
| ( ( ! [SY1561: $i] :
( ~ ( rel_s4 @ SV111 @ SY1561 )
| ~ ( v1 @ SY1561 ) ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(525,plain,
! [SV95: $i,SV68: $i,SV124: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV124 )
| ! [SY1567: $i] :
( ~ ( rel_s4 @ SV124 @ SY1567 )
| ( v3 @ SY1567 ) ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV68 @ SV95 )
= $false )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(526,plain,
! [SV96: $i,SV69: $i,SV125: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV125 )
| ! [SY1568: $i] :
( ~ ( rel_s4 @ SV125 @ SY1568 )
| ( v4 @ SY1568 ) ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV69 @ SV96 )
= $false )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(527,plain,
! [SV97: $i,SV70: $i,SV126: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV126 )
| ! [SY1569: $i] :
( ~ ( rel_s4 @ SV126 @ SY1569 )
| ~ ( v2 @ SY1569 ) ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(528,plain,
! [SV50: $i,SV26: $i,SV98: $i] :
( ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( ! [SY1493: $i] :
( ~ ( rel_s4 @ SV26 @ SY1493 )
| ! [SY311: $i] :
( ~ ( rel_s4 @ SY1493 @ SY311 )
| ~ ( v1 @ SY311 ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(529,plain,
! [SV51: $i,SV27: $i,SV99: $i] :
( ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( ! [SY1497: $i] :
( ~ ( rel_s4 @ SV27 @ SY1497 )
| ! [SY266: $i] :
( ~ ( rel_s4 @ SY1497 @ SY266 )
| ~ ( v3 @ SY266 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(530,plain,
! [SV75: $i,SV52: $i,SV112: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV112 ) )
= $true )
| ( ( ! [SY1562: $i] :
( ~ ( rel_s4 @ SV112 @ SY1562 )
| ( v4 @ SY1562 ) ) )
= $true )
| ( ( ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(531,plain,
! [SV53: $i,SV29: $i,SV113: $i,SV87: $i] :
( ( ( ~ ( rel_s4 @ SV87 @ SV113 ) )
= $true )
| ( ( ~ ( v1 @ SV113 ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(532,plain,
! [SV76: $i,SV54: $i,SV114: $i,SV30: $i] :
( ( ( ~ ( rel_s4 @ SV30 @ SV114 ) )
= $true )
| ( ( ! [SY1563: $i] :
( ~ ( rel_s4 @ SV114 @ SY1563 )
| ( v3 @ SY1563 ) ) )
= $true )
| ( ( ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(533,plain,
! [SV77: $i,SV55: $i,SV115: $i,SV31: $i] :
( ( ( ~ ( rel_s4 @ SV31 @ SV115 ) )
= $true )
| ( ( ! [SY1564: $i] :
( ~ ( rel_s4 @ SV115 @ SY1564 )
| ( v3 @ SY1564 ) ) )
= $true )
| ( ( ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(534,plain,
! [SV71: $i,SV48: $i,SV103: $i,SV2: $i] :
( ( ( rel_s4 @ SV2 @ SV103 )
= $false )
| ( ( ! [SY1557: $i] :
( ~ ( rel_s4 @ SV103 @ SY1557 )
| ~ ( v2 @ SY1557 ) ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( v1 @ SV71 )
= $false )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(535,plain,
! [SV78: $i,SV56: $i,SV104: $i,SV3: $i] :
( ( ( rel_s4 @ SV3 @ SV104 )
= $false )
| ( ( ! [SY1558: $i] :
( ~ ( rel_s4 @ SV104 @ SY1558 )
| ~ ( v1 @ SY1558 ) ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(536,plain,
! [SV57: $i,SV4: $i,SV116: $i,SV88: $i] :
( ( ( ~ ( rel_s4 @ SV88 @ SV116 ) )
= $true )
| ( ( v1 @ SV116 )
= $true )
| ( ( rel_s4 @ SV4 @ SV88 )
= $false )
| ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( v4 @ SV57 )
= $false )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(537,plain,
! [SV79: $i,SV58: $i,SV105: $i,SV5: $i] :
( ( ( rel_s4 @ SV5 @ SV105 )
= $false )
| ( ( ! [SY1559: $i] :
( ~ ( rel_s4 @ SV105 @ SY1559 )
| ~ ( v3 @ SY1559 ) ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(538,plain,
! [SV40: $i,SV100: $i,SV72: $i,SV127: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV127 )
| ! [SY1570: $i] :
( ~ ( rel_s4 @ SV127 @ SY1570 )
| ~ ( v2 @ SY1570 ) ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(539,plain,
! [SV41: $i,SV7: $i,SV106: $i,SV80: $i] :
( ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( ! [SY1420: $i] :
( ~ ( rel_s4 @ SV7 @ SY1420 )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1132 )
| ~ ( v2 @ SY1132 ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(540,plain,
! [SV42: $i,SV8: $i,SV107: $i,SV81: $i] :
( ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( ~ ( v1 @ SV107 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(541,plain,
! [SV59: $i,SV9: $i,SV117: $i,SV89: $i] :
( ( ( ~ ( rel_s4 @ SV89 @ SV117 ) )
= $true )
| ( ( ~ ( v3 @ SV117 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV89 )
= $false )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( v3 @ SV59 )
= $false )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(542,plain,
! [SV60: $i,SV10: $i,SV118: $i,SV90: $i] :
( ( ( ~ ( rel_s4 @ SV90 @ SV118 ) )
= $true )
| ( ( ~ ( v3 @ SV118 ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV90 )
= $false )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( v3 @ SV60 )
= $false )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(543,plain,
! [SV61: $i,SV11: $i,SV119: $i,SV91: $i] :
( ( ( ~ ( rel_s4 @ SV91 @ SV119 ) )
= $true )
| ( ( ~ ( v4 @ SV119 ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV91 )
= $false )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( v4 @ SV61 )
= $false )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(544,plain,
! [SV43: $i,SV73: $i,SV108: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV108 )
= $false )
| ( ( ! [SY1560: $i] :
( ~ ( rel_s4 @ SV108 @ SY1560 )
| ~ ( v3 @ SY1560 ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( v4 @ SV73 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(545,plain,
! [SV49: $i,SV13: $i,SV109: $i,SV82: $i] :
( ( ( rel_s4 @ SV82 @ SV109 )
= $false )
| ( ( v1 @ SV109 )
= $true )
| ( ( rel_s4 @ SV13 @ SV82 )
= $false )
| ( ( rel_s4 @ SV13 @ SV49 )
= $false )
| ( ( v4 @ SV49 )
= $false )
| ( ( v4 @ SV13 )
= $true )
| ( ( v3 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(546,plain,
! [SV62: $i,SV15: $i,SV120: $i,SV93: $i] :
( ( ( ~ ( rel_s4 @ SV93 @ SV120 ) )
= $true )
| ( ( v4 @ SV120 )
= $true )
| ( ( rel_s4 @ SV15 @ SV93 )
= $false )
| ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( v3 @ SV62 )
= $false )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(547,plain,
! [SV83: $i,SV63: $i,SV121: $i,SV16: $i] :
( ( ( ~ ( rel_s4 @ SV16 @ SV121 ) )
= $true )
| ( ( ! [SY1565: $i] :
( ~ ( rel_s4 @ SV121 @ SY1565 )
| ~ ( v4 @ SY1565 ) ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( v2 @ SV83 )
= $false )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(548,plain,
! [SV44: $i,SV101: $i,SV74: $i,SV128: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV128 )
| ! [SY1571: $i] :
( ~ ( rel_s4 @ SV128 @ SY1571 )
| ( v3 @ SY1571 ) ) )
= $true )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV74 @ SV101 )
= $false )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(549,plain,
! [SV45: $i,SV84: $i,SV122: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV122 ) )
= $true )
| ( ( ! [SY1566: $i] :
( ~ ( rel_s4 @ SV122 @ SY1566 )
| ~ ( v3 @ SY1566 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(550,plain,
! [SV46: $i,SV19: $i,SV110: $i,SV85: $i] :
( ( ( rel_s4 @ SV85 @ SV110 )
= $false )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV19 @ SY1464 )
| ! [SY634: $i] :
( ~ ( rel_s4 @ SY1464 @ SY634 )
| ( v3 @ SY634 ) ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(551,plain,
! [SV67: $i,SV47: $i,SV20: $i,SV129: $i,SV102: $i] :
( ( ( ~ ( rel_s4 @ SV102 @ SV129 )
| ~ ( v3 @ SV129 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(552,plain,
! [SV64: $i,SV21: $i,SV123: $i,SV94: $i] :
( ( ( ~ ( rel_s4 @ SV94 @ SV123 ) )
= $true )
| ( ( v2 @ SV123 )
= $true )
| ( ( rel_s4 @ SV21 @ SV94 )
= $false )
| ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( v1 @ SV64 )
= $false )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(553,plain,
! [SV86: $i,SV65: $i,SV111: $i,SV22: $i] :
( ( ( rel_s4 @ SV22 @ SV111 )
= $false )
| ( ( ! [SY1561: $i] :
( ~ ( rel_s4 @ SV111 @ SY1561 )
| ~ ( v1 @ SY1561 ) ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(554,plain,
! [SV95: $i,SV68: $i,SV124: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV124 ) )
= $true )
| ( ( ! [SY1567: $i] :
( ~ ( rel_s4 @ SV124 @ SY1567 )
| ( v3 @ SY1567 ) ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV68 @ SV95 )
= $false )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(555,plain,
! [SV96: $i,SV69: $i,SV125: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV125 ) )
= $true )
| ( ( ! [SY1568: $i] :
( ~ ( rel_s4 @ SV125 @ SY1568 )
| ( v4 @ SY1568 ) ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV69 @ SV96 )
= $false )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(556,plain,
! [SV97: $i,SV70: $i,SV126: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV126 ) )
= $true )
| ( ( ! [SY1569: $i] :
( ~ ( rel_s4 @ SV126 @ SY1569 )
| ~ ( v2 @ SY1569 ) ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(557,plain,
! [SV50: $i,SV98: $i,SV130: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV130 )
| ! [SY1572: $i] :
( ~ ( rel_s4 @ SV130 @ SY1572 )
| ~ ( v1 @ SY1572 ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(558,plain,
! [SV51: $i,SV99: $i,SV131: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV131 )
| ! [SY1573: $i] :
( ~ ( rel_s4 @ SV131 @ SY1573 )
| ~ ( v3 @ SY1573 ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(559,plain,
! [SV75: $i,SV52: $i,SV112: $i,SV28: $i] :
( ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( ! [SY1562: $i] :
( ~ ( rel_s4 @ SV112 @ SY1562 )
| ( v4 @ SY1562 ) ) )
= $true )
| ( ( ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(560,plain,
! [SV53: $i,SV29: $i,SV113: $i,SV87: $i] :
( ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( ~ ( v1 @ SV113 ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(561,plain,
! [SV76: $i,SV54: $i,SV114: $i,SV30: $i] :
( ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( ! [SY1563: $i] :
( ~ ( rel_s4 @ SV114 @ SY1563 )
| ( v3 @ SY1563 ) ) )
= $true )
| ( ( ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(562,plain,
! [SV77: $i,SV55: $i,SV115: $i,SV31: $i] :
( ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( ! [SY1564: $i] :
( ~ ( rel_s4 @ SV115 @ SY1564 )
| ( v3 @ SY1564 ) ) )
= $true )
| ( ( ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(563,plain,
! [SV71: $i,SV48: $i,SV2: $i,SV132: $i,SV103: $i] :
( ( ( ~ ( rel_s4 @ SV103 @ SV132 )
| ~ ( v2 @ SV132 ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV103 )
= $false )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( v1 @ SV71 )
= $false )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(564,plain,
! [SV78: $i,SV56: $i,SV3: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( rel_s4 @ SV104 @ SV133 )
| ~ ( v1 @ SV133 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV104 )
= $false )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(565,plain,
! [SV57: $i,SV4: $i,SV116: $i,SV88: $i] :
( ( ( rel_s4 @ SV88 @ SV116 )
= $false )
| ( ( v1 @ SV116 )
= $true )
| ( ( rel_s4 @ SV4 @ SV88 )
= $false )
| ( ( rel_s4 @ SV4 @ SV57 )
= $false )
| ( ( v4 @ SV57 )
= $false )
| ( ( v3 @ SV4 )
= $false )
| ( ( v1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(566,plain,
! [SV79: $i,SV58: $i,SV5: $i,SV134: $i,SV105: $i] :
( ( ( ~ ( rel_s4 @ SV105 @ SV134 )
| ~ ( v3 @ SV134 ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV105 )
= $false )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(567,plain,
! [SV40: $i,SV100: $i,SV72: $i,SV127: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV127 ) )
= $true )
| ( ( ! [SY1570: $i] :
( ~ ( rel_s4 @ SV127 @ SY1570 )
| ~ ( v2 @ SY1570 ) ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(568,plain,
! [SV41: $i,SV106: $i,SV80: $i,SV135: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV135 )
| ! [SY1574: $i] :
( ~ ( rel_s4 @ SV135 @ SY1574 )
| ~ ( v2 @ SY1574 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(569,plain,
! [SV42: $i,SV8: $i,SV81: $i,SV107: $i] :
( ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( ! [SY1425: $i] :
( ~ ( rel_s4 @ SV8 @ SY1425 )
| ! [SY1080: $i] :
( ~ ( rel_s4 @ SY1425 @ SY1080 )
| ~ ( v4 @ SY1080 ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(570,plain,
! [SV59: $i,SV9: $i,SV117: $i,SV89: $i] :
( ( ( rel_s4 @ SV89 @ SV117 )
= $false )
| ( ( ~ ( v3 @ SV117 ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV89 )
= $false )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( v3 @ SV59 )
= $false )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(571,plain,
! [SV60: $i,SV10: $i,SV118: $i,SV90: $i] :
( ( ( rel_s4 @ SV90 @ SV118 )
= $false )
| ( ( ~ ( v3 @ SV118 ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV90 )
= $false )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( v3 @ SV60 )
= $false )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(572,plain,
! [SV61: $i,SV11: $i,SV119: $i,SV91: $i] :
( ( ( rel_s4 @ SV91 @ SV119 )
= $false )
| ( ( ~ ( v4 @ SV119 ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV91 )
= $false )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( v4 @ SV61 )
= $false )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(573,plain,
! [SV43: $i,SV73: $i,SV12: $i,SV136: $i,SV108: $i] :
( ( ( ~ ( rel_s4 @ SV108 @ SV136 )
| ~ ( v3 @ SV136 ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV108 )
= $false )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( v4 @ SV73 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(574,plain,
! [SV62: $i,SV15: $i,SV120: $i,SV93: $i] :
( ( ( rel_s4 @ SV93 @ SV120 )
= $false )
| ( ( v4 @ SV120 )
= $true )
| ( ( rel_s4 @ SV15 @ SV93 )
= $false )
| ( ( rel_s4 @ SV15 @ SV62 )
= $false )
| ( ( v3 @ SV62 )
= $false )
| ( ( v1 @ SV15 )
= $false )
| ( ( v3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(575,plain,
! [SV83: $i,SV63: $i,SV121: $i,SV16: $i] :
( ( ( rel_s4 @ SV16 @ SV121 )
= $false )
| ( ( ! [SY1565: $i] :
( ~ ( rel_s4 @ SV121 @ SY1565 )
| ~ ( v4 @ SY1565 ) ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( v2 @ SV83 )
= $false )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(576,plain,
! [SV44: $i,SV101: $i,SV74: $i,SV128: $i,SV17: $i] :
( ( ( ~ ( rel_s4 @ SV17 @ SV128 ) )
= $true )
| ( ( ! [SY1571: $i] :
( ~ ( rel_s4 @ SV128 @ SY1571 )
| ( v3 @ SY1571 ) ) )
= $true )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV74 @ SV101 )
= $false )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(577,plain,
! [SV45: $i,SV84: $i,SV122: $i,SV18: $i] :
( ( ( rel_s4 @ SV18 @ SV122 )
= $false )
| ( ( ! [SY1566: $i] :
( ~ ( rel_s4 @ SV122 @ SY1566 )
| ~ ( v3 @ SY1566 ) ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(578,plain,
! [SV46: $i,SV110: $i,SV85: $i,SV137: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV137 )
| ! [SY1575: $i] :
( ~ ( rel_s4 @ SV137 @ SY1575 )
| ( v3 @ SY1575 ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV85 @ SV110 )
= $false )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(579,plain,
! [SV67: $i,SV47: $i,SV20: $i,SV129: $i,SV102: $i] :
( ( ( ~ ( rel_s4 @ SV102 @ SV129 ) )
= $true )
| ( ( ~ ( v3 @ SV129 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(580,plain,
! [SV64: $i,SV21: $i,SV123: $i,SV94: $i] :
( ( ( rel_s4 @ SV94 @ SV123 )
= $false )
| ( ( v2 @ SV123 )
= $true )
| ( ( rel_s4 @ SV21 @ SV94 )
= $false )
| ( ( rel_s4 @ SV21 @ SV64 )
= $false )
| ( ( v1 @ SV64 )
= $false )
| ( ( v2 @ SV21 )
= $false )
| ( ( v4 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(581,plain,
! [SV86: $i,SV65: $i,SV22: $i,SV138: $i,SV111: $i] :
( ( ( ~ ( rel_s4 @ SV111 @ SV138 )
| ~ ( v1 @ SV138 ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV111 )
= $false )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(582,plain,
! [SV95: $i,SV68: $i,SV124: $i,SV23: $i] :
( ( ( rel_s4 @ SV23 @ SV124 )
= $false )
| ( ( ! [SY1567: $i] :
( ~ ( rel_s4 @ SV124 @ SY1567 )
| ( v3 @ SY1567 ) ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV68 @ SV95 )
= $false )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(583,plain,
! [SV96: $i,SV69: $i,SV125: $i,SV24: $i] :
( ( ( rel_s4 @ SV24 @ SV125 )
= $false )
| ( ( ! [SY1568: $i] :
( ~ ( rel_s4 @ SV125 @ SY1568 )
| ( v4 @ SY1568 ) ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV69 @ SV96 )
= $false )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(584,plain,
! [SV97: $i,SV70: $i,SV126: $i,SV25: $i] :
( ( ( rel_s4 @ SV25 @ SV126 )
= $false )
| ( ( ! [SY1569: $i] :
( ~ ( rel_s4 @ SV126 @ SY1569 )
| ~ ( v2 @ SY1569 ) ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(585,plain,
! [SV50: $i,SV98: $i,SV130: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV130 ) )
= $true )
| ( ( ! [SY1572: $i] :
( ~ ( rel_s4 @ SV130 @ SY1572 )
| ~ ( v1 @ SY1572 ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(586,plain,
! [SV51: $i,SV99: $i,SV131: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV131 ) )
= $true )
| ( ( ! [SY1573: $i] :
( ~ ( rel_s4 @ SV131 @ SY1573 )
| ~ ( v3 @ SY1573 ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(587,plain,
! [SV75: $i,SV52: $i,SV28: $i,SV139: $i,SV112: $i] :
( ( ( ~ ( rel_s4 @ SV112 @ SV139 )
| ( v4 @ SV139 ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(588,plain,
! [SV53: $i,SV29: $i,SV87: $i,SV113: $i] :
( ( ( v1 @ SV113 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( ! [SY1508: $i] :
( ~ ( rel_s4 @ SV29 @ SY1508 )
| ! [SY156: $i] :
( ~ ( rel_s4 @ SY1508 @ SY156 )
| ~ ( v3 @ SY156 ) ) ) )
= $true )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(589,plain,
! [SV76: $i,SV54: $i,SV30: $i,SV140: $i,SV114: $i] :
( ( ( ~ ( rel_s4 @ SV114 @ SV140 )
| ( v3 @ SV140 ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(590,plain,
! [SV77: $i,SV55: $i,SV31: $i,SV141: $i,SV115: $i] :
( ( ( ~ ( rel_s4 @ SV115 @ SV141 )
| ( v3 @ SV141 ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(591,plain,
! [SV71: $i,SV48: $i,SV2: $i,SV132: $i,SV103: $i] :
( ( ( ~ ( rel_s4 @ SV103 @ SV132 ) )
= $true )
| ( ( ~ ( v2 @ SV132 ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV103 )
= $false )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( v1 @ SV71 )
= $false )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(592,plain,
! [SV78: $i,SV56: $i,SV3: $i,SV133: $i,SV104: $i] :
( ( ( ~ ( rel_s4 @ SV104 @ SV133 ) )
= $true )
| ( ( ~ ( v1 @ SV133 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV104 )
= $false )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(593,plain,
! [SV79: $i,SV58: $i,SV5: $i,SV134: $i,SV105: $i] :
( ( ( ~ ( rel_s4 @ SV105 @ SV134 ) )
= $true )
| ( ( ~ ( v3 @ SV134 ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV105 )
= $false )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(594,plain,
! [SV40: $i,SV100: $i,SV72: $i,SV127: $i,SV6: $i] :
( ( ( rel_s4 @ SV6 @ SV127 )
= $false )
| ( ( ! [SY1570: $i] :
( ~ ( rel_s4 @ SV127 @ SY1570 )
| ~ ( v2 @ SY1570 ) ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(595,plain,
! [SV41: $i,SV106: $i,SV80: $i,SV135: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV135 ) )
= $true )
| ( ( ! [SY1574: $i] :
( ~ ( rel_s4 @ SV135 @ SY1574 )
| ~ ( v2 @ SY1574 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(596,plain,
! [SV42: $i,SV107: $i,SV81: $i,SV142: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV142 )
| ! [SY1576: $i] :
( ~ ( rel_s4 @ SV142 @ SY1576 )
| ~ ( v4 @ SY1576 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(597,plain,
! [SV59: $i,SV9: $i,SV89: $i,SV117: $i] :
( ( ( v3 @ SV117 )
= $false )
| ( ( rel_s4 @ SV89 @ SV117 )
= $false )
| ( ( rel_s4 @ SV9 @ SV89 )
= $false )
| ( ( rel_s4 @ SV9 @ SV59 )
= $false )
| ( ( v3 @ SV59 )
= $false )
| ( ( v1 @ SV9 )
= $false )
| ( ( v2 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(598,plain,
! [SV60: $i,SV10: $i,SV90: $i,SV118: $i] :
( ( ( v3 @ SV118 )
= $false )
| ( ( rel_s4 @ SV90 @ SV118 )
= $false )
| ( ( rel_s4 @ SV10 @ SV90 )
= $false )
| ( ( rel_s4 @ SV10 @ SV60 )
= $false )
| ( ( v3 @ SV60 )
= $false )
| ( ( v3 @ SV10 )
= $false )
| ( ( v2 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(599,plain,
! [SV61: $i,SV11: $i,SV91: $i,SV119: $i] :
( ( ( v4 @ SV119 )
= $false )
| ( ( rel_s4 @ SV91 @ SV119 )
= $false )
| ( ( rel_s4 @ SV11 @ SV91 )
= $false )
| ( ( rel_s4 @ SV11 @ SV61 )
= $false )
| ( ( v4 @ SV61 )
= $false )
| ( ( v4 @ SV11 )
= $false )
| ( ( v2 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(600,plain,
! [SV43: $i,SV73: $i,SV12: $i,SV136: $i,SV108: $i] :
( ( ( ~ ( rel_s4 @ SV108 @ SV136 ) )
= $true )
| ( ( ~ ( v3 @ SV136 ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV108 )
= $false )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( v4 @ SV73 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(601,plain,
! [SV83: $i,SV63: $i,SV16: $i,SV143: $i,SV121: $i] :
( ( ( ~ ( rel_s4 @ SV121 @ SV143 )
| ~ ( v4 @ SV143 ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV121 )
= $false )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( v2 @ SV83 )
= $false )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(602,plain,
! [SV44: $i,SV101: $i,SV74: $i,SV128: $i,SV17: $i] :
( ( ( rel_s4 @ SV17 @ SV128 )
= $false )
| ( ( ! [SY1571: $i] :
( ~ ( rel_s4 @ SV128 @ SY1571 )
| ( v3 @ SY1571 ) ) )
= $true )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV74 @ SV101 )
= $false )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(603,plain,
! [SV45: $i,SV84: $i,SV18: $i,SV144: $i,SV122: $i] :
( ( ( ~ ( rel_s4 @ SV122 @ SV144 )
| ~ ( v3 @ SV144 ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV122 )
= $false )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(604,plain,
! [SV46: $i,SV110: $i,SV85: $i,SV137: $i,SV19: $i] :
( ( ( ~ ( rel_s4 @ SV19 @ SV137 ) )
= $true )
| ( ( ! [SY1575: $i] :
( ~ ( rel_s4 @ SV137 @ SY1575 )
| ( v3 @ SY1575 ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV85 @ SV110 )
= $false )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(605,plain,
! [SV67: $i,SV47: $i,SV20: $i,SV129: $i,SV102: $i] :
( ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( ~ ( v3 @ SV129 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(606,plain,
! [SV86: $i,SV65: $i,SV22: $i,SV138: $i,SV111: $i] :
( ( ( ~ ( rel_s4 @ SV111 @ SV138 ) )
= $true )
| ( ( ~ ( v1 @ SV138 ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV111 )
= $false )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(607,plain,
! [SV95: $i,SV68: $i,SV23: $i,SV145: $i,SV124: $i] :
( ( ( ~ ( rel_s4 @ SV124 @ SV145 )
| ( v3 @ SV145 ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV124 )
= $false )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV68 @ SV95 )
= $false )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(608,plain,
! [SV96: $i,SV69: $i,SV24: $i,SV146: $i,SV125: $i] :
( ( ( ~ ( rel_s4 @ SV125 @ SV146 )
| ( v4 @ SV146 ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV125 )
= $false )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV69 @ SV96 )
= $false )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(609,plain,
! [SV97: $i,SV70: $i,SV25: $i,SV147: $i,SV126: $i] :
( ( ( ~ ( rel_s4 @ SV126 @ SV147 )
| ~ ( v2 @ SV147 ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV126 )
= $false )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(610,plain,
! [SV50: $i,SV98: $i,SV130: $i,SV26: $i] :
( ( ( rel_s4 @ SV26 @ SV130 )
= $false )
| ( ( ! [SY1572: $i] :
( ~ ( rel_s4 @ SV130 @ SY1572 )
| ~ ( v1 @ SY1572 ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(611,plain,
! [SV51: $i,SV99: $i,SV131: $i,SV27: $i] :
( ( ( rel_s4 @ SV27 @ SV131 )
= $false )
| ( ( ! [SY1573: $i] :
( ~ ( rel_s4 @ SV131 @ SY1573 )
| ~ ( v3 @ SY1573 ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(612,plain,
! [SV75: $i,SV52: $i,SV28: $i,SV139: $i,SV112: $i] :
( ( ( ~ ( rel_s4 @ SV112 @ SV139 ) )
= $true )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(613,plain,
! [SV53: $i,SV113: $i,SV87: $i,SV148: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV148 )
| ! [SY1577: $i] :
( ~ ( rel_s4 @ SV148 @ SY1577 )
| ~ ( v3 @ SY1577 ) ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( v1 @ SV113 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(614,plain,
! [SV76: $i,SV54: $i,SV30: $i,SV140: $i,SV114: $i] :
( ( ( ~ ( rel_s4 @ SV114 @ SV140 ) )
= $true )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(615,plain,
! [SV77: $i,SV55: $i,SV31: $i,SV141: $i,SV115: $i] :
( ( ( ~ ( rel_s4 @ SV115 @ SV141 ) )
= $true )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(616,plain,
! [SV71: $i,SV48: $i,SV2: $i,SV132: $i,SV103: $i] :
( ( ( rel_s4 @ SV103 @ SV132 )
= $false )
| ( ( ~ ( v2 @ SV132 ) )
= $true )
| ( ( rel_s4 @ SV2 @ SV103 )
= $false )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( v1 @ SV71 )
= $false )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(617,plain,
! [SV78: $i,SV56: $i,SV3: $i,SV133: $i,SV104: $i] :
( ( ( rel_s4 @ SV104 @ SV133 )
= $false )
| ( ( ~ ( v1 @ SV133 ) )
= $true )
| ( ( rel_s4 @ SV3 @ SV104 )
= $false )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(618,plain,
! [SV79: $i,SV58: $i,SV5: $i,SV134: $i,SV105: $i] :
( ( ( rel_s4 @ SV105 @ SV134 )
= $false )
| ( ( ~ ( v3 @ SV134 ) )
= $true )
| ( ( rel_s4 @ SV5 @ SV105 )
= $false )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(619,plain,
! [SV40: $i,SV100: $i,SV72: $i,SV6: $i,SV149: $i,SV127: $i] :
( ( ( ~ ( rel_s4 @ SV127 @ SV149 )
| ~ ( v2 @ SV149 ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV127 )
= $false )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(620,plain,
! [SV41: $i,SV106: $i,SV80: $i,SV135: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV135 )
= $false )
| ( ( ! [SY1574: $i] :
( ~ ( rel_s4 @ SV135 @ SY1574 )
| ~ ( v2 @ SY1574 ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(621,plain,
! [SV42: $i,SV107: $i,SV81: $i,SV142: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV142 ) )
= $true )
| ( ( ! [SY1576: $i] :
( ~ ( rel_s4 @ SV142 @ SY1576 )
| ~ ( v4 @ SY1576 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(622,plain,
! [SV43: $i,SV73: $i,SV12: $i,SV136: $i,SV108: $i] :
( ( ( rel_s4 @ SV108 @ SV136 )
= $false )
| ( ( ~ ( v3 @ SV136 ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV108 )
= $false )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( v4 @ SV73 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(623,plain,
! [SV83: $i,SV63: $i,SV16: $i,SV143: $i,SV121: $i] :
( ( ( ~ ( rel_s4 @ SV121 @ SV143 ) )
= $true )
| ( ( ~ ( v4 @ SV143 ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV121 )
= $false )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( v2 @ SV83 )
= $false )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(624,plain,
! [SV44: $i,SV101: $i,SV74: $i,SV17: $i,SV150: $i,SV128: $i] :
( ( ( ~ ( rel_s4 @ SV128 @ SV150 )
| ( v3 @ SV150 ) )
= $true )
| ( ( rel_s4 @ SV17 @ SV128 )
= $false )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV74 @ SV101 )
= $false )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(625,plain,
! [SV45: $i,SV84: $i,SV18: $i,SV144: $i,SV122: $i] :
( ( ( ~ ( rel_s4 @ SV122 @ SV144 ) )
= $true )
| ( ( ~ ( v3 @ SV144 ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV122 )
= $false )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(626,plain,
! [SV46: $i,SV110: $i,SV85: $i,SV137: $i,SV19: $i] :
( ( ( rel_s4 @ SV19 @ SV137 )
= $false )
| ( ( ! [SY1575: $i] :
( ~ ( rel_s4 @ SV137 @ SY1575 )
| ( v3 @ SY1575 ) ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV85 @ SV110 )
= $false )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(627,plain,
! [SV67: $i,SV47: $i,SV20: $i,SV102: $i,SV129: $i] :
( ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV20 @ SY1470 )
| ! [SY579: $i] :
( ~ ( rel_s4 @ SY1470 @ SY579 )
| ~ ( v4 @ SY579 ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(628,plain,
! [SV86: $i,SV65: $i,SV22: $i,SV138: $i,SV111: $i] :
( ( ( rel_s4 @ SV111 @ SV138 )
= $false )
| ( ( ~ ( v1 @ SV138 ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV111 )
= $false )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(629,plain,
! [SV95: $i,SV68: $i,SV23: $i,SV145: $i,SV124: $i] :
( ( ( ~ ( rel_s4 @ SV124 @ SV145 ) )
= $true )
| ( ( v3 @ SV145 )
= $true )
| ( ( rel_s4 @ SV23 @ SV124 )
= $false )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV68 @ SV95 )
= $false )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(630,plain,
! [SV96: $i,SV69: $i,SV24: $i,SV146: $i,SV125: $i] :
( ( ( ~ ( rel_s4 @ SV125 @ SV146 ) )
= $true )
| ( ( v4 @ SV146 )
= $true )
| ( ( rel_s4 @ SV24 @ SV125 )
= $false )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV69 @ SV96 )
= $false )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(631,plain,
! [SV97: $i,SV70: $i,SV25: $i,SV147: $i,SV126: $i] :
( ( ( ~ ( rel_s4 @ SV126 @ SV147 ) )
= $true )
| ( ( ~ ( v2 @ SV147 ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV126 )
= $false )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(632,plain,
! [SV50: $i,SV98: $i,SV26: $i,SV151: $i,SV130: $i] :
( ( ( ~ ( rel_s4 @ SV130 @ SV151 )
| ~ ( v1 @ SV151 ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV130 )
= $false )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(633,plain,
! [SV51: $i,SV99: $i,SV27: $i,SV152: $i,SV131: $i] :
( ( ( ~ ( rel_s4 @ SV131 @ SV152 )
| ~ ( v3 @ SV152 ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV131 )
= $false )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(634,plain,
! [SV75: $i,SV52: $i,SV28: $i,SV139: $i,SV112: $i] :
( ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( ! [SY1503: $i] :
( ~ ( rel_s4 @ SV28 @ SY1503 )
| ! [SY212: $i] :
( ~ ( rel_s4 @ SY1503 @ SY212 )
| ~ ( v2 @ SY212 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(635,plain,
! [SV53: $i,SV113: $i,SV87: $i,SV148: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV148 ) )
= $true )
| ( ( ! [SY1577: $i] :
( ~ ( rel_s4 @ SV148 @ SY1577 )
| ~ ( v3 @ SY1577 ) ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( v1 @ SV113 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(636,plain,
! [SV76: $i,SV54: $i,SV30: $i,SV140: $i,SV114: $i] :
( ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( ! [SY1514: $i] :
( ~ ( rel_s4 @ SV30 @ SY1514 )
| ! [SY99: $i] :
( ~ ( rel_s4 @ SY1514 @ SY99 )
| ~ ( v3 @ SY99 ) ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(637,plain,
! [SV77: $i,SV55: $i,SV31: $i,SV141: $i,SV115: $i] :
( ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( ! [SY1520: $i] :
( ~ ( rel_s4 @ SV31 @ SY1520 )
| ! [SY39: $i] :
( ~ ( rel_s4 @ SY1520 @ SY39 )
| ~ ( v4 @ SY39 ) ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(638,plain,
! [SV71: $i,SV48: $i,SV2: $i,SV103: $i,SV132: $i] :
( ( ( v2 @ SV132 )
= $false )
| ( ( rel_s4 @ SV103 @ SV132 )
= $false )
| ( ( rel_s4 @ SV2 @ SV103 )
= $false )
| ( ( rel_s4 @ SV2 @ SV48 )
= $false )
| ( ( rel_s4 @ SV48 @ SV71 )
= $false )
| ( ( v1 @ SV71 )
= $false )
| ( ( v3 @ SV2 )
= $true )
| ( ( v1 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(639,plain,
! [SV78: $i,SV56: $i,SV3: $i,SV104: $i,SV133: $i] :
( ( ( v1 @ SV133 )
= $false )
| ( ( rel_s4 @ SV104 @ SV133 )
= $false )
| ( ( rel_s4 @ SV3 @ SV104 )
= $false )
| ( ( rel_s4 @ SV3 @ SV56 )
= $false )
| ( ( v4 @ SV78 )
= $true )
| ( ( rel_s4 @ SV56 @ SV78 )
= $false )
| ( ( v2 @ SV3 )
= $false )
| ( ( v1 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(640,plain,
! [SV79: $i,SV58: $i,SV5: $i,SV105: $i,SV134: $i] :
( ( ( v3 @ SV134 )
= $false )
| ( ( rel_s4 @ SV105 @ SV134 )
= $false )
| ( ( rel_s4 @ SV5 @ SV105 )
= $false )
| ( ( rel_s4 @ SV5 @ SV58 )
= $false )
| ( ( v2 @ SV79 )
= $true )
| ( ( rel_s4 @ SV58 @ SV79 )
= $false )
| ( ( v3 @ SV5 )
= $false )
| ( ( v1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(641,plain,
! [SV40: $i,SV100: $i,SV72: $i,SV6: $i,SV149: $i,SV127: $i] :
( ( ( ~ ( rel_s4 @ SV127 @ SV149 ) )
= $true )
| ( ( ~ ( v2 @ SV149 ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV127 )
= $false )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(642,plain,
! [SV41: $i,SV106: $i,SV80: $i,SV7: $i,SV153: $i,SV135: $i] :
( ( ( ~ ( rel_s4 @ SV135 @ SV153 )
| ~ ( v2 @ SV153 ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV135 )
= $false )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(643,plain,
! [SV42: $i,SV107: $i,SV81: $i,SV142: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV142 )
= $false )
| ( ( ! [SY1576: $i] :
( ~ ( rel_s4 @ SV142 @ SY1576 )
| ~ ( v4 @ SY1576 ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(644,plain,
! [SV43: $i,SV73: $i,SV12: $i,SV108: $i,SV136: $i] :
( ( ( v3 @ SV136 )
= $false )
| ( ( rel_s4 @ SV108 @ SV136 )
= $false )
| ( ( rel_s4 @ SV12 @ SV108 )
= $false )
| ( ( rel_s4 @ SV12 @ SV73 )
= $false )
| ( ( v4 @ SV73 )
= $false )
| ( ( v4 @ SV43 )
= $true )
| ( ( rel_s4 @ SV12 @ SV43 )
= $false )
| ( ( v2 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(645,plain,
! [SV83: $i,SV63: $i,SV16: $i,SV143: $i,SV121: $i] :
( ( ( rel_s4 @ SV121 @ SV143 )
= $false )
| ( ( ~ ( v4 @ SV143 ) )
= $true )
| ( ( rel_s4 @ SV16 @ SV121 )
= $false )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( v2 @ SV83 )
= $false )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(646,plain,
! [SV44: $i,SV101: $i,SV74: $i,SV17: $i,SV150: $i,SV128: $i] :
( ( ( ~ ( rel_s4 @ SV128 @ SV150 ) )
= $true )
| ( ( v3 @ SV150 )
= $true )
| ( ( rel_s4 @ SV17 @ SV128 )
= $false )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV74 @ SV101 )
= $false )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(647,plain,
! [SV45: $i,SV84: $i,SV18: $i,SV144: $i,SV122: $i] :
( ( ( rel_s4 @ SV122 @ SV144 )
= $false )
| ( ( ~ ( v3 @ SV144 ) )
= $true )
| ( ( rel_s4 @ SV18 @ SV122 )
= $false )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(648,plain,
! [SV46: $i,SV110: $i,SV85: $i,SV19: $i,SV154: $i,SV137: $i] :
( ( ( ~ ( rel_s4 @ SV137 @ SV154 )
| ( v3 @ SV154 ) )
= $true )
| ( ( rel_s4 @ SV19 @ SV137 )
= $false )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV85 @ SV110 )
= $false )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(649,plain,
! [SV67: $i,SV47: $i,SV129: $i,SV102: $i,SV155: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV155 )
| ! [SY1578: $i] :
( ~ ( rel_s4 @ SV155 @ SY1578 )
| ~ ( v4 @ SY1578 ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(650,plain,
! [SV86: $i,SV65: $i,SV22: $i,SV111: $i,SV138: $i] :
( ( ( v1 @ SV138 )
= $false )
| ( ( rel_s4 @ SV111 @ SV138 )
= $false )
| ( ( rel_s4 @ SV22 @ SV111 )
= $false )
| ( ( rel_s4 @ SV22 @ SV65 )
= $false )
| ( ( v3 @ SV86 )
= $true )
| ( ( rel_s4 @ SV65 @ SV86 )
= $false )
| ( ( v2 @ SV22 )
= $false )
| ( ( v4 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(651,plain,
! [SV95: $i,SV68: $i,SV23: $i,SV145: $i,SV124: $i] :
( ( ( rel_s4 @ SV124 @ SV145 )
= $false )
| ( ( v3 @ SV145 )
= $true )
| ( ( rel_s4 @ SV23 @ SV124 )
= $false )
| ( ( rel_s4 @ SV23 @ SV68 )
= $false )
| ( ( v2 @ SV95 )
= $true )
| ( ( rel_s4 @ SV68 @ SV95 )
= $false )
| ( ( v3 @ SV23 )
= $false )
| ( ( v1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(652,plain,
! [SV96: $i,SV69: $i,SV24: $i,SV146: $i,SV125: $i] :
( ( ( rel_s4 @ SV125 @ SV146 )
= $false )
| ( ( v4 @ SV146 )
= $true )
| ( ( rel_s4 @ SV24 @ SV125 )
= $false )
| ( ( rel_s4 @ SV24 @ SV69 )
= $false )
| ( ( v1 @ SV96 )
= $true )
| ( ( rel_s4 @ SV69 @ SV96 )
= $false )
| ( ( v4 @ SV24 )
= $false )
| ( ( v1 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(653,plain,
! [SV97: $i,SV70: $i,SV25: $i,SV147: $i,SV126: $i] :
( ( ( rel_s4 @ SV126 @ SV147 )
= $false )
| ( ( ~ ( v2 @ SV147 ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV126 )
= $false )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(654,plain,
! [SV50: $i,SV98: $i,SV26: $i,SV151: $i,SV130: $i] :
( ( ( ~ ( rel_s4 @ SV130 @ SV151 ) )
= $true )
| ( ( ~ ( v1 @ SV151 ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV130 )
= $false )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(655,plain,
! [SV51: $i,SV99: $i,SV27: $i,SV152: $i,SV131: $i] :
( ( ( ~ ( rel_s4 @ SV131 @ SV152 ) )
= $true )
| ( ( ~ ( v3 @ SV152 ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV131 )
= $false )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(656,plain,
! [SV75: $i,SV52: $i,SV139: $i,SV112: $i,SV156: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV156 )
| ! [SY1579: $i] :
( ~ ( rel_s4 @ SV156 @ SY1579 )
| ~ ( v2 @ SY1579 ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(657,plain,
! [SV53: $i,SV113: $i,SV87: $i,SV148: $i,SV29: $i] :
( ( ( rel_s4 @ SV29 @ SV148 )
= $false )
| ( ( ! [SY1577: $i] :
( ~ ( rel_s4 @ SV148 @ SY1577 )
| ~ ( v3 @ SY1577 ) ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( v1 @ SV113 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(658,plain,
! [SV76: $i,SV54: $i,SV140: $i,SV114: $i,SV157: $i,SV30: $i] :
( ( ( ~ ( rel_s4 @ SV30 @ SV157 )
| ! [SY1580: $i] :
( ~ ( rel_s4 @ SV157 @ SY1580 )
| ~ ( v3 @ SY1580 ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(659,plain,
! [SV77: $i,SV55: $i,SV141: $i,SV115: $i,SV158: $i,SV31: $i] :
( ( ( ~ ( rel_s4 @ SV31 @ SV158 )
| ! [SY1581: $i] :
( ~ ( rel_s4 @ SV158 @ SY1581 )
| ~ ( v4 @ SY1581 ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(660,plain,
! [SV40: $i,SV100: $i,SV72: $i,SV6: $i,SV149: $i,SV127: $i] :
( ( ( rel_s4 @ SV127 @ SV149 )
= $false )
| ( ( ~ ( v2 @ SV149 ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV127 )
= $false )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(661,plain,
! [SV41: $i,SV106: $i,SV80: $i,SV7: $i,SV153: $i,SV135: $i] :
( ( ( ~ ( rel_s4 @ SV135 @ SV153 ) )
= $true )
| ( ( ~ ( v2 @ SV153 ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV135 )
= $false )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(662,plain,
! [SV42: $i,SV107: $i,SV81: $i,SV8: $i,SV159: $i,SV142: $i] :
( ( ( ~ ( rel_s4 @ SV142 @ SV159 )
| ~ ( v4 @ SV159 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV142 )
= $false )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(663,plain,
! [SV83: $i,SV63: $i,SV16: $i,SV121: $i,SV143: $i] :
( ( ( v4 @ SV143 )
= $false )
| ( ( rel_s4 @ SV121 @ SV143 )
= $false )
| ( ( rel_s4 @ SV16 @ SV121 )
= $false )
| ( ( rel_s4 @ SV16 @ SV63 )
= $false )
| ( ( rel_s4 @ SV63 @ SV83 )
= $false )
| ( ( v2 @ SV83 )
= $false )
| ( ( v2 @ SV16 )
= $false )
| ( ( v3 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(664,plain,
! [SV44: $i,SV101: $i,SV74: $i,SV17: $i,SV150: $i,SV128: $i] :
( ( ( rel_s4 @ SV128 @ SV150 )
= $false )
| ( ( v3 @ SV150 )
= $true )
| ( ( rel_s4 @ SV17 @ SV128 )
= $false )
| ( ( rel_s4 @ SV17 @ SV74 )
= $false )
| ( ( v2 @ SV101 )
= $true )
| ( ( rel_s4 @ SV74 @ SV101 )
= $false )
| ( ( v4 @ SV44 )
= $true )
| ( ( rel_s4 @ SV17 @ SV44 )
= $false )
| ( ( v3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(665,plain,
! [SV45: $i,SV84: $i,SV18: $i,SV122: $i,SV144: $i] :
( ( ( v3 @ SV144 )
= $false )
| ( ( rel_s4 @ SV122 @ SV144 )
= $false )
| ( ( rel_s4 @ SV18 @ SV122 )
= $false )
| ( ( rel_s4 @ SV18 @ SV84 )
= $false )
| ( ( v3 @ SV84 )
= $false )
| ( ( rel_s4 @ SV18 @ SV45 )
= $false )
| ( ( v2 @ SV45 )
= $false )
| ( ( v3 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(666,plain,
! [SV46: $i,SV110: $i,SV85: $i,SV19: $i,SV154: $i,SV137: $i] :
( ( ( ~ ( rel_s4 @ SV137 @ SV154 ) )
= $true )
| ( ( v3 @ SV154 )
= $true )
| ( ( rel_s4 @ SV19 @ SV137 )
= $false )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV85 @ SV110 )
= $false )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(667,plain,
! [SV67: $i,SV47: $i,SV129: $i,SV102: $i,SV155: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV155 ) )
= $true )
| ( ( ! [SY1578: $i] :
( ~ ( rel_s4 @ SV155 @ SY1578 )
| ~ ( v4 @ SY1578 ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(668,plain,
! [SV97: $i,SV70: $i,SV25: $i,SV126: $i,SV147: $i] :
( ( ( v2 @ SV147 )
= $false )
| ( ( rel_s4 @ SV126 @ SV147 )
= $false )
| ( ( rel_s4 @ SV25 @ SV126 )
= $false )
| ( ( rel_s4 @ SV25 @ SV70 )
= $false )
| ( ( v3 @ SV97 )
= $true )
| ( ( rel_s4 @ SV70 @ SV97 )
= $false )
| ( ( v4 @ SV25 )
= $false )
| ( ( v1 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(669,plain,
! [SV50: $i,SV98: $i,SV26: $i,SV151: $i,SV130: $i] :
( ( ( rel_s4 @ SV130 @ SV151 )
= $false )
| ( ( ~ ( v1 @ SV151 ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV130 )
= $false )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(670,plain,
! [SV51: $i,SV99: $i,SV27: $i,SV152: $i,SV131: $i] :
( ( ( rel_s4 @ SV131 @ SV152 )
= $false )
| ( ( ~ ( v3 @ SV152 ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV131 )
= $false )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(671,plain,
! [SV75: $i,SV52: $i,SV139: $i,SV112: $i,SV156: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV156 ) )
= $true )
| ( ( ! [SY1579: $i] :
( ~ ( rel_s4 @ SV156 @ SY1579 )
| ~ ( v2 @ SY1579 ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(672,plain,
! [SV53: $i,SV113: $i,SV87: $i,SV29: $i,SV160: $i,SV148: $i] :
( ( ( ~ ( rel_s4 @ SV148 @ SV160 )
| ~ ( v3 @ SV160 ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV148 )
= $false )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( v1 @ SV113 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(673,plain,
! [SV76: $i,SV54: $i,SV140: $i,SV114: $i,SV157: $i,SV30: $i] :
( ( ( ~ ( rel_s4 @ SV30 @ SV157 ) )
= $true )
| ( ( ! [SY1580: $i] :
( ~ ( rel_s4 @ SV157 @ SY1580 )
| ~ ( v3 @ SY1580 ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(674,plain,
! [SV77: $i,SV55: $i,SV141: $i,SV115: $i,SV158: $i,SV31: $i] :
( ( ( ~ ( rel_s4 @ SV31 @ SV158 ) )
= $true )
| ( ( ! [SY1581: $i] :
( ~ ( rel_s4 @ SV158 @ SY1581 )
| ~ ( v4 @ SY1581 ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(675,plain,
! [SV40: $i,SV100: $i,SV72: $i,SV6: $i,SV127: $i,SV149: $i] :
( ( ( v2 @ SV149 )
= $false )
| ( ( rel_s4 @ SV127 @ SV149 )
= $false )
| ( ( rel_s4 @ SV6 @ SV127 )
= $false )
| ( ( rel_s4 @ SV6 @ SV72 )
= $false )
| ( ( v4 @ SV100 )
= $true )
| ( ( rel_s4 @ SV72 @ SV100 )
= $false )
| ( ( v1 @ SV40 )
= $true )
| ( ( rel_s4 @ SV6 @ SV40 )
= $false )
| ( ( v1 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(676,plain,
! [SV41: $i,SV106: $i,SV80: $i,SV7: $i,SV153: $i,SV135: $i] :
( ( ( rel_s4 @ SV135 @ SV153 )
= $false )
| ( ( ~ ( v2 @ SV153 ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV135 )
= $false )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(677,plain,
! [SV42: $i,SV107: $i,SV81: $i,SV8: $i,SV159: $i,SV142: $i] :
( ( ( ~ ( rel_s4 @ SV142 @ SV159 ) )
= $true )
| ( ( ~ ( v4 @ SV159 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV142 )
= $false )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(678,plain,
! [SV46: $i,SV110: $i,SV85: $i,SV19: $i,SV154: $i,SV137: $i] :
( ( ( rel_s4 @ SV137 @ SV154 )
= $false )
| ( ( v3 @ SV154 )
= $true )
| ( ( rel_s4 @ SV19 @ SV137 )
= $false )
| ( ( rel_s4 @ SV19 @ SV85 )
= $false )
| ( ( v2 @ SV110 )
= $true )
| ( ( rel_s4 @ SV85 @ SV110 )
= $false )
| ( ( rel_s4 @ SV19 @ SV46 )
= $false )
| ( ( v3 @ SV46 )
= $false )
| ( ( v3 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(679,plain,
! [SV67: $i,SV47: $i,SV129: $i,SV102: $i,SV155: $i,SV20: $i] :
( ( ( rel_s4 @ SV20 @ SV155 )
= $false )
| ( ( ! [SY1578: $i] :
( ~ ( rel_s4 @ SV155 @ SY1578 )
| ~ ( v4 @ SY1578 ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(680,plain,
! [SV50: $i,SV98: $i,SV26: $i,SV130: $i,SV151: $i] :
( ( ( v1 @ SV151 )
= $false )
| ( ( rel_s4 @ SV130 @ SV151 )
= $false )
| ( ( rel_s4 @ SV26 @ SV130 )
= $false )
| ( ( rel_s4 @ SV26 @ SV98 )
= $false )
| ( ( v3 @ SV98 )
= $false )
| ( ( rel_s4 @ SV26 @ SV50 )
= $false )
| ( ( v1 @ SV50 )
= $false )
| ( ( v1 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(681,plain,
! [SV51: $i,SV99: $i,SV27: $i,SV131: $i,SV152: $i] :
( ( ( v3 @ SV152 )
= $false )
| ( ( rel_s4 @ SV131 @ SV152 )
= $false )
| ( ( rel_s4 @ SV27 @ SV131 )
= $false )
| ( ( rel_s4 @ SV27 @ SV99 )
= $false )
| ( ( v4 @ SV99 )
= $false )
| ( ( rel_s4 @ SV27 @ SV51 )
= $false )
| ( ( v2 @ SV51 )
= $false )
| ( ( v3 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(682,plain,
! [SV75: $i,SV52: $i,SV139: $i,SV112: $i,SV156: $i,SV28: $i] :
( ( ( rel_s4 @ SV28 @ SV156 )
= $false )
| ( ( ! [SY1579: $i] :
( ~ ( rel_s4 @ SV156 @ SY1579 )
| ~ ( v2 @ SY1579 ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(683,plain,
! [SV53: $i,SV113: $i,SV87: $i,SV29: $i,SV160: $i,SV148: $i] :
( ( ( ~ ( rel_s4 @ SV148 @ SV160 ) )
= $true )
| ( ( ~ ( v3 @ SV160 ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV148 )
= $false )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( v1 @ SV113 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(684,plain,
! [SV76: $i,SV54: $i,SV140: $i,SV114: $i,SV157: $i,SV30: $i] :
( ( ( rel_s4 @ SV30 @ SV157 )
= $false )
| ( ( ! [SY1580: $i] :
( ~ ( rel_s4 @ SV157 @ SY1580 )
| ~ ( v3 @ SY1580 ) ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(685,plain,
! [SV77: $i,SV55: $i,SV141: $i,SV115: $i,SV158: $i,SV31: $i] :
( ( ( rel_s4 @ SV31 @ SV158 )
= $false )
| ( ( ! [SY1581: $i] :
( ~ ( rel_s4 @ SV158 @ SY1581 )
| ~ ( v4 @ SY1581 ) ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(686,plain,
! [SV41: $i,SV106: $i,SV80: $i,SV7: $i,SV135: $i,SV153: $i] :
( ( ( v2 @ SV153 )
= $false )
| ( ( rel_s4 @ SV135 @ SV153 )
= $false )
| ( ( rel_s4 @ SV7 @ SV135 )
= $false )
| ( ( rel_s4 @ SV7 @ SV80 )
= $false )
| ( ( v2 @ SV106 )
= $true )
| ( ( rel_s4 @ SV80 @ SV106 )
= $false )
| ( ( rel_s4 @ SV7 @ SV41 )
= $false )
| ( ( v2 @ SV41 )
= $false )
| ( ( v1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(687,plain,
! [SV42: $i,SV107: $i,SV81: $i,SV8: $i,SV159: $i,SV142: $i] :
( ( ( rel_s4 @ SV142 @ SV159 )
= $false )
| ( ( ~ ( v4 @ SV159 ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV142 )
= $false )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(688,plain,
! [SV67: $i,SV47: $i,SV129: $i,SV102: $i,SV20: $i,SV161: $i,SV155: $i] :
( ( ( ~ ( rel_s4 @ SV155 @ SV161 )
| ~ ( v4 @ SV161 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV155 )
= $false )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(689,plain,
! [SV75: $i,SV52: $i,SV139: $i,SV112: $i,SV28: $i,SV162: $i,SV156: $i] :
( ( ( ~ ( rel_s4 @ SV156 @ SV162 )
| ~ ( v2 @ SV162 ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV156 )
= $false )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(690,plain,
! [SV53: $i,SV113: $i,SV87: $i,SV29: $i,SV160: $i,SV148: $i] :
( ( ( rel_s4 @ SV148 @ SV160 )
= $false )
| ( ( ~ ( v3 @ SV160 ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV148 )
= $false )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( v1 @ SV113 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(691,plain,
! [SV76: $i,SV54: $i,SV140: $i,SV114: $i,SV30: $i,SV163: $i,SV157: $i] :
( ( ( ~ ( rel_s4 @ SV157 @ SV163 )
| ~ ( v3 @ SV163 ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV157 )
= $false )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(692,plain,
! [SV77: $i,SV55: $i,SV141: $i,SV115: $i,SV31: $i,SV164: $i,SV158: $i] :
( ( ( ~ ( rel_s4 @ SV158 @ SV164 )
| ~ ( v4 @ SV164 ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV158 )
= $false )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(693,plain,
! [SV42: $i,SV107: $i,SV81: $i,SV8: $i,SV142: $i,SV159: $i] :
( ( ( v4 @ SV159 )
= $false )
| ( ( rel_s4 @ SV142 @ SV159 )
= $false )
| ( ( rel_s4 @ SV8 @ SV142 )
= $false )
| ( ( rel_s4 @ SV8 @ SV81 )
= $false )
| ( ( rel_s4 @ SV81 @ SV107 )
= $false )
| ( ( v1 @ SV107 )
= $false )
| ( ( rel_s4 @ SV8 @ SV42 )
= $false )
| ( ( v3 @ SV42 )
= $false )
| ( ( v1 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(694,plain,
! [SV67: $i,SV47: $i,SV129: $i,SV102: $i,SV20: $i,SV161: $i,SV155: $i] :
( ( ( ~ ( rel_s4 @ SV155 @ SV161 ) )
= $true )
| ( ( ~ ( v4 @ SV161 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV155 )
= $false )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(695,plain,
! [SV75: $i,SV52: $i,SV139: $i,SV112: $i,SV28: $i,SV162: $i,SV156: $i] :
( ( ( ~ ( rel_s4 @ SV156 @ SV162 ) )
= $true )
| ( ( ~ ( v2 @ SV162 ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV156 )
= $false )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(696,plain,
! [SV53: $i,SV113: $i,SV87: $i,SV29: $i,SV148: $i,SV160: $i] :
( ( ( v3 @ SV160 )
= $false )
| ( ( rel_s4 @ SV148 @ SV160 )
= $false )
| ( ( rel_s4 @ SV29 @ SV148 )
= $false )
| ( ( rel_s4 @ SV29 @ SV87 )
= $false )
| ( ( rel_s4 @ SV87 @ SV113 )
= $false )
| ( ( v1 @ SV113 )
= $false )
| ( ( v3 @ SV53 )
= $true )
| ( ( rel_s4 @ SV29 @ SV53 )
= $false )
| ( ( v4 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(697,plain,
! [SV76: $i,SV54: $i,SV140: $i,SV114: $i,SV30: $i,SV163: $i,SV157: $i] :
( ( ( ~ ( rel_s4 @ SV157 @ SV163 ) )
= $true )
| ( ( ~ ( v3 @ SV163 ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV157 )
= $false )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(698,plain,
! [SV77: $i,SV55: $i,SV141: $i,SV115: $i,SV31: $i,SV164: $i,SV158: $i] :
( ( ( ~ ( rel_s4 @ SV158 @ SV164 ) )
= $true )
| ( ( ~ ( v4 @ SV164 ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV158 )
= $false )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(699,plain,
! [SV67: $i,SV47: $i,SV129: $i,SV102: $i,SV20: $i,SV161: $i,SV155: $i] :
( ( ( rel_s4 @ SV155 @ SV161 )
= $false )
| ( ( ~ ( v4 @ SV161 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV155 )
= $false )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(700,plain,
! [SV75: $i,SV52: $i,SV139: $i,SV112: $i,SV28: $i,SV162: $i,SV156: $i] :
( ( ( rel_s4 @ SV156 @ SV162 )
= $false )
| ( ( ~ ( v2 @ SV162 ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV156 )
= $false )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(701,plain,
! [SV76: $i,SV54: $i,SV140: $i,SV114: $i,SV30: $i,SV163: $i,SV157: $i] :
( ( ( rel_s4 @ SV157 @ SV163 )
= $false )
| ( ( ~ ( v3 @ SV163 ) )
= $true )
| ( ( rel_s4 @ SV30 @ SV157 )
= $false )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(702,plain,
! [SV77: $i,SV55: $i,SV141: $i,SV115: $i,SV31: $i,SV164: $i,SV158: $i] :
( ( ( rel_s4 @ SV158 @ SV164 )
= $false )
| ( ( ~ ( v4 @ SV164 ) )
= $true )
| ( ( rel_s4 @ SV31 @ SV158 )
= $false )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(703,plain,
! [SV67: $i,SV47: $i,SV129: $i,SV102: $i,SV20: $i,SV155: $i,SV161: $i] :
( ( ( v4 @ SV161 )
= $false )
| ( ( rel_s4 @ SV155 @ SV161 )
= $false )
| ( ( rel_s4 @ SV20 @ SV155 )
= $false )
| ( ( rel_s4 @ SV20 @ SV102 )
= $false )
| ( ( rel_s4 @ SV102 @ SV129 )
= $false )
| ( ( v3 @ SV129 )
= $false )
| ( ( rel_s4 @ SV20 @ SV47 )
= $false )
| ( ( v3 @ SV67 )
= $true )
| ( ( rel_s4 @ SV47 @ SV67 )
= $false )
| ( ( v3 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(704,plain,
! [SV75: $i,SV52: $i,SV139: $i,SV112: $i,SV28: $i,SV156: $i,SV162: $i] :
( ( ( v2 @ SV162 )
= $false )
| ( ( rel_s4 @ SV156 @ SV162 )
= $false )
| ( ( rel_s4 @ SV28 @ SV156 )
= $false )
| ( ( rel_s4 @ SV28 @ SV112 )
= $false )
| ( ( v4 @ SV139 )
= $true )
| ( ( rel_s4 @ SV112 @ SV139 )
= $false )
| ( ( rel_s4 @ SV28 @ SV52 )
= $false )
| ( ( v2 @ SV75 )
= $true )
| ( ( rel_s4 @ SV52 @ SV75 )
= $false )
| ( ( v3 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(705,plain,
! [SV76: $i,SV54: $i,SV140: $i,SV114: $i,SV30: $i,SV157: $i,SV163: $i] :
( ( ( v3 @ SV163 )
= $false )
| ( ( rel_s4 @ SV157 @ SV163 )
= $false )
| ( ( rel_s4 @ SV30 @ SV157 )
= $false )
| ( ( rel_s4 @ SV30 @ SV114 )
= $false )
| ( ( v3 @ SV140 )
= $true )
| ( ( rel_s4 @ SV114 @ SV140 )
= $false )
| ( ( rel_s4 @ SV30 @ SV54 )
= $false )
| ( ( v1 @ SV76 )
= $true )
| ( ( rel_s4 @ SV54 @ SV76 )
= $false )
| ( ( v4 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(706,plain,
! [SV77: $i,SV55: $i,SV141: $i,SV115: $i,SV31: $i,SV158: $i,SV164: $i] :
( ( ( v4 @ SV164 )
= $false )
| ( ( rel_s4 @ SV158 @ SV164 )
= $false )
| ( ( rel_s4 @ SV31 @ SV158 )
= $false )
| ( ( rel_s4 @ SV31 @ SV115 )
= $false )
| ( ( v3 @ SV141 )
= $true )
| ( ( rel_s4 @ SV115 @ SV141 )
= $false )
| ( ( rel_s4 @ SV31 @ SV55 )
= $false )
| ( ( v2 @ SV77 )
= $true )
| ( ( rel_s4 @ SV55 @ SV77 )
= $false )
| ( ( v4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(707,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[111,706,705,704,703,696,693,686,681,680,678,675,668,665,664,663,652,651,650,644,640,639,638,599,598,597,580,574,565,545,487,414,413,284,283,250,115]) ).
thf(708,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.15 % Computer : n018.cluster.edu
% 0.12/0.15 % Model : x86_64 x86_64
% 0.12/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.15 % Memory : 8046.5625MB
% 0.12/0.15 % OS : Linux 6.8.0-71-generic
% 0.12/0.15 % CPULimit : 300
% 0.12/0.15 % WCLimit : 300
% 0.12/0.15 % DateTime : Tue Oct 6 17:29:37 UTC 2026
% 0.12/0.15 % CPUTime :
% 0.12/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.64/3.66
% 20.64/3.66 No.of.Axioms: 35
% 20.64/3.66
% 20.64/3.66 Length.of.Defs: 5540
% 20.64/3.66
% 20.64/3.66 Contains.Choice.Funs: false
% 20.64/3.66 ....................................
% 20.64/3.66
% 20.64/3.66 ********************************
% 20.64/3.66 * All subproblems solved! *
% 20.64/3.66 ********************************
% 20.64/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:707,loop_count:0,foatp_calls:1,translation:fof_full)
% 20.64/3.66
% 20.64/3.66 %**** Beginning of derivation protocol ****
% 20.64/3.66 % SZS output start CNFRefutation
% See solution above
% 20.64/3.67
% 20.64/3.67 %**** End of derivation protocol ****
% 20.64/3.67 %**** no. of clauses in derivation: 708 ****
% 20.64/3.67 %**** clause counter: 707 ****
% 20.64/3.67
% 20.64/3.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:35,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:707,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------