%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET925^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:42:34 AM UTC 2026
% Result : Theorem 5.97s 1.22s
% Output : CNFRefutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 48
% Syntax : Number of formulae : 627 ( 151 unt; 0 typ; 32 def)
% Number of atoms : 12031 (3127 equ; 0 cnn)
% Maximal formula atoms : 18 ( 19 avg)
% Number of connectives : 30636 (3890 ~;4898 |; 64 &;21739 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 66 usr; 13 con; 0-8 aty)
% Number of variables : 4175 ( 79 ^;4090 !; 6 ?;4175 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_empty,type,
empty: mu > $i > $o ).
thf(tp_empty_set,type,
empty_set: mu ).
thf(tp_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(tp_in,type,
in: mu > mu > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox_s4,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(tp_mcountersatisfiable,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(tp_mdia,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia_s4,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(tp_meq_prop,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meuclidean,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfunctional,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mpartially_functional,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(tp_mreflexive,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(tp_msatisfiable,type,
msatisfiable: ( $i > $o ) > $o ).
thf(tp_mserial,type,
mserial: ( $i > $i > $o ) > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtransitive,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mweakly_connected,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_dense,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(tp_mweakly_directed,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(tp_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(tp_sK10_REN,type,
sK10_REN: $o ).
thf(tp_sK11_SY241,type,
sK11_SY241: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK12_SY238,type,
sK12_SY238: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK13_SY344,type,
sK13_SY344: $i > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK14_SY342,type,
sK14_SY342: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK15_SY472,type,
sK15_SY472: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK16_SY471,type,
sK16_SY471: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK17_SY609,type,
sK17_SY609: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK18_SY608,type,
sK18_SY608: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK19_SY719,type,
sK19_SY719: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK1_SY120,type,
sK1_SY120: $i ).
thf(tp_sK20_SY718,type,
sK20_SY718: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK21_SY796,type,
sK21_SY796: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK22_SY893,type,
sK22_SY893: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK23_SY998,type,
sK23_SY998: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK24_SY1105,type,
sK24_SY1105: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK25_SY1130,type,
sK25_SY1130: $i > mu > $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK26_SY1216,type,
sK26_SY1216: $i > mu > $i > mu > $i > $i > $i ).
thf(tp_sK2_SY1273,type,
sK2_SY1273: $i ).
thf(tp_sK3_SY1283,type,
sK3_SY1283: mu ).
thf(tp_sK4_SY1292,type,
sK4_SY1292: $i ).
thf(tp_sK5_SY1300,type,
sK5_SY1300: mu ).
thf(tp_sK6_SY1310,type,
sK6_SY1310: $i ).
thf(tp_sK7_SY1314,type,
sK7_SY1314: $i ).
thf(tp_sK8_SY1307,type,
sK8_SY1307: $i ).
thf(tp_sK9_SY1316,type,
sK9_SY1316: $i ).
thf(tp_set_difference,type,
set_difference: mu > mu > mu ).
thf(tp_singleton,type,
singleton: mu > mu ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(4,axiom,
mvalid @ ( mbox_s4 @ ( empty @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(5,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( in @ B @ A ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(6,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( in @ C @ A ) ) ) @ ( mbox_s4 @ ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_2) ).
thf(7,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( in @ A @ C ) ) ) @ ( mbox_s4 @ ( in @ B @ C ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_1) ).
thf(8,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( empty @ A ) ) ) @ ( mbox_s4 @ ( empty @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_substitution_1) ).
thf(9,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(10,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_substitution_2) ).
thf(11,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_substitution_1) ).
thf(12,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(13,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(14,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(15,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_set_difference_ax) ).
thf(16,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_singleton_ax) ).
thf(17,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(22,conjecture,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(23,negated_conjecture,
( ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) @ ( mbox_s4 @ ( in @ A @ B ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( in @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,plain,
( ( ! [SY120: $i,SY121: $i] :
( ~ ( rel_s4 @ SY120 @ SY121 )
| ! [SY111: mu] :
( ( exists_in_world @ SY111 @ SY121 )
=> ! [SY112: $i] :
( ~ ( rel_s4 @ SY121 @ SY112 )
| ! [SY94: mu] :
( ( exists_in_world @ SY94 @ SY112 )
=> ~ ( ~ ! [SY95: $i] :
( ~ ( rel_s4 @ SY112 @ SY95 )
| ~ ! [SY96: $i] :
( ~ ( rel_s4 @ SY95 @ SY96 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY111 ) @ SY94 ) @ empty_set @ SY96 ) )
| ! [SY97: $i] :
( ~ ( rel_s4 @ SY95 @ SY97 )
| ( in @ SY111 @ SY94 @ SY97 ) ) )
| ~ ! [SY98: $i] :
( ~ ( rel_s4 @ SY112 @ SY98 )
| ~ ! [SY99: $i] :
( ~ ( rel_s4 @ SY98 @ SY99 )
| ( in @ SY111 @ SY94 @ SY99 ) )
| ! [SY100: $i] :
( ~ ( rel_s4 @ SY98 @ SY100 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY111 ) @ SY94 ) @ empty_set @ SY100 ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[23,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(25,plain,
( ( ! [SY262: $i,SY263: $i] :
( ~ ( rel_s4 @ SY262 @ SY263 )
| ! [SY253: mu] :
( ( exists_in_world @ SY253 @ SY263 )
=> ! [SY254: $i] :
( ~ ( rel_s4 @ SY263 @ SY254 )
| ! [SY236: mu] :
( ( exists_in_world @ SY236 @ SY254 )
=> ~ ( ~ ! [SY237: $i] :
( ~ ( rel_s4 @ SY254 @ SY237 )
| ~ ! [SY238: $i] :
( ~ ( rel_s4 @ SY237 @ SY238 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY253 ) @ SY236 ) @ empty_set @ SY238 ) )
| ! [SY239: $i] :
( ~ ( rel_s4 @ SY237 @ SY239 )
| ( in @ SY253 @ SY236 @ SY239 ) ) )
| ~ ! [SY240: $i] :
( ~ ( rel_s4 @ SY254 @ SY240 )
| ~ ! [SY241: $i] :
( ~ ( rel_s4 @ SY240 @ SY241 )
| ( in @ SY253 @ SY236 @ SY241 ) )
| ! [SY242: $i] :
( ~ ( rel_s4 @ SY240 @ SY242 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY253 ) @ SY236 ) @ empty_set @ SY242 ) ) ) ) ) ) ) ) )
= $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(26,plain,
( ( ! [SY286: $i,SY287: $i] :
( ~ ( rel_s4 @ SY286 @ SY287 )
| ( empty @ empty_set @ SY287 ) ) )
= $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(27,plain,
( ( ! [SY360: $i,SY361: $i] :
( ~ ( rel_s4 @ SY360 @ SY361 )
| ! [SY353: mu] :
( ( exists_in_world @ SY353 @ SY361 )
=> ! [SY354: $i] :
( ~ ( rel_s4 @ SY361 @ SY354 )
| ! [SY340: mu] :
( ( exists_in_world @ SY340 @ SY354 )
=> ! [SY341: $i] :
( ~ ( rel_s4 @ SY354 @ SY341 )
| ~ ! [SY342: $i] :
( ~ ( rel_s4 @ SY341 @ SY342 )
| ( in @ SY353 @ SY340 @ SY342 ) )
| ! [SY343: $i] :
( ~ ( rel_s4 @ SY341 @ SY343 )
| ~ ! [SY344: $i] :
( ~ ( rel_s4 @ SY343 @ SY344 )
| ( in @ SY340 @ SY353 @ SY344 ) ) ) ) ) ) ) ) )
= $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(28,plain,
( ( ! [SY493: $i,SY494: $i] :
( ~ ( rel_s4 @ SY493 @ SY494 )
| ! [SY484: mu] :
( ( exists_in_world @ SY484 @ SY494 )
=> ! [SY485: $i] :
( ~ ( rel_s4 @ SY494 @ SY485 )
| ! [SY467: mu] :
( ( exists_in_world @ SY467 @ SY485 )
=> ! [SY468: $i] :
( ~ ( rel_s4 @ SY485 @ SY468 )
| ! [SY469: mu] :
( ( exists_in_world @ SY469 @ SY468 )
=> ! [SY470: $i] :
( ~ ( rel_s4 @ SY468 @ SY470 )
| ~ ~ ( ~ ! [SY471: $i] :
( ~ ( rel_s4 @ SY470 @ SY471 )
| ( qmltpeq @ SY484 @ SY467 @ SY471 ) )
| ~ ! [SY472: $i] :
( ~ ( rel_s4 @ SY470 @ SY472 )
| ( in @ SY469 @ SY484 @ SY472 ) ) )
| ! [SY447: $i] :
( ~ ( rel_s4 @ SY470 @ SY447 )
| ( in @ SY469 @ SY467 @ SY447 ) ) ) ) ) ) ) ) ) )
= $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(29,plain,
( ( ! [SY630: $i,SY631: $i] :
( ~ ( rel_s4 @ SY630 @ SY631 )
| ! [SY621: mu] :
( ( exists_in_world @ SY621 @ SY631 )
=> ! [SY622: $i] :
( ~ ( rel_s4 @ SY631 @ SY622 )
| ! [SY604: mu] :
( ( exists_in_world @ SY604 @ SY622 )
=> ! [SY605: $i] :
( ~ ( rel_s4 @ SY622 @ SY605 )
| ! [SY606: mu] :
( ( exists_in_world @ SY606 @ SY605 )
=> ! [SY607: $i] :
( ~ ( rel_s4 @ SY605 @ SY607 )
| ~ ~ ( ~ ! [SY608: $i] :
( ~ ( rel_s4 @ SY607 @ SY608 )
| ( qmltpeq @ SY621 @ SY604 @ SY608 ) )
| ~ ! [SY609: $i] :
( ~ ( rel_s4 @ SY607 @ SY609 )
| ( in @ SY621 @ SY606 @ SY609 ) ) )
| ! [SY584: $i] :
( ~ ( rel_s4 @ SY607 @ SY584 )
| ( in @ SY604 @ SY606 @ SY584 ) ) ) ) ) ) ) ) ) )
= $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(30,plain,
( ( ! [SY736: $i,SY737: $i] :
( ~ ( rel_s4 @ SY736 @ SY737 )
| ! [SY729: mu] :
( ( exists_in_world @ SY729 @ SY737 )
=> ! [SY730: $i] :
( ~ ( rel_s4 @ SY737 @ SY730 )
| ! [SY716: mu] :
( ( exists_in_world @ SY716 @ SY730 )
=> ! [SY717: $i] :
( ~ ( rel_s4 @ SY730 @ SY717 )
| ~ ~ ( ~ ! [SY718: $i] :
( ~ ( rel_s4 @ SY717 @ SY718 )
| ( qmltpeq @ SY729 @ SY716 @ SY718 ) )
| ~ ! [SY719: $i] :
( ~ ( rel_s4 @ SY717 @ SY719 )
| ( empty @ SY729 @ SY719 ) ) )
| ! [SY700: $i] :
( ~ ( rel_s4 @ SY717 @ SY700 )
| ( empty @ SY716 @ SY700 ) ) ) ) ) ) ) )
= $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(31,plain,
( ( ! [SY811: $i,SY812: $i] :
( ~ ( rel_s4 @ SY811 @ SY812 )
| ! [SY805: mu] :
( ( exists_in_world @ SY805 @ SY812 )
=> ! [SY806: $i] :
( ~ ( rel_s4 @ SY812 @ SY806 )
| ! [SY794: mu] :
( ( exists_in_world @ SY794 @ SY806 )
=> ! [SY795: $i] :
( ~ ( rel_s4 @ SY806 @ SY795 )
| ~ ! [SY796: $i] :
( ~ ( rel_s4 @ SY795 @ SY796 )
| ( qmltpeq @ SY805 @ SY794 @ SY796 ) )
| ! [SY797: $i] :
( ~ ( rel_s4 @ SY795 @ SY797 )
| ( qmltpeq @ ( singleton @ SY805 ) @ ( singleton @ SY794 ) @ SY797 ) ) ) ) ) ) ) )
= $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(32,plain,
( ( ! [SY912: $i,SY913: $i] :
( ~ ( rel_s4 @ SY912 @ SY913 )
| ! [SY904: mu] :
( ( exists_in_world @ SY904 @ SY913 )
=> ! [SY905: $i] :
( ~ ( rel_s4 @ SY913 @ SY905 )
| ! [SY889: mu] :
( ( exists_in_world @ SY889 @ SY905 )
=> ! [SY890: $i] :
( ~ ( rel_s4 @ SY905 @ SY890 )
| ! [SY891: mu] :
( ( exists_in_world @ SY891 @ SY890 )
=> ! [SY892: $i] :
( ~ ( rel_s4 @ SY890 @ SY892 )
| ~ ! [SY893: $i] :
( ~ ( rel_s4 @ SY892 @ SY893 )
| ( qmltpeq @ SY904 @ SY889 @ SY893 ) )
| ! [SY894: $i] :
( ~ ( rel_s4 @ SY892 @ SY894 )
| ( qmltpeq @ ( set_difference @ SY891 @ SY904 ) @ ( set_difference @ SY891 @ SY889 ) @ SY894 ) ) ) ) ) ) ) ) ) )
= $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(33,plain,
( ( ! [SY1017: $i,SY1018: $i] :
( ~ ( rel_s4 @ SY1017 @ SY1018 )
| ! [SY1009: mu] :
( ( exists_in_world @ SY1009 @ SY1018 )
=> ! [SY1010: $i] :
( ~ ( rel_s4 @ SY1018 @ SY1010 )
| ! [SY994: mu] :
( ( exists_in_world @ SY994 @ SY1010 )
=> ! [SY995: $i] :
( ~ ( rel_s4 @ SY1010 @ SY995 )
| ! [SY996: mu] :
( ( exists_in_world @ SY996 @ SY995 )
=> ! [SY997: $i] :
( ~ ( rel_s4 @ SY995 @ SY997 )
| ~ ! [SY998: $i] :
( ~ ( rel_s4 @ SY997 @ SY998 )
| ( qmltpeq @ SY1009 @ SY994 @ SY998 ) )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY997 @ SY999 )
| ( qmltpeq @ ( set_difference @ SY1009 @ SY996 ) @ ( set_difference @ SY994 @ SY996 ) @ SY999 ) ) ) ) ) ) ) ) ) )
= $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(34,plain,
( ( ! [SY1152: $i,SY1153: $i] :
( ~ ( rel_s4 @ SY1152 @ SY1153 )
| ! [SY1143: mu] :
( ( exists_in_world @ SY1143 @ SY1153 )
=> ! [SY1144: $i] :
( ~ ( rel_s4 @ SY1153 @ SY1144 )
| ! [SY1126: mu] :
( ( exists_in_world @ SY1126 @ SY1144 )
=> ! [SY1127: $i] :
( ~ ( rel_s4 @ SY1144 @ SY1127 )
| ! [SY1128: mu] :
( ( exists_in_world @ SY1128 @ SY1127 )
=> ! [SY1129: $i] :
( ~ ( rel_s4 @ SY1127 @ SY1129 )
| ~ ~ ( ~ ! [SY1130: $i] :
( ~ ( rel_s4 @ SY1129 @ SY1130 )
| ( qmltpeq @ SY1143 @ SY1126 @ SY1130 ) )
| ~ ! [SY1105: $i] :
( ~ ( rel_s4 @ SY1129 @ SY1105 )
| ( qmltpeq @ SY1126 @ SY1128 @ SY1105 ) ) )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1129 @ SY1132 )
| ( qmltpeq @ SY1143 @ SY1128 @ SY1132 ) ) ) ) ) ) ) ) ) )
= $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(35,plain,
( ( ! [SY1231: $i,SY1232: $i] :
( ~ ( rel_s4 @ SY1231 @ SY1232 )
| ! [SY1225: mu] :
( ( exists_in_world @ SY1225 @ SY1232 )
=> ! [SY1226: $i] :
( ~ ( rel_s4 @ SY1232 @ SY1226 )
| ! [SY1214: mu] :
( ( exists_in_world @ SY1214 @ SY1226 )
=> ! [SY1215: $i] :
( ~ ( rel_s4 @ SY1226 @ SY1215 )
| ~ ! [SY1216: $i] :
( ~ ( rel_s4 @ SY1215 @ SY1216 )
| ( qmltpeq @ SY1225 @ SY1214 @ SY1216 ) )
| ! [SY1217: $i] :
( ~ ( rel_s4 @ SY1215 @ SY1217 )
| ( qmltpeq @ SY1214 @ SY1225 @ SY1217 ) ) ) ) ) ) ) )
= $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(36,plain,
( ( ! [SY1259: $i,SY1260: $i] :
( ~ ( rel_s4 @ SY1259 @ SY1260 )
| ! [SY1257: mu] :
( ( exists_in_world @ SY1257 @ SY1260 )
=> ! [SY1258: $i] :
( ~ ( rel_s4 @ SY1260 @ SY1258 )
| ( qmltpeq @ SY1257 @ SY1257 @ SY1258 ) ) ) ) )
= $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(37,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ) )
= $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(38,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) )
= $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(39,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $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(40,plain,
( ( ! [SY1273: $i] :
( ~ ( rel_s4 @ sK1_SY120 @ SY1273 )
| ! [SY111: mu] :
( ( exists_in_world @ SY111 @ SY1273 )
=> ! [SY112: $i] :
( ~ ( rel_s4 @ SY1273 @ SY112 )
| ! [SY94: mu] :
( ( exists_in_world @ SY94 @ SY112 )
=> ~ ( ~ ! [SY95: $i] :
( ~ ( rel_s4 @ SY112 @ SY95 )
| ~ ! [SY96: $i] :
( ~ ( rel_s4 @ SY95 @ SY96 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY111 ) @ SY94 ) @ empty_set @ SY96 ) )
| ! [SY97: $i] :
( ~ ( rel_s4 @ SY95 @ SY97 )
| ( in @ SY111 @ SY94 @ SY97 ) ) )
| ~ ! [SY98: $i] :
( ~ ( rel_s4 @ SY112 @ SY98 )
| ~ ! [SY99: $i] :
( ~ ( rel_s4 @ SY98 @ SY99 )
| ( in @ SY111 @ SY94 @ SY99 ) )
| ! [SY100: $i] :
( ~ ( rel_s4 @ SY98 @ SY100 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY111 ) @ SY94 ) @ empty_set @ SY100 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(41,plain,
( ( ~ ( rel_s4 @ sK1_SY120 @ sK2_SY1273 )
| ! [SY1283: mu] :
( ( exists_in_world @ SY1283 @ sK2_SY1273 )
=> ! [SY1284: $i] :
( ~ ( rel_s4 @ sK2_SY1273 @ SY1284 )
| ! [SY94: mu] :
( ( exists_in_world @ SY94 @ SY1284 )
=> ~ ( ~ ! [SY95: $i] :
( ~ ( rel_s4 @ SY1284 @ SY95 )
| ~ ! [SY96: $i] :
( ~ ( rel_s4 @ SY95 @ SY96 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1283 ) @ SY94 ) @ empty_set @ SY96 ) )
| ! [SY97: $i] :
( ~ ( rel_s4 @ SY95 @ SY97 )
| ( in @ SY1283 @ SY94 @ SY97 ) ) )
| ~ ! [SY98: $i] :
( ~ ( rel_s4 @ SY1284 @ SY98 )
| ~ ! [SY99: $i] :
( ~ ( rel_s4 @ SY98 @ SY99 )
| ( in @ SY1283 @ SY94 @ SY99 ) )
| ! [SY100: $i] :
( ~ ( rel_s4 @ SY98 @ SY100 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1283 ) @ SY94 ) @ empty_set @ SY100 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(42,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY120 @ sK2_SY1273 )
| ! [SY1283: mu] :
( ( exists_in_world @ SY1283 @ sK2_SY1273 )
=> ! [SY1284: $i] :
( ~ ( rel_s4 @ sK2_SY1273 @ SY1284 )
| ! [SY94: mu] :
( ( exists_in_world @ SY94 @ SY1284 )
=> ~ ( ~ ! [SY95: $i] :
( ~ ( rel_s4 @ SY1284 @ SY95 )
| ~ ! [SY96: $i] :
( ~ ( rel_s4 @ SY95 @ SY96 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1283 ) @ SY94 ) @ empty_set @ SY96 ) )
| ! [SY97: $i] :
( ~ ( rel_s4 @ SY95 @ SY97 )
| ( in @ SY1283 @ SY94 @ SY97 ) ) )
| ~ ! [SY98: $i] :
( ~ ( rel_s4 @ SY1284 @ SY98 )
| ~ ! [SY99: $i] :
( ~ ( rel_s4 @ SY98 @ SY99 )
| ( in @ SY1283 @ SY94 @ SY99 ) )
| ! [SY100: $i] :
( ~ ( rel_s4 @ SY98 @ SY100 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1283 ) @ SY94 ) @ empty_set @ SY100 ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(43,plain,
( ( ( rel_s4 @ sK1_SY120 @ sK2_SY1273 )
& ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
& ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
& ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
& ( sK10_REN
| ( ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
& ! [SY1313: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SY1313 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SY1313 ) )
& ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) )
& ( sK10_REN
=> ( ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
& ! [SY1315: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SY1315 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SY1315 ) )
& ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
& ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(44,plain,
( ( ! [SY262: $i,SY263: $i] :
( ~ ( rel_s4 @ SY262 @ SY263 )
| ! [SY253: mu] :
( ~ ( exists_in_world @ SY253 @ SY263 )
| ! [SY254: $i] :
( ~ ( rel_s4 @ SY263 @ SY254 )
| ( ! [SY236: mu] :
( ~ ( exists_in_world @ SY236 @ SY254 )
| ! [SY237: $i] :
( ~ ( rel_s4 @ SY254 @ SY237 )
| ( ( rel_s4 @ SY237 @ ( sK12_SY238 @ SY237 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY253 ) @ SY236 ) @ empty_set @ ( sK12_SY238 @ SY237 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) ) )
| ! [SY239: $i] :
( ~ ( rel_s4 @ SY237 @ SY239 )
| ( in @ SY253 @ SY236 @ SY239 ) ) ) )
& ! [SY236: mu] :
( ~ ( exists_in_world @ SY236 @ SY254 )
| ! [SY240: $i] :
( ~ ( rel_s4 @ SY254 @ SY240 )
| ( ( rel_s4 @ SY240 @ ( sK11_SY241 @ SY240 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) )
& ~ ( in @ SY253 @ SY236 @ ( sK11_SY241 @ SY240 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) ) )
| ! [SY242: $i] :
( ~ ( rel_s4 @ SY240 @ SY242 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY253 ) @ SY236 ) @ empty_set @ SY242 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(45,plain,
( ( ! [SY360: $i,SY361: $i] :
( ~ ( rel_s4 @ SY360 @ SY361 )
| ! [SY353: mu] :
( ~ ( exists_in_world @ SY353 @ SY361 )
| ! [SY354: $i] :
( ~ ( rel_s4 @ SY361 @ SY354 )
| ! [SY340: mu] :
( ~ ( exists_in_world @ SY340 @ SY354 )
| ! [SY341: $i] :
( ~ ( rel_s4 @ SY354 @ SY341 )
| ( ( rel_s4 @ SY341 @ ( sK14_SY342 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) )
& ~ ( in @ SY353 @ SY340 @ ( sK14_SY342 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) ) )
| ! [SY343: $i] :
( ~ ( rel_s4 @ SY341 @ SY343 )
| ( ( rel_s4 @ SY343 @ ( sK13_SY344 @ SY343 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) )
& ~ ( in @ SY340 @ SY353 @ ( sK13_SY344 @ SY343 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(46,plain,
( ( ! [SY493: $i,SY494: $i] :
( ~ ( rel_s4 @ SY493 @ SY494 )
| ! [SY484: mu] :
( ~ ( exists_in_world @ SY484 @ SY494 )
| ! [SY485: $i] :
( ~ ( rel_s4 @ SY494 @ SY485 )
| ! [SY467: mu] :
( ~ ( exists_in_world @ SY467 @ SY485 )
| ! [SY468: $i] :
( ~ ( rel_s4 @ SY485 @ SY468 )
| ! [SY469: mu] :
( ~ ( exists_in_world @ SY469 @ SY468 )
| ! [SY470: $i] :
( ~ ( rel_s4 @ SY468 @ SY470 )
| ( ( rel_s4 @ SY470 @ ( sK16_SY471 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) )
& ~ ( qmltpeq @ SY484 @ SY467 @ ( sK16_SY471 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) ) )
| ( ( rel_s4 @ SY470 @ ( sK15_SY472 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) )
& ~ ( in @ SY469 @ SY484 @ ( sK15_SY472 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) ) )
| ! [SY447: $i] :
( ~ ( rel_s4 @ SY470 @ SY447 )
| ( in @ SY469 @ SY467 @ SY447 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(47,plain,
( ( ! [SY630: $i,SY631: $i] :
( ~ ( rel_s4 @ SY630 @ SY631 )
| ! [SY621: mu] :
( ~ ( exists_in_world @ SY621 @ SY631 )
| ! [SY622: $i] :
( ~ ( rel_s4 @ SY631 @ SY622 )
| ! [SY604: mu] :
( ~ ( exists_in_world @ SY604 @ SY622 )
| ! [SY605: $i] :
( ~ ( rel_s4 @ SY622 @ SY605 )
| ! [SY606: mu] :
( ~ ( exists_in_world @ SY606 @ SY605 )
| ! [SY607: $i] :
( ~ ( rel_s4 @ SY605 @ SY607 )
| ( ( rel_s4 @ SY607 @ ( sK18_SY608 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) )
& ~ ( qmltpeq @ SY621 @ SY604 @ ( sK18_SY608 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) ) )
| ( ( rel_s4 @ SY607 @ ( sK17_SY609 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) )
& ~ ( in @ SY621 @ SY606 @ ( sK17_SY609 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) ) )
| ! [SY584: $i] :
( ~ ( rel_s4 @ SY607 @ SY584 )
| ( in @ SY604 @ SY606 @ SY584 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(48,plain,
( ( ! [SY736: $i,SY737: $i] :
( ~ ( rel_s4 @ SY736 @ SY737 )
| ! [SY729: mu] :
( ~ ( exists_in_world @ SY729 @ SY737 )
| ! [SY730: $i] :
( ~ ( rel_s4 @ SY737 @ SY730 )
| ! [SY716: mu] :
( ~ ( exists_in_world @ SY716 @ SY730 )
| ! [SY717: $i] :
( ~ ( rel_s4 @ SY730 @ SY717 )
| ( ( rel_s4 @ SY717 @ ( sK20_SY718 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) )
& ~ ( qmltpeq @ SY729 @ SY716 @ ( sK20_SY718 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) ) )
| ( ( rel_s4 @ SY717 @ ( sK19_SY719 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) )
& ~ ( empty @ SY729 @ ( sK19_SY719 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) ) )
| ! [SY700: $i] :
( ~ ( rel_s4 @ SY717 @ SY700 )
| ( empty @ SY716 @ SY700 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(49,plain,
( ( ! [SY811: $i,SY812: $i] :
( ~ ( rel_s4 @ SY811 @ SY812 )
| ! [SY805: mu] :
( ~ ( exists_in_world @ SY805 @ SY812 )
| ! [SY806: $i] :
( ~ ( rel_s4 @ SY812 @ SY806 )
| ! [SY794: mu] :
( ~ ( exists_in_world @ SY794 @ SY806 )
| ! [SY795: $i] :
( ~ ( rel_s4 @ SY806 @ SY795 )
| ( ( rel_s4 @ SY795 @ ( sK21_SY796 @ SY795 @ SY794 @ SY806 @ SY805 @ SY812 @ SY811 ) )
& ~ ( qmltpeq @ SY805 @ SY794 @ ( sK21_SY796 @ SY795 @ SY794 @ SY806 @ SY805 @ SY812 @ SY811 ) ) )
| ! [SY797: $i] :
( ~ ( rel_s4 @ SY795 @ SY797 )
| ( qmltpeq @ ( singleton @ SY805 ) @ ( singleton @ SY794 ) @ SY797 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(50,plain,
( ( ! [SY912: $i,SY913: $i] :
( ~ ( rel_s4 @ SY912 @ SY913 )
| ! [SY904: mu] :
( ~ ( exists_in_world @ SY904 @ SY913 )
| ! [SY905: $i] :
( ~ ( rel_s4 @ SY913 @ SY905 )
| ! [SY889: mu] :
( ~ ( exists_in_world @ SY889 @ SY905 )
| ! [SY890: $i] :
( ~ ( rel_s4 @ SY905 @ SY890 )
| ! [SY891: mu] :
( ~ ( exists_in_world @ SY891 @ SY890 )
| ! [SY892: $i] :
( ~ ( rel_s4 @ SY890 @ SY892 )
| ( ( rel_s4 @ SY892 @ ( sK22_SY893 @ SY892 @ SY891 @ SY890 @ SY889 @ SY905 @ SY904 @ SY913 @ SY912 ) )
& ~ ( qmltpeq @ SY904 @ SY889 @ ( sK22_SY893 @ SY892 @ SY891 @ SY890 @ SY889 @ SY905 @ SY904 @ SY913 @ SY912 ) ) )
| ! [SY894: $i] :
( ~ ( rel_s4 @ SY892 @ SY894 )
| ( qmltpeq @ ( set_difference @ SY891 @ SY904 ) @ ( set_difference @ SY891 @ SY889 ) @ SY894 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(51,plain,
( ( ! [SY1017: $i,SY1018: $i] :
( ~ ( rel_s4 @ SY1017 @ SY1018 )
| ! [SY1009: mu] :
( ~ ( exists_in_world @ SY1009 @ SY1018 )
| ! [SY1010: $i] :
( ~ ( rel_s4 @ SY1018 @ SY1010 )
| ! [SY994: mu] :
( ~ ( exists_in_world @ SY994 @ SY1010 )
| ! [SY995: $i] :
( ~ ( rel_s4 @ SY1010 @ SY995 )
| ! [SY996: mu] :
( ~ ( exists_in_world @ SY996 @ SY995 )
| ! [SY997: $i] :
( ~ ( rel_s4 @ SY995 @ SY997 )
| ( ( rel_s4 @ SY997 @ ( sK23_SY998 @ SY997 @ SY996 @ SY995 @ SY994 @ SY1010 @ SY1009 @ SY1018 @ SY1017 ) )
& ~ ( qmltpeq @ SY1009 @ SY994 @ ( sK23_SY998 @ SY997 @ SY996 @ SY995 @ SY994 @ SY1010 @ SY1009 @ SY1018 @ SY1017 ) ) )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY997 @ SY999 )
| ( qmltpeq @ ( set_difference @ SY1009 @ SY996 ) @ ( set_difference @ SY994 @ SY996 ) @ SY999 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(52,plain,
( ( ! [SY1152: $i,SY1153: $i] :
( ~ ( rel_s4 @ SY1152 @ SY1153 )
| ! [SY1143: mu] :
( ~ ( exists_in_world @ SY1143 @ SY1153 )
| ! [SY1144: $i] :
( ~ ( rel_s4 @ SY1153 @ SY1144 )
| ! [SY1126: mu] :
( ~ ( exists_in_world @ SY1126 @ SY1144 )
| ! [SY1127: $i] :
( ~ ( rel_s4 @ SY1144 @ SY1127 )
| ! [SY1128: mu] :
( ~ ( exists_in_world @ SY1128 @ SY1127 )
| ! [SY1129: $i] :
( ~ ( rel_s4 @ SY1127 @ SY1129 )
| ( ( rel_s4 @ SY1129 @ ( sK25_SY1130 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) )
& ~ ( qmltpeq @ SY1143 @ SY1126 @ ( sK25_SY1130 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) ) )
| ( ( rel_s4 @ SY1129 @ ( sK24_SY1105 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) )
& ~ ( qmltpeq @ SY1126 @ SY1128 @ ( sK24_SY1105 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) ) )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1129 @ SY1132 )
| ( qmltpeq @ SY1143 @ SY1128 @ SY1132 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(53,plain,
( ( ! [SY1231: $i,SY1232: $i] :
( ~ ( rel_s4 @ SY1231 @ SY1232 )
| ! [SY1225: mu] :
( ~ ( exists_in_world @ SY1225 @ SY1232 )
| ! [SY1226: $i] :
( ~ ( rel_s4 @ SY1232 @ SY1226 )
| ! [SY1214: mu] :
( ~ ( exists_in_world @ SY1214 @ SY1226 )
| ! [SY1215: $i] :
( ~ ( rel_s4 @ SY1226 @ SY1215 )
| ( ( rel_s4 @ SY1215 @ ( sK26_SY1216 @ SY1215 @ SY1214 @ SY1226 @ SY1225 @ SY1232 @ SY1231 ) )
& ~ ( qmltpeq @ SY1225 @ SY1214 @ ( sK26_SY1216 @ SY1215 @ SY1214 @ SY1226 @ SY1225 @ SY1232 @ SY1231 ) ) )
| ! [SY1217: $i] :
( ~ ( rel_s4 @ SY1215 @ SY1217 )
| ( qmltpeq @ SY1214 @ SY1225 @ SY1217 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(54,plain,
( ( ! [SY1259: $i,SY1260: $i] :
( ~ ( rel_s4 @ SY1259 @ SY1260 )
| ! [SY1257: mu] :
( ~ ( exists_in_world @ SY1257 @ SY1260 )
| ! [SY1258: $i] :
( ~ ( rel_s4 @ SY1260 @ SY1258 )
| ( qmltpeq @ SY1257 @ SY1257 @ SY1258 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(55,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(56,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(57,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(58,plain,
( ( ! [SY1259: $i,SY1260: $i] :
( ~ ( rel_s4 @ SY1259 @ SY1260 )
| ! [SY1257: mu] :
( ~ ( exists_in_world @ SY1257 @ SY1260 )
| ! [SY1258: $i] :
( ~ ( rel_s4 @ SY1260 @ SY1258 )
| ( qmltpeq @ SY1257 @ SY1257 @ SY1258 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(59,plain,
( ( ! [SY1231: $i,SY1232: $i] :
( ~ ( rel_s4 @ SY1231 @ SY1232 )
| ! [SY1225: mu] :
( ~ ( exists_in_world @ SY1225 @ SY1232 )
| ! [SY1226: $i] :
( ~ ( rel_s4 @ SY1232 @ SY1226 )
| ! [SY1214: mu] :
( ~ ( exists_in_world @ SY1214 @ SY1226 )
| ! [SY1215: $i] :
( ~ ( rel_s4 @ SY1226 @ SY1215 )
| ( ( rel_s4 @ SY1215 @ ( sK26_SY1216 @ SY1215 @ SY1214 @ SY1226 @ SY1225 @ SY1232 @ SY1231 ) )
& ~ ( qmltpeq @ SY1225 @ SY1214 @ ( sK26_SY1216 @ SY1215 @ SY1214 @ SY1226 @ SY1225 @ SY1232 @ SY1231 ) ) )
| ! [SY1217: $i] :
( ~ ( rel_s4 @ SY1215 @ SY1217 )
| ( qmltpeq @ SY1214 @ SY1225 @ SY1217 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(60,plain,
( ( ! [SY1152: $i,SY1153: $i] :
( ~ ( rel_s4 @ SY1152 @ SY1153 )
| ! [SY1143: mu] :
( ~ ( exists_in_world @ SY1143 @ SY1153 )
| ! [SY1144: $i] :
( ~ ( rel_s4 @ SY1153 @ SY1144 )
| ! [SY1126: mu] :
( ~ ( exists_in_world @ SY1126 @ SY1144 )
| ! [SY1127: $i] :
( ~ ( rel_s4 @ SY1144 @ SY1127 )
| ! [SY1128: mu] :
( ~ ( exists_in_world @ SY1128 @ SY1127 )
| ! [SY1129: $i] :
( ~ ( rel_s4 @ SY1127 @ SY1129 )
| ( ( rel_s4 @ SY1129 @ ( sK25_SY1130 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) )
& ~ ( qmltpeq @ SY1143 @ SY1126 @ ( sK25_SY1130 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) ) )
| ( ( rel_s4 @ SY1129 @ ( sK24_SY1105 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) )
& ~ ( qmltpeq @ SY1126 @ SY1128 @ ( sK24_SY1105 @ SY1129 @ SY1128 @ SY1127 @ SY1126 @ SY1144 @ SY1143 @ SY1153 @ SY1152 ) ) )
| ! [SY1132: $i] :
( ~ ( rel_s4 @ SY1129 @ SY1132 )
| ( qmltpeq @ SY1143 @ SY1128 @ SY1132 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(61,plain,
( ( ! [SY1017: $i,SY1018: $i] :
( ~ ( rel_s4 @ SY1017 @ SY1018 )
| ! [SY1009: mu] :
( ~ ( exists_in_world @ SY1009 @ SY1018 )
| ! [SY1010: $i] :
( ~ ( rel_s4 @ SY1018 @ SY1010 )
| ! [SY994: mu] :
( ~ ( exists_in_world @ SY994 @ SY1010 )
| ! [SY995: $i] :
( ~ ( rel_s4 @ SY1010 @ SY995 )
| ! [SY996: mu] :
( ~ ( exists_in_world @ SY996 @ SY995 )
| ! [SY997: $i] :
( ~ ( rel_s4 @ SY995 @ SY997 )
| ( ( rel_s4 @ SY997 @ ( sK23_SY998 @ SY997 @ SY996 @ SY995 @ SY994 @ SY1010 @ SY1009 @ SY1018 @ SY1017 ) )
& ~ ( qmltpeq @ SY1009 @ SY994 @ ( sK23_SY998 @ SY997 @ SY996 @ SY995 @ SY994 @ SY1010 @ SY1009 @ SY1018 @ SY1017 ) ) )
| ! [SY999: $i] :
( ~ ( rel_s4 @ SY997 @ SY999 )
| ( qmltpeq @ ( set_difference @ SY1009 @ SY996 ) @ ( set_difference @ SY994 @ SY996 ) @ SY999 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(62,plain,
( ( ! [SY912: $i,SY913: $i] :
( ~ ( rel_s4 @ SY912 @ SY913 )
| ! [SY904: mu] :
( ~ ( exists_in_world @ SY904 @ SY913 )
| ! [SY905: $i] :
( ~ ( rel_s4 @ SY913 @ SY905 )
| ! [SY889: mu] :
( ~ ( exists_in_world @ SY889 @ SY905 )
| ! [SY890: $i] :
( ~ ( rel_s4 @ SY905 @ SY890 )
| ! [SY891: mu] :
( ~ ( exists_in_world @ SY891 @ SY890 )
| ! [SY892: $i] :
( ~ ( rel_s4 @ SY890 @ SY892 )
| ( ( rel_s4 @ SY892 @ ( sK22_SY893 @ SY892 @ SY891 @ SY890 @ SY889 @ SY905 @ SY904 @ SY913 @ SY912 ) )
& ~ ( qmltpeq @ SY904 @ SY889 @ ( sK22_SY893 @ SY892 @ SY891 @ SY890 @ SY889 @ SY905 @ SY904 @ SY913 @ SY912 ) ) )
| ! [SY894: $i] :
( ~ ( rel_s4 @ SY892 @ SY894 )
| ( qmltpeq @ ( set_difference @ SY891 @ SY904 ) @ ( set_difference @ SY891 @ SY889 ) @ SY894 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(63,plain,
( ( ! [SY811: $i,SY812: $i] :
( ~ ( rel_s4 @ SY811 @ SY812 )
| ! [SY805: mu] :
( ~ ( exists_in_world @ SY805 @ SY812 )
| ! [SY806: $i] :
( ~ ( rel_s4 @ SY812 @ SY806 )
| ! [SY794: mu] :
( ~ ( exists_in_world @ SY794 @ SY806 )
| ! [SY795: $i] :
( ~ ( rel_s4 @ SY806 @ SY795 )
| ( ( rel_s4 @ SY795 @ ( sK21_SY796 @ SY795 @ SY794 @ SY806 @ SY805 @ SY812 @ SY811 ) )
& ~ ( qmltpeq @ SY805 @ SY794 @ ( sK21_SY796 @ SY795 @ SY794 @ SY806 @ SY805 @ SY812 @ SY811 ) ) )
| ! [SY797: $i] :
( ~ ( rel_s4 @ SY795 @ SY797 )
| ( qmltpeq @ ( singleton @ SY805 ) @ ( singleton @ SY794 ) @ SY797 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(64,plain,
( ( ! [SY736: $i,SY737: $i] :
( ~ ( rel_s4 @ SY736 @ SY737 )
| ! [SY729: mu] :
( ~ ( exists_in_world @ SY729 @ SY737 )
| ! [SY730: $i] :
( ~ ( rel_s4 @ SY737 @ SY730 )
| ! [SY716: mu] :
( ~ ( exists_in_world @ SY716 @ SY730 )
| ! [SY717: $i] :
( ~ ( rel_s4 @ SY730 @ SY717 )
| ( ( rel_s4 @ SY717 @ ( sK20_SY718 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) )
& ~ ( qmltpeq @ SY729 @ SY716 @ ( sK20_SY718 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) ) )
| ( ( rel_s4 @ SY717 @ ( sK19_SY719 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) )
& ~ ( empty @ SY729 @ ( sK19_SY719 @ SY717 @ SY716 @ SY730 @ SY729 @ SY737 @ SY736 ) ) )
| ! [SY700: $i] :
( ~ ( rel_s4 @ SY717 @ SY700 )
| ( empty @ SY716 @ SY700 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(65,plain,
( ( ! [SY630: $i,SY631: $i] :
( ~ ( rel_s4 @ SY630 @ SY631 )
| ! [SY621: mu] :
( ~ ( exists_in_world @ SY621 @ SY631 )
| ! [SY622: $i] :
( ~ ( rel_s4 @ SY631 @ SY622 )
| ! [SY604: mu] :
( ~ ( exists_in_world @ SY604 @ SY622 )
| ! [SY605: $i] :
( ~ ( rel_s4 @ SY622 @ SY605 )
| ! [SY606: mu] :
( ~ ( exists_in_world @ SY606 @ SY605 )
| ! [SY607: $i] :
( ~ ( rel_s4 @ SY605 @ SY607 )
| ( ( rel_s4 @ SY607 @ ( sK18_SY608 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) )
& ~ ( qmltpeq @ SY621 @ SY604 @ ( sK18_SY608 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) ) )
| ( ( rel_s4 @ SY607 @ ( sK17_SY609 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) )
& ~ ( in @ SY621 @ SY606 @ ( sK17_SY609 @ SY607 @ SY606 @ SY605 @ SY604 @ SY622 @ SY621 @ SY631 @ SY630 ) ) )
| ! [SY584: $i] :
( ~ ( rel_s4 @ SY607 @ SY584 )
| ( in @ SY604 @ SY606 @ SY584 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(66,plain,
( ( ! [SY493: $i,SY494: $i] :
( ~ ( rel_s4 @ SY493 @ SY494 )
| ! [SY484: mu] :
( ~ ( exists_in_world @ SY484 @ SY494 )
| ! [SY485: $i] :
( ~ ( rel_s4 @ SY494 @ SY485 )
| ! [SY467: mu] :
( ~ ( exists_in_world @ SY467 @ SY485 )
| ! [SY468: $i] :
( ~ ( rel_s4 @ SY485 @ SY468 )
| ! [SY469: mu] :
( ~ ( exists_in_world @ SY469 @ SY468 )
| ! [SY470: $i] :
( ~ ( rel_s4 @ SY468 @ SY470 )
| ( ( rel_s4 @ SY470 @ ( sK16_SY471 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) )
& ~ ( qmltpeq @ SY484 @ SY467 @ ( sK16_SY471 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) ) )
| ( ( rel_s4 @ SY470 @ ( sK15_SY472 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) )
& ~ ( in @ SY469 @ SY484 @ ( sK15_SY472 @ SY470 @ SY469 @ SY468 @ SY467 @ SY485 @ SY484 @ SY494 @ SY493 ) ) )
| ! [SY447: $i] :
( ~ ( rel_s4 @ SY470 @ SY447 )
| ( in @ SY469 @ SY467 @ SY447 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(67,plain,
( ( ! [SY360: $i,SY361: $i] :
( ~ ( rel_s4 @ SY360 @ SY361 )
| ! [SY353: mu] :
( ~ ( exists_in_world @ SY353 @ SY361 )
| ! [SY354: $i] :
( ~ ( rel_s4 @ SY361 @ SY354 )
| ! [SY340: mu] :
( ~ ( exists_in_world @ SY340 @ SY354 )
| ! [SY341: $i] :
( ~ ( rel_s4 @ SY354 @ SY341 )
| ( ( rel_s4 @ SY341 @ ( sK14_SY342 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) )
& ~ ( in @ SY353 @ SY340 @ ( sK14_SY342 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) ) )
| ! [SY343: $i] :
( ~ ( rel_s4 @ SY341 @ SY343 )
| ( ( rel_s4 @ SY343 @ ( sK13_SY344 @ SY343 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) )
& ~ ( in @ SY340 @ SY353 @ ( sK13_SY344 @ SY343 @ SY341 @ SY340 @ SY354 @ SY353 @ SY361 @ SY360 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(68,plain,
( ( ! [SY286: $i,SY287: $i] :
( ~ ( rel_s4 @ SY286 @ SY287 )
| ( empty @ empty_set @ SY287 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(69,plain,
( ( ! [SY262: $i,SY263: $i] :
( ~ ( rel_s4 @ SY262 @ SY263 )
| ! [SY253: mu] :
( ~ ( exists_in_world @ SY253 @ SY263 )
| ! [SY254: $i] :
( ~ ( rel_s4 @ SY263 @ SY254 )
| ( ! [SY236: mu] :
( ~ ( exists_in_world @ SY236 @ SY254 )
| ! [SY237: $i] :
( ~ ( rel_s4 @ SY254 @ SY237 )
| ( ( rel_s4 @ SY237 @ ( sK12_SY238 @ SY237 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY253 ) @ SY236 ) @ empty_set @ ( sK12_SY238 @ SY237 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) ) )
| ! [SY239: $i] :
( ~ ( rel_s4 @ SY237 @ SY239 )
| ( in @ SY253 @ SY236 @ SY239 ) ) ) )
& ! [SY236: mu] :
( ~ ( exists_in_world @ SY236 @ SY254 )
| ! [SY240: $i] :
( ~ ( rel_s4 @ SY254 @ SY240 )
| ( ( rel_s4 @ SY240 @ ( sK11_SY241 @ SY240 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) )
& ~ ( in @ SY253 @ SY236 @ ( sK11_SY241 @ SY240 @ SY236 @ SY254 @ SY253 @ SY263 @ SY262 ) ) )
| ! [SY242: $i] :
( ~ ( rel_s4 @ SY240 @ SY242 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY253 ) @ SY236 ) @ empty_set @ SY242 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(70,plain,
( ( ( rel_s4 @ sK1_SY120 @ sK2_SY1273 )
& ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
& ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
& ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
& ( sK10_REN
| ( ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
& ! [SY1313: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SY1313 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SY1313 ) )
& ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
& ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) )
& ( sK10_REN
=> ( ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
& ! [SY1315: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SY1315 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SY1315 ) )
& ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
& ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ! [SX7: $i] :
( ~ ( rel_s4 @ SX5 @ SX7 )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK16_SY471 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK16_SY471 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK15_SY472 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX6 @ SX2 @ ( sK15_SY472 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SX7 @ SX8 )
| ( in @ SX6 @ SX4 @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66,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,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK20_SY718 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK20_SY718 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK19_SY719 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( empty @ SX2 @ ( sK19_SY719 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( empty @ SX4 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64,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,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ! [SX7: $i] :
( ~ ( rel_s4 @ SX5 @ SX7 )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK18_SY608 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK18_SY608 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK17_SY609 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX2 @ SX6 @ ( sK17_SY609 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SX7 @ SX8 )
| ( in @ SX4 @ SX6 @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65,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,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ! [SX7: $i] :
( ~ ( rel_s4 @ SX5 @ SX7 )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK23_SY998 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK23_SY998 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SX7 @ SX8 )
| ( qmltpeq @ ( set_difference @ SX2 @ SX6 ) @ ( set_difference @ SX4 @ SX6 ) @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61,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(75,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK26_SY1216 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK26_SY1216 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( qmltpeq @ SX4 @ SX2 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59,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(76,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ! [SX7: $i] :
( ~ ( rel_s4 @ SX5 @ SX7 )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK25_SY1130 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK25_SY1130 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK24_SY1105 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX4 @ SX6 @ ( sK24_SY1105 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SX7 @ SX8 )
| ( qmltpeq @ SX2 @ SX6 @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60,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(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK14_SY342 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX2 @ SX4 @ ( sK14_SY342 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ~ ( ~ ( rel_s4 @ SX6 @ ( sK13_SY344 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX4 @ SX2 @ ( sK13_SY344 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67,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(78,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK21_SY796 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK21_SY796 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( qmltpeq @ ( singleton @ SX2 ) @ ( singleton @ SX4 ) @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63,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(79,plain,
( ( ~ ( ~ ( rel_s4 @ sK1_SY120 @ sK2_SY1273 )
| ~ ~ ( ~ ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70,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(80,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ~ ( ~ ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK12_SY238 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX2 ) @ SX4 ) @ empty_set @ ( sK12_SY238 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( in @ SX2 @ SX4 @ SX6 ) ) ) )
| ~ ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ~ ( ~ ( rel_s4 @ SX5 @ ( sK11_SY241 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( in @ SX2 @ SX4 @ ( sK11_SY241 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SX5 @ SX6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX2 ) @ SX4 ) @ empty_set @ SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69,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(81,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_s4 @ SX0 @ SX1 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( rel_s4 @ SX1 @ SX3 )
| ! [SX4: mu] :
( ~ ( exists_in_world @ SX4 @ SX3 )
| ! [SX5: $i] :
( ~ ( rel_s4 @ SX3 @ SX5 )
| ! [SX6: mu] :
( ~ ( exists_in_world @ SX6 @ SX5 )
| ! [SX7: $i] :
( ~ ( rel_s4 @ SX5 @ SX7 )
| ~ ( ~ ( rel_s4 @ SX7 @ ( sK22_SY893 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( qmltpeq @ SX2 @ SX4 @ ( sK22_SY893 @ SX7 @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SX7 @ SX8 )
| ( qmltpeq @ ( set_difference @ SX6 @ SX2 ) @ ( set_difference @ SX6 @ SX4 ) @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62,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(82,plain,
! [SV1: $i] :
( ( exists_in_world @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(83,plain,
! [SV2: $i] :
( ( ! [SY1317: mu] : ( exists_in_world @ ( singleton @ SY1317 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(84,plain,
! [SV3: $i] :
( ( ! [SY1318: mu,SY1319: mu] : ( exists_in_world @ ( set_difference @ SY1318 @ SY1319 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(85,plain,
! [SV4: $i] :
( ( ! [SY1320: $i] :
( ~ ( rel_s4 @ SV4 @ SY1320 )
| ! [SY1257: mu] :
( ~ ( exists_in_world @ SY1257 @ SY1320 )
| ! [SY1258: $i] :
( ~ ( rel_s4 @ SY1320 @ SY1258 )
| ( qmltpeq @ SY1257 @ SY1257 @ SY1258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(86,plain,
! [SV5: $i] :
( ( ! [SY1323: $i] :
( ~ ( rel_s4 @ SV5 @ SY1323 )
| ( empty @ empty_set @ SY1323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(87,plain,
! [SV6: $i] :
( ( ! [SY1324: $i] :
( ~ ( rel_s4 @ SV6 @ SY1324 )
| ! [SY1325: mu] :
( ~ ( exists_in_world @ SY1325 @ SY1324 )
| ! [SY1326: $i] :
( ~ ( rel_s4 @ SY1324 @ SY1326 )
| ! [SY1327: mu] :
( ~ ( exists_in_world @ SY1327 @ SY1326 )
| ! [SY1328: $i] :
( ~ ( rel_s4 @ SY1326 @ SY1328 )
| ! [SY1329: mu] :
( ~ ( exists_in_world @ SY1329 @ SY1328 )
| ! [SY1330: $i] :
( ~ ( rel_s4 @ SY1328 @ SY1330 )
| ~ ( ~ ( rel_s4 @ SY1330 @ ( sK16_SY471 @ SY1330 @ SY1329 @ SY1328 @ SY1327 @ SY1326 @ SY1325 @ SY1324 @ SV6 ) )
| ~ ~ ( qmltpeq @ SY1325 @ SY1327 @ ( sK16_SY471 @ SY1330 @ SY1329 @ SY1328 @ SY1327 @ SY1326 @ SY1325 @ SY1324 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1330 @ ( sK15_SY472 @ SY1330 @ SY1329 @ SY1328 @ SY1327 @ SY1326 @ SY1325 @ SY1324 @ SV6 ) )
| ~ ~ ( in @ SY1329 @ SY1325 @ ( sK15_SY472 @ SY1330 @ SY1329 @ SY1328 @ SY1327 @ SY1326 @ SY1325 @ SY1324 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1330 @ SX8 )
| ( in @ SY1329 @ SY1327 @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(88,plain,
! [SV7: $i] :
( ( ! [SY1332: $i] :
( ~ ( rel_s4 @ SV7 @ SY1332 )
| ! [SY1333: mu] :
( ~ ( exists_in_world @ SY1333 @ SY1332 )
| ! [SY1334: $i] :
( ~ ( rel_s4 @ SY1332 @ SY1334 )
| ! [SY1335: mu] :
( ~ ( exists_in_world @ SY1335 @ SY1334 )
| ! [SY1336: $i] :
( ~ ( rel_s4 @ SY1334 @ SY1336 )
| ~ ( ~ ( rel_s4 @ SY1336 @ ( sK20_SY718 @ SY1336 @ SY1335 @ SY1334 @ SY1333 @ SY1332 @ SV7 ) )
| ~ ~ ( qmltpeq @ SY1333 @ SY1335 @ ( sK20_SY718 @ SY1336 @ SY1335 @ SY1334 @ SY1333 @ SY1332 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1336 @ ( sK19_SY719 @ SY1336 @ SY1335 @ SY1334 @ SY1333 @ SY1332 @ SV7 ) )
| ~ ~ ( empty @ SY1333 @ ( sK19_SY719 @ SY1336 @ SY1335 @ SY1334 @ SY1333 @ SY1332 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1336 @ SX6 )
| ( empty @ SY1335 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(89,plain,
! [SV8: $i] :
( ( ! [SY1338: $i] :
( ~ ( rel_s4 @ SV8 @ SY1338 )
| ! [SY1339: mu] :
( ~ ( exists_in_world @ SY1339 @ SY1338 )
| ! [SY1340: $i] :
( ~ ( rel_s4 @ SY1338 @ SY1340 )
| ! [SY1341: mu] :
( ~ ( exists_in_world @ SY1341 @ SY1340 )
| ! [SY1342: $i] :
( ~ ( rel_s4 @ SY1340 @ SY1342 )
| ! [SY1343: mu] :
( ~ ( exists_in_world @ SY1343 @ SY1342 )
| ! [SY1344: $i] :
( ~ ( rel_s4 @ SY1342 @ SY1344 )
| ~ ( ~ ( rel_s4 @ SY1344 @ ( sK18_SY608 @ SY1344 @ SY1343 @ SY1342 @ SY1341 @ SY1340 @ SY1339 @ SY1338 @ SV8 ) )
| ~ ~ ( qmltpeq @ SY1339 @ SY1341 @ ( sK18_SY608 @ SY1344 @ SY1343 @ SY1342 @ SY1341 @ SY1340 @ SY1339 @ SY1338 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1344 @ ( sK17_SY609 @ SY1344 @ SY1343 @ SY1342 @ SY1341 @ SY1340 @ SY1339 @ SY1338 @ SV8 ) )
| ~ ~ ( in @ SY1339 @ SY1343 @ ( sK17_SY609 @ SY1344 @ SY1343 @ SY1342 @ SY1341 @ SY1340 @ SY1339 @ SY1338 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1344 @ SX8 )
| ( in @ SY1341 @ SY1343 @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(90,plain,
! [SV9: $i] :
( ( ! [SY1346: $i] :
( ~ ( rel_s4 @ SV9 @ SY1346 )
| ! [SY1347: mu] :
( ~ ( exists_in_world @ SY1347 @ SY1346 )
| ! [SY1348: $i] :
( ~ ( rel_s4 @ SY1346 @ SY1348 )
| ! [SY1349: mu] :
( ~ ( exists_in_world @ SY1349 @ SY1348 )
| ! [SY1350: $i] :
( ~ ( rel_s4 @ SY1348 @ SY1350 )
| ! [SY1351: mu] :
( ~ ( exists_in_world @ SY1351 @ SY1350 )
| ! [SY1352: $i] :
( ~ ( rel_s4 @ SY1350 @ SY1352 )
| ~ ( ~ ( rel_s4 @ SY1352 @ ( sK23_SY998 @ SY1352 @ SY1351 @ SY1350 @ SY1349 @ SY1348 @ SY1347 @ SY1346 @ SV9 ) )
| ~ ~ ( qmltpeq @ SY1347 @ SY1349 @ ( sK23_SY998 @ SY1352 @ SY1351 @ SY1350 @ SY1349 @ SY1348 @ SY1347 @ SY1346 @ SV9 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1352 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1347 @ SY1351 ) @ ( set_difference @ SY1349 @ SY1351 ) @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(91,plain,
! [SV10: $i] :
( ( ! [SY1354: $i] :
( ~ ( rel_s4 @ SV10 @ SY1354 )
| ! [SY1355: mu] :
( ~ ( exists_in_world @ SY1355 @ SY1354 )
| ! [SY1356: $i] :
( ~ ( rel_s4 @ SY1354 @ SY1356 )
| ! [SY1357: mu] :
( ~ ( exists_in_world @ SY1357 @ SY1356 )
| ! [SY1358: $i] :
( ~ ( rel_s4 @ SY1356 @ SY1358 )
| ~ ( ~ ( rel_s4 @ SY1358 @ ( sK26_SY1216 @ SY1358 @ SY1357 @ SY1356 @ SY1355 @ SY1354 @ SV10 ) )
| ~ ~ ( qmltpeq @ SY1355 @ SY1357 @ ( sK26_SY1216 @ SY1358 @ SY1357 @ SY1356 @ SY1355 @ SY1354 @ SV10 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1358 @ SX6 )
| ( qmltpeq @ SY1357 @ SY1355 @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(92,plain,
! [SV11: $i] :
( ( ! [SY1360: $i] :
( ~ ( rel_s4 @ SV11 @ SY1360 )
| ! [SY1361: mu] :
( ~ ( exists_in_world @ SY1361 @ SY1360 )
| ! [SY1362: $i] :
( ~ ( rel_s4 @ SY1360 @ SY1362 )
| ! [SY1363: mu] :
( ~ ( exists_in_world @ SY1363 @ SY1362 )
| ! [SY1364: $i] :
( ~ ( rel_s4 @ SY1362 @ SY1364 )
| ! [SY1365: mu] :
( ~ ( exists_in_world @ SY1365 @ SY1364 )
| ! [SY1366: $i] :
( ~ ( rel_s4 @ SY1364 @ SY1366 )
| ~ ( ~ ( rel_s4 @ SY1366 @ ( sK25_SY1130 @ SY1366 @ SY1365 @ SY1364 @ SY1363 @ SY1362 @ SY1361 @ SY1360 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1361 @ SY1363 @ ( sK25_SY1130 @ SY1366 @ SY1365 @ SY1364 @ SY1363 @ SY1362 @ SY1361 @ SY1360 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1366 @ ( sK24_SY1105 @ SY1366 @ SY1365 @ SY1364 @ SY1363 @ SY1362 @ SY1361 @ SY1360 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1363 @ SY1365 @ ( sK24_SY1105 @ SY1366 @ SY1365 @ SY1364 @ SY1363 @ SY1362 @ SY1361 @ SY1360 @ SV11 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1366 @ SX8 )
| ( qmltpeq @ SY1361 @ SY1365 @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(93,plain,
! [SV12: $i] :
( ( ! [SY1368: $i] :
( ~ ( rel_s4 @ SV12 @ SY1368 )
| ! [SY1369: mu] :
( ~ ( exists_in_world @ SY1369 @ SY1368 )
| ! [SY1370: $i] :
( ~ ( rel_s4 @ SY1368 @ SY1370 )
| ! [SY1371: mu] :
( ~ ( exists_in_world @ SY1371 @ SY1370 )
| ! [SY1372: $i] :
( ~ ( rel_s4 @ SY1370 @ SY1372 )
| ~ ( ~ ( rel_s4 @ SY1372 @ ( sK14_SY342 @ SY1372 @ SY1371 @ SY1370 @ SY1369 @ SY1368 @ SV12 ) )
| ~ ~ ( in @ SY1369 @ SY1371 @ ( sK14_SY342 @ SY1372 @ SY1371 @ SY1370 @ SY1369 @ SY1368 @ SV12 ) ) )
| ! [SY1373: $i] :
( ~ ( rel_s4 @ SY1372 @ SY1373 )
| ~ ( ~ ( rel_s4 @ SY1373 @ ( sK13_SY344 @ SY1373 @ SY1372 @ SY1371 @ SY1370 @ SY1369 @ SY1368 @ SV12 ) )
| ~ ~ ( in @ SY1371 @ SY1369 @ ( sK13_SY344 @ SY1373 @ SY1372 @ SY1371 @ SY1370 @ SY1369 @ SY1368 @ SV12 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV13: $i] :
( ( ! [SY1374: $i] :
( ~ ( rel_s4 @ SV13 @ SY1374 )
| ! [SY1375: mu] :
( ~ ( exists_in_world @ SY1375 @ SY1374 )
| ! [SY1376: $i] :
( ~ ( rel_s4 @ SY1374 @ SY1376 )
| ! [SY1377: mu] :
( ~ ( exists_in_world @ SY1377 @ SY1376 )
| ! [SY1378: $i] :
( ~ ( rel_s4 @ SY1376 @ SY1378 )
| ~ ( ~ ( rel_s4 @ SY1378 @ ( sK21_SY796 @ SY1378 @ SY1377 @ SY1376 @ SY1375 @ SY1374 @ SV13 ) )
| ~ ~ ( qmltpeq @ SY1375 @ SY1377 @ ( sK21_SY796 @ SY1378 @ SY1377 @ SY1376 @ SY1375 @ SY1374 @ SV13 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1378 @ SX6 )
| ( qmltpeq @ ( singleton @ SY1375 ) @ ( singleton @ SY1377 ) @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(95,plain,
( ( ~ ( rel_s4 @ sK1_SY120 @ sK2_SY1273 )
| ~ ~ ( ~ ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(96,plain,
! [SV14: $i] :
( ( ! [SY1380: $i] :
( ~ ( rel_s4 @ SV14 @ SY1380 )
| ! [SY1381: mu] :
( ~ ( exists_in_world @ SY1381 @ SY1380 )
| ! [SY1382: $i] :
( ~ ( rel_s4 @ SY1380 @ SY1382 )
| ~ ( ~ ! [SY1383: mu] :
( ~ ( exists_in_world @ SY1383 @ SY1382 )
| ! [SY1384: $i] :
( ~ ( rel_s4 @ SY1382 @ SY1384 )
| ~ ( ~ ( rel_s4 @ SY1384 @ ( sK12_SY238 @ SY1384 @ SY1383 @ SY1382 @ SY1381 @ SY1380 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY1381 ) @ SY1383 ) @ empty_set @ ( sK12_SY238 @ SY1384 @ SY1383 @ SY1382 @ SY1381 @ SY1380 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1384 @ SX6 )
| ( in @ SY1381 @ SY1383 @ SX6 ) ) ) )
| ~ ! [SY1386: mu] :
( ~ ( exists_in_world @ SY1386 @ SY1382 )
| ! [SY1387: $i] :
( ~ ( rel_s4 @ SY1382 @ SY1387 )
| ~ ( ~ ( rel_s4 @ SY1387 @ ( sK11_SY241 @ SY1387 @ SY1386 @ SY1382 @ SY1381 @ SY1380 @ SV14 ) )
| ~ ~ ( in @ SY1381 @ SY1386 @ ( sK11_SY241 @ SY1387 @ SY1386 @ SY1382 @ SY1381 @ SY1380 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1387 @ SX6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1381 ) @ SY1386 ) @ empty_set @ SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV15: $i] :
( ( ! [SY1389: $i] :
( ~ ( rel_s4 @ SV15 @ SY1389 )
| ! [SY1390: mu] :
( ~ ( exists_in_world @ SY1390 @ SY1389 )
| ! [SY1391: $i] :
( ~ ( rel_s4 @ SY1389 @ SY1391 )
| ! [SY1392: mu] :
( ~ ( exists_in_world @ SY1392 @ SY1391 )
| ! [SY1393: $i] :
( ~ ( rel_s4 @ SY1391 @ SY1393 )
| ! [SY1394: mu] :
( ~ ( exists_in_world @ SY1394 @ SY1393 )
| ! [SY1395: $i] :
( ~ ( rel_s4 @ SY1393 @ SY1395 )
| ~ ( ~ ( rel_s4 @ SY1395 @ ( sK22_SY893 @ SY1395 @ SY1394 @ SY1393 @ SY1392 @ SY1391 @ SY1390 @ SY1389 @ SV15 ) )
| ~ ~ ( qmltpeq @ SY1390 @ SY1392 @ ( sK22_SY893 @ SY1395 @ SY1394 @ SY1393 @ SY1392 @ SY1391 @ SY1390 @ SY1389 @ SV15 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1395 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1394 @ SY1390 ) @ ( set_difference @ SY1394 @ SY1392 ) @ SX8 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV2: $i,SV16: mu] :
( ( exists_in_world @ ( singleton @ SV16 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV3: $i,SV17: mu] :
( ( ! [SY1397: mu] : ( exists_in_world @ ( set_difference @ SV17 @ SY1397 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV18: $i,SV4: $i] :
( ( ~ ( rel_s4 @ SV4 @ SV18 )
| ! [SY1398: mu] :
( ~ ( exists_in_world @ SY1398 @ SV18 )
| ! [SY1399: $i] :
( ~ ( rel_s4 @ SV18 @ SY1399 )
| ( qmltpeq @ SY1398 @ SY1398 @ SY1399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( rel_s4 @ SV5 @ SV19 )
| ( empty @ empty_set @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV20: $i,SV6: $i] :
( ( ~ ( rel_s4 @ SV6 @ SV20 )
| ! [SY1400: mu] :
( ~ ( exists_in_world @ SY1400 @ SV20 )
| ! [SY1401: $i] :
( ~ ( rel_s4 @ SV20 @ SY1401 )
| ! [SY1402: mu] :
( ~ ( exists_in_world @ SY1402 @ SY1401 )
| ! [SY1403: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1403 )
| ! [SY1404: mu] :
( ~ ( exists_in_world @ SY1404 @ SY1403 )
| ! [SY1405: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1405 )
| ~ ( ~ ( rel_s4 @ SY1405 @ ( sK16_SY471 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SY1400 @ SY1402 @ ( sK16_SY471 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1405 @ ( sK15_SY472 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1404 @ SY1400 @ ( sK15_SY472 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1405 @ SX8 )
| ( in @ SY1404 @ SY1402 @ SX8 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( rel_s4 @ SV7 @ SV21 )
| ! [SY1407: mu] :
( ~ ( exists_in_world @ SY1407 @ SV21 )
| ! [SY1408: $i] :
( ~ ( rel_s4 @ SV21 @ SY1408 )
| ! [SY1409: mu] :
( ~ ( exists_in_world @ SY1409 @ SY1408 )
| ! [SY1410: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1410 )
| ~ ( ~ ( rel_s4 @ SY1410 @ ( sK20_SY718 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SY1407 @ SY1409 @ ( sK20_SY718 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1410 @ ( sK19_SY719 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SY1407 @ ( sK19_SY719 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1410 @ SX6 )
| ( empty @ SY1409 @ SX6 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( rel_s4 @ SV8 @ SV22 )
| ! [SY1412: mu] :
( ~ ( exists_in_world @ SY1412 @ SV22 )
| ! [SY1413: $i] :
( ~ ( rel_s4 @ SV22 @ SY1413 )
| ! [SY1414: mu] :
( ~ ( exists_in_world @ SY1414 @ SY1413 )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1415 )
| ! [SY1416: mu] :
( ~ ( exists_in_world @ SY1416 @ SY1415 )
| ! [SY1417: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1417 )
| ~ ( ~ ( rel_s4 @ SY1417 @ ( sK18_SY608 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SY1412 @ SY1414 @ ( sK18_SY608 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1417 @ ( sK17_SY609 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SY1412 @ SY1416 @ ( sK17_SY609 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1417 @ SX8 )
| ( in @ SY1414 @ SY1416 @ SX8 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV23: $i,SV9: $i] :
( ( ~ ( rel_s4 @ SV9 @ SV23 )
| ! [SY1419: mu] :
( ~ ( exists_in_world @ SY1419 @ SV23 )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV23 @ SY1420 )
| ! [SY1421: mu] :
( ~ ( exists_in_world @ SY1421 @ SY1420 )
| ! [SY1422: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1422 )
| ! [SY1423: mu] :
( ~ ( exists_in_world @ SY1423 @ SY1422 )
| ! [SY1424: $i] :
( ~ ( rel_s4 @ SY1422 @ SY1424 )
| ~ ( ~ ( rel_s4 @ SY1424 @ ( sK23_SY998 @ SY1424 @ SY1423 @ SY1422 @ SY1421 @ SY1420 @ SY1419 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SY1419 @ SY1421 @ ( sK23_SY998 @ SY1424 @ SY1423 @ SY1422 @ SY1421 @ SY1420 @ SY1419 @ SV23 @ SV9 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1424 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1419 @ SY1423 ) @ ( set_difference @ SY1421 @ SY1423 ) @ SX8 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( rel_s4 @ SV10 @ SV24 )
| ! [SY1426: mu] :
( ~ ( exists_in_world @ SY1426 @ SV24 )
| ! [SY1427: $i] :
( ~ ( rel_s4 @ SV24 @ SY1427 )
| ! [SY1428: mu] :
( ~ ( exists_in_world @ SY1428 @ SY1427 )
| ! [SY1429: $i] :
( ~ ( rel_s4 @ SY1427 @ SY1429 )
| ~ ( ~ ( rel_s4 @ SY1429 @ ( sK26_SY1216 @ SY1429 @ SY1428 @ SY1427 @ SY1426 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SY1426 @ SY1428 @ ( sK26_SY1216 @ SY1429 @ SY1428 @ SY1427 @ SY1426 @ SV24 @ SV10 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1429 @ SX6 )
| ( qmltpeq @ SY1428 @ SY1426 @ SX6 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( rel_s4 @ SV11 @ SV25 )
| ! [SY1431: mu] :
( ~ ( exists_in_world @ SY1431 @ SV25 )
| ! [SY1432: $i] :
( ~ ( rel_s4 @ SV25 @ SY1432 )
| ! [SY1433: mu] :
( ~ ( exists_in_world @ SY1433 @ SY1432 )
| ! [SY1434: $i] :
( ~ ( rel_s4 @ SY1432 @ SY1434 )
| ! [SY1435: mu] :
( ~ ( exists_in_world @ SY1435 @ SY1434 )
| ! [SY1436: $i] :
( ~ ( rel_s4 @ SY1434 @ SY1436 )
| ~ ( ~ ( rel_s4 @ SY1436 @ ( sK25_SY1130 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1431 @ SY1433 @ ( sK25_SY1130 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1436 @ ( sK24_SY1105 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1433 @ SY1435 @ ( sK24_SY1105 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1436 @ SX8 )
| ( qmltpeq @ SY1431 @ SY1435 @ SX8 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( rel_s4 @ SV12 @ SV26 )
| ! [SY1438: mu] :
( ~ ( exists_in_world @ SY1438 @ SV26 )
| ! [SY1439: $i] :
( ~ ( rel_s4 @ SV26 @ SY1439 )
| ! [SY1440: mu] :
( ~ ( exists_in_world @ SY1440 @ SY1439 )
| ! [SY1441: $i] :
( ~ ( rel_s4 @ SY1439 @ SY1441 )
| ~ ( ~ ( rel_s4 @ SY1441 @ ( sK14_SY342 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1438 @ SY1440 @ ( sK14_SY342 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) ) )
| ! [SY1442: $i] :
( ~ ( rel_s4 @ SY1441 @ SY1442 )
| ~ ( ~ ( rel_s4 @ SY1442 @ ( sK13_SY344 @ SY1442 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1440 @ SY1438 @ ( sK13_SY344 @ SY1442 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( rel_s4 @ SV13 @ SV27 )
| ! [SY1443: mu] :
( ~ ( exists_in_world @ SY1443 @ SV27 )
| ! [SY1444: $i] :
( ~ ( rel_s4 @ SV27 @ SY1444 )
| ! [SY1445: mu] :
( ~ ( exists_in_world @ SY1445 @ SY1444 )
| ! [SY1446: $i] :
( ~ ( rel_s4 @ SY1444 @ SY1446 )
| ~ ( ~ ( rel_s4 @ SY1446 @ ( sK21_SY796 @ SY1446 @ SY1445 @ SY1444 @ SY1443 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SY1443 @ SY1445 @ ( sK21_SY796 @ SY1446 @ SY1445 @ SY1444 @ SY1443 @ SV27 @ SV13 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1446 @ SX6 )
| ( qmltpeq @ ( singleton @ SY1443 ) @ ( singleton @ SY1445 ) @ SX6 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
( ( ~ ( rel_s4 @ sK1_SY120 @ sK2_SY1273 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(111,plain,
( ( ~ ~ ( ~ ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(112,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ( rel_s4 @ SV14 @ SV28 )
| ! [SY1448: mu] :
( ~ ( exists_in_world @ SY1448 @ SV28 )
| ! [SY1449: $i] :
( ~ ( rel_s4 @ SV28 @ SY1449 )
| ~ ( ~ ! [SY1450: mu] :
( ~ ( exists_in_world @ SY1450 @ SY1449 )
| ! [SY1451: $i] :
( ~ ( rel_s4 @ SY1449 @ SY1451 )
| ~ ( ~ ( rel_s4 @ SY1451 @ ( sK12_SY238 @ SY1451 @ SY1450 @ SY1449 @ SY1448 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY1448 ) @ SY1450 ) @ empty_set @ ( sK12_SY238 @ SY1451 @ SY1450 @ SY1449 @ SY1448 @ SV28 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1451 @ SX6 )
| ( in @ SY1448 @ SY1450 @ SX6 ) ) ) )
| ~ ! [SY1453: mu] :
( ~ ( exists_in_world @ SY1453 @ SY1449 )
| ! [SY1454: $i] :
( ~ ( rel_s4 @ SY1449 @ SY1454 )
| ~ ( ~ ( rel_s4 @ SY1454 @ ( sK11_SY241 @ SY1454 @ SY1453 @ SY1449 @ SY1448 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SY1448 @ SY1453 @ ( sK11_SY241 @ SY1454 @ SY1453 @ SY1449 @ SY1448 @ SV28 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1454 @ SX6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1448 ) @ SY1453 ) @ empty_set @ SX6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( rel_s4 @ SV15 @ SV29 )
| ! [SY1456: mu] :
( ~ ( exists_in_world @ SY1456 @ SV29 )
| ! [SY1457: $i] :
( ~ ( rel_s4 @ SV29 @ SY1457 )
| ! [SY1458: mu] :
( ~ ( exists_in_world @ SY1458 @ SY1457 )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SY1457 @ SY1459 )
| ! [SY1460: mu] :
( ~ ( exists_in_world @ SY1460 @ SY1459 )
| ! [SY1461: $i] :
( ~ ( rel_s4 @ SY1459 @ SY1461 )
| ~ ( ~ ( rel_s4 @ SY1461 @ ( sK22_SY893 @ SY1461 @ SY1460 @ SY1459 @ SY1458 @ SY1457 @ SY1456 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SY1456 @ SY1458 @ ( sK22_SY893 @ SY1461 @ SY1460 @ SY1459 @ SY1458 @ SY1457 @ SY1456 @ SV29 @ SV15 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1461 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1460 @ SY1456 ) @ ( set_difference @ SY1460 @ SY1458 ) @ SX8 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV3: $i,SV30: mu,SV17: mu] :
( ( exists_in_world @ ( set_difference @ SV17 @ SV30 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV18: $i,SV4: $i] :
( ( ( ~ ( rel_s4 @ SV4 @ SV18 ) )
= $true )
| ( ( ! [SY1398: mu] :
( ~ ( exists_in_world @ SY1398 @ SV18 )
| ! [SY1399: $i] :
( ~ ( rel_s4 @ SV18 @ SY1399 )
| ( qmltpeq @ SY1398 @ SY1398 @ SY1399 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( rel_s4 @ SV5 @ SV19 ) )
= $true )
| ( ( empty @ empty_set @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( rel_s4 @ SV6 @ SV20 ) )
= $true )
| ( ( ! [SY1400: mu] :
( ~ ( exists_in_world @ SY1400 @ SV20 )
| ! [SY1401: $i] :
( ~ ( rel_s4 @ SV20 @ SY1401 )
| ! [SY1402: mu] :
( ~ ( exists_in_world @ SY1402 @ SY1401 )
| ! [SY1403: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1403 )
| ! [SY1404: mu] :
( ~ ( exists_in_world @ SY1404 @ SY1403 )
| ! [SY1405: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1405 )
| ~ ( ~ ( rel_s4 @ SY1405 @ ( sK16_SY471 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SY1400 @ SY1402 @ ( sK16_SY471 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1405 @ ( sK15_SY472 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1404 @ SY1400 @ ( sK15_SY472 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1405 @ SX8 )
| ( in @ SY1404 @ SY1402 @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( rel_s4 @ SV7 @ SV21 ) )
= $true )
| ( ( ! [SY1407: mu] :
( ~ ( exists_in_world @ SY1407 @ SV21 )
| ! [SY1408: $i] :
( ~ ( rel_s4 @ SV21 @ SY1408 )
| ! [SY1409: mu] :
( ~ ( exists_in_world @ SY1409 @ SY1408 )
| ! [SY1410: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1410 )
| ~ ( ~ ( rel_s4 @ SY1410 @ ( sK20_SY718 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SY1407 @ SY1409 @ ( sK20_SY718 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1410 @ ( sK19_SY719 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SY1407 @ ( sK19_SY719 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1410 @ SX6 )
| ( empty @ SY1409 @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( rel_s4 @ SV8 @ SV22 ) )
= $true )
| ( ( ! [SY1412: mu] :
( ~ ( exists_in_world @ SY1412 @ SV22 )
| ! [SY1413: $i] :
( ~ ( rel_s4 @ SV22 @ SY1413 )
| ! [SY1414: mu] :
( ~ ( exists_in_world @ SY1414 @ SY1413 )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1415 )
| ! [SY1416: mu] :
( ~ ( exists_in_world @ SY1416 @ SY1415 )
| ! [SY1417: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1417 )
| ~ ( ~ ( rel_s4 @ SY1417 @ ( sK18_SY608 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SY1412 @ SY1414 @ ( sK18_SY608 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1417 @ ( sK17_SY609 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SY1412 @ SY1416 @ ( sK17_SY609 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1417 @ SX8 )
| ( in @ SY1414 @ SY1416 @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV23: $i,SV9: $i] :
( ( ( ~ ( rel_s4 @ SV9 @ SV23 ) )
= $true )
| ( ( ! [SY1419: mu] :
( ~ ( exists_in_world @ SY1419 @ SV23 )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV23 @ SY1420 )
| ! [SY1421: mu] :
( ~ ( exists_in_world @ SY1421 @ SY1420 )
| ! [SY1422: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1422 )
| ! [SY1423: mu] :
( ~ ( exists_in_world @ SY1423 @ SY1422 )
| ! [SY1424: $i] :
( ~ ( rel_s4 @ SY1422 @ SY1424 )
| ~ ( ~ ( rel_s4 @ SY1424 @ ( sK23_SY998 @ SY1424 @ SY1423 @ SY1422 @ SY1421 @ SY1420 @ SY1419 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SY1419 @ SY1421 @ ( sK23_SY998 @ SY1424 @ SY1423 @ SY1422 @ SY1421 @ SY1420 @ SY1419 @ SV23 @ SV9 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1424 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1419 @ SY1423 ) @ ( set_difference @ SY1421 @ SY1423 ) @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( rel_s4 @ SV10 @ SV24 ) )
= $true )
| ( ( ! [SY1426: mu] :
( ~ ( exists_in_world @ SY1426 @ SV24 )
| ! [SY1427: $i] :
( ~ ( rel_s4 @ SV24 @ SY1427 )
| ! [SY1428: mu] :
( ~ ( exists_in_world @ SY1428 @ SY1427 )
| ! [SY1429: $i] :
( ~ ( rel_s4 @ SY1427 @ SY1429 )
| ~ ( ~ ( rel_s4 @ SY1429 @ ( sK26_SY1216 @ SY1429 @ SY1428 @ SY1427 @ SY1426 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SY1426 @ SY1428 @ ( sK26_SY1216 @ SY1429 @ SY1428 @ SY1427 @ SY1426 @ SV24 @ SV10 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1429 @ SX6 )
| ( qmltpeq @ SY1428 @ SY1426 @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( rel_s4 @ SV11 @ SV25 ) )
= $true )
| ( ( ! [SY1431: mu] :
( ~ ( exists_in_world @ SY1431 @ SV25 )
| ! [SY1432: $i] :
( ~ ( rel_s4 @ SV25 @ SY1432 )
| ! [SY1433: mu] :
( ~ ( exists_in_world @ SY1433 @ SY1432 )
| ! [SY1434: $i] :
( ~ ( rel_s4 @ SY1432 @ SY1434 )
| ! [SY1435: mu] :
( ~ ( exists_in_world @ SY1435 @ SY1434 )
| ! [SY1436: $i] :
( ~ ( rel_s4 @ SY1434 @ SY1436 )
| ~ ( ~ ( rel_s4 @ SY1436 @ ( sK25_SY1130 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1431 @ SY1433 @ ( sK25_SY1130 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1436 @ ( sK24_SY1105 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1433 @ SY1435 @ ( sK24_SY1105 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1436 @ SX8 )
| ( qmltpeq @ SY1431 @ SY1435 @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( rel_s4 @ SV12 @ SV26 ) )
= $true )
| ( ( ! [SY1438: mu] :
( ~ ( exists_in_world @ SY1438 @ SV26 )
| ! [SY1439: $i] :
( ~ ( rel_s4 @ SV26 @ SY1439 )
| ! [SY1440: mu] :
( ~ ( exists_in_world @ SY1440 @ SY1439 )
| ! [SY1441: $i] :
( ~ ( rel_s4 @ SY1439 @ SY1441 )
| ~ ( ~ ( rel_s4 @ SY1441 @ ( sK14_SY342 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1438 @ SY1440 @ ( sK14_SY342 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) ) )
| ! [SY1442: $i] :
( ~ ( rel_s4 @ SY1441 @ SY1442 )
| ~ ( ~ ( rel_s4 @ SY1442 @ ( sK13_SY344 @ SY1442 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1440 @ SY1438 @ ( sK13_SY344 @ SY1442 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( rel_s4 @ SV13 @ SV27 ) )
= $true )
| ( ( ! [SY1443: mu] :
( ~ ( exists_in_world @ SY1443 @ SV27 )
| ! [SY1444: $i] :
( ~ ( rel_s4 @ SV27 @ SY1444 )
| ! [SY1445: mu] :
( ~ ( exists_in_world @ SY1445 @ SY1444 )
| ! [SY1446: $i] :
( ~ ( rel_s4 @ SY1444 @ SY1446 )
| ~ ( ~ ( rel_s4 @ SY1446 @ ( sK21_SY796 @ SY1446 @ SY1445 @ SY1444 @ SY1443 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SY1443 @ SY1445 @ ( sK21_SY796 @ SY1446 @ SY1445 @ SY1444 @ SY1443 @ SV27 @ SV13 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1446 @ SX6 )
| ( qmltpeq @ ( singleton @ SY1443 ) @ ( singleton @ SY1445 ) @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(125,plain,
( ( rel_s4 @ sK1_SY120 @ sK2_SY1273 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(126,plain,
( ( ~ ( ~ ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(127,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( rel_s4 @ SV14 @ SV28 ) )
= $true )
| ( ( ! [SY1448: mu] :
( ~ ( exists_in_world @ SY1448 @ SV28 )
| ! [SY1449: $i] :
( ~ ( rel_s4 @ SV28 @ SY1449 )
| ~ ( ~ ! [SY1450: mu] :
( ~ ( exists_in_world @ SY1450 @ SY1449 )
| ! [SY1451: $i] :
( ~ ( rel_s4 @ SY1449 @ SY1451 )
| ~ ( ~ ( rel_s4 @ SY1451 @ ( sK12_SY238 @ SY1451 @ SY1450 @ SY1449 @ SY1448 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY1448 ) @ SY1450 ) @ empty_set @ ( sK12_SY238 @ SY1451 @ SY1450 @ SY1449 @ SY1448 @ SV28 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1451 @ SX6 )
| ( in @ SY1448 @ SY1450 @ SX6 ) ) ) )
| ~ ! [SY1453: mu] :
( ~ ( exists_in_world @ SY1453 @ SY1449 )
| ! [SY1454: $i] :
( ~ ( rel_s4 @ SY1449 @ SY1454 )
| ~ ( ~ ( rel_s4 @ SY1454 @ ( sK11_SY241 @ SY1454 @ SY1453 @ SY1449 @ SY1448 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SY1448 @ SY1453 @ ( sK11_SY241 @ SY1454 @ SY1453 @ SY1449 @ SY1448 @ SV28 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1454 @ SX6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1448 ) @ SY1453 ) @ empty_set @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( rel_s4 @ SV15 @ SV29 ) )
= $true )
| ( ( ! [SY1456: mu] :
( ~ ( exists_in_world @ SY1456 @ SV29 )
| ! [SY1457: $i] :
( ~ ( rel_s4 @ SV29 @ SY1457 )
| ! [SY1458: mu] :
( ~ ( exists_in_world @ SY1458 @ SY1457 )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SY1457 @ SY1459 )
| ! [SY1460: mu] :
( ~ ( exists_in_world @ SY1460 @ SY1459 )
| ! [SY1461: $i] :
( ~ ( rel_s4 @ SY1459 @ SY1461 )
| ~ ( ~ ( rel_s4 @ SY1461 @ ( sK22_SY893 @ SY1461 @ SY1460 @ SY1459 @ SY1458 @ SY1457 @ SY1456 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SY1456 @ SY1458 @ ( sK22_SY893 @ SY1461 @ SY1460 @ SY1459 @ SY1458 @ SY1457 @ SY1456 @ SV29 @ SV15 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1461 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1460 @ SY1456 ) @ ( set_difference @ SY1460 @ SY1458 ) @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV18: $i,SV4: $i] :
( ( ( rel_s4 @ SV4 @ SV18 )
= $false )
| ( ( ! [SY1398: mu] :
( ~ ( exists_in_world @ SY1398 @ SV18 )
| ! [SY1399: $i] :
( ~ ( rel_s4 @ SV18 @ SY1399 )
| ( qmltpeq @ SY1398 @ SY1398 @ SY1399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV19: $i,SV5: $i] :
( ( ( rel_s4 @ SV5 @ SV19 )
= $false )
| ( ( empty @ empty_set @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV20: $i,SV6: $i] :
( ( ( rel_s4 @ SV6 @ SV20 )
= $false )
| ( ( ! [SY1400: mu] :
( ~ ( exists_in_world @ SY1400 @ SV20 )
| ! [SY1401: $i] :
( ~ ( rel_s4 @ SV20 @ SY1401 )
| ! [SY1402: mu] :
( ~ ( exists_in_world @ SY1402 @ SY1401 )
| ! [SY1403: $i] :
( ~ ( rel_s4 @ SY1401 @ SY1403 )
| ! [SY1404: mu] :
( ~ ( exists_in_world @ SY1404 @ SY1403 )
| ! [SY1405: $i] :
( ~ ( rel_s4 @ SY1403 @ SY1405 )
| ~ ( ~ ( rel_s4 @ SY1405 @ ( sK16_SY471 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SY1400 @ SY1402 @ ( sK16_SY471 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1405 @ ( sK15_SY472 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1404 @ SY1400 @ ( sK15_SY472 @ SY1405 @ SY1404 @ SY1403 @ SY1402 @ SY1401 @ SY1400 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1405 @ SX8 )
| ( in @ SY1404 @ SY1402 @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV21: $i,SV7: $i] :
( ( ( rel_s4 @ SV7 @ SV21 )
= $false )
| ( ( ! [SY1407: mu] :
( ~ ( exists_in_world @ SY1407 @ SV21 )
| ! [SY1408: $i] :
( ~ ( rel_s4 @ SV21 @ SY1408 )
| ! [SY1409: mu] :
( ~ ( exists_in_world @ SY1409 @ SY1408 )
| ! [SY1410: $i] :
( ~ ( rel_s4 @ SY1408 @ SY1410 )
| ~ ( ~ ( rel_s4 @ SY1410 @ ( sK20_SY718 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SY1407 @ SY1409 @ ( sK20_SY718 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1410 @ ( sK19_SY719 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SY1407 @ ( sK19_SY719 @ SY1410 @ SY1409 @ SY1408 @ SY1407 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1410 @ SX6 )
| ( empty @ SY1409 @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV22: $i,SV8: $i] :
( ( ( rel_s4 @ SV8 @ SV22 )
= $false )
| ( ( ! [SY1412: mu] :
( ~ ( exists_in_world @ SY1412 @ SV22 )
| ! [SY1413: $i] :
( ~ ( rel_s4 @ SV22 @ SY1413 )
| ! [SY1414: mu] :
( ~ ( exists_in_world @ SY1414 @ SY1413 )
| ! [SY1415: $i] :
( ~ ( rel_s4 @ SY1413 @ SY1415 )
| ! [SY1416: mu] :
( ~ ( exists_in_world @ SY1416 @ SY1415 )
| ! [SY1417: $i] :
( ~ ( rel_s4 @ SY1415 @ SY1417 )
| ~ ( ~ ( rel_s4 @ SY1417 @ ( sK18_SY608 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SY1412 @ SY1414 @ ( sK18_SY608 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1417 @ ( sK17_SY609 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SY1412 @ SY1416 @ ( sK17_SY609 @ SY1417 @ SY1416 @ SY1415 @ SY1414 @ SY1413 @ SY1412 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1417 @ SX8 )
| ( in @ SY1414 @ SY1416 @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV23: $i,SV9: $i] :
( ( ( rel_s4 @ SV9 @ SV23 )
= $false )
| ( ( ! [SY1419: mu] :
( ~ ( exists_in_world @ SY1419 @ SV23 )
| ! [SY1420: $i] :
( ~ ( rel_s4 @ SV23 @ SY1420 )
| ! [SY1421: mu] :
( ~ ( exists_in_world @ SY1421 @ SY1420 )
| ! [SY1422: $i] :
( ~ ( rel_s4 @ SY1420 @ SY1422 )
| ! [SY1423: mu] :
( ~ ( exists_in_world @ SY1423 @ SY1422 )
| ! [SY1424: $i] :
( ~ ( rel_s4 @ SY1422 @ SY1424 )
| ~ ( ~ ( rel_s4 @ SY1424 @ ( sK23_SY998 @ SY1424 @ SY1423 @ SY1422 @ SY1421 @ SY1420 @ SY1419 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SY1419 @ SY1421 @ ( sK23_SY998 @ SY1424 @ SY1423 @ SY1422 @ SY1421 @ SY1420 @ SY1419 @ SV23 @ SV9 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1424 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1419 @ SY1423 ) @ ( set_difference @ SY1421 @ SY1423 ) @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV24: $i,SV10: $i] :
( ( ( rel_s4 @ SV10 @ SV24 )
= $false )
| ( ( ! [SY1426: mu] :
( ~ ( exists_in_world @ SY1426 @ SV24 )
| ! [SY1427: $i] :
( ~ ( rel_s4 @ SV24 @ SY1427 )
| ! [SY1428: mu] :
( ~ ( exists_in_world @ SY1428 @ SY1427 )
| ! [SY1429: $i] :
( ~ ( rel_s4 @ SY1427 @ SY1429 )
| ~ ( ~ ( rel_s4 @ SY1429 @ ( sK26_SY1216 @ SY1429 @ SY1428 @ SY1427 @ SY1426 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SY1426 @ SY1428 @ ( sK26_SY1216 @ SY1429 @ SY1428 @ SY1427 @ SY1426 @ SV24 @ SV10 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1429 @ SX6 )
| ( qmltpeq @ SY1428 @ SY1426 @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV25: $i,SV11: $i] :
( ( ( rel_s4 @ SV11 @ SV25 )
= $false )
| ( ( ! [SY1431: mu] :
( ~ ( exists_in_world @ SY1431 @ SV25 )
| ! [SY1432: $i] :
( ~ ( rel_s4 @ SV25 @ SY1432 )
| ! [SY1433: mu] :
( ~ ( exists_in_world @ SY1433 @ SY1432 )
| ! [SY1434: $i] :
( ~ ( rel_s4 @ SY1432 @ SY1434 )
| ! [SY1435: mu] :
( ~ ( exists_in_world @ SY1435 @ SY1434 )
| ! [SY1436: $i] :
( ~ ( rel_s4 @ SY1434 @ SY1436 )
| ~ ( ~ ( rel_s4 @ SY1436 @ ( sK25_SY1130 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1431 @ SY1433 @ ( sK25_SY1130 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1436 @ ( sK24_SY1105 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1433 @ SY1435 @ ( sK24_SY1105 @ SY1436 @ SY1435 @ SY1434 @ SY1433 @ SY1432 @ SY1431 @ SV25 @ SV11 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1436 @ SX8 )
| ( qmltpeq @ SY1431 @ SY1435 @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV26: $i,SV12: $i] :
( ( ( rel_s4 @ SV12 @ SV26 )
= $false )
| ( ( ! [SY1438: mu] :
( ~ ( exists_in_world @ SY1438 @ SV26 )
| ! [SY1439: $i] :
( ~ ( rel_s4 @ SV26 @ SY1439 )
| ! [SY1440: mu] :
( ~ ( exists_in_world @ SY1440 @ SY1439 )
| ! [SY1441: $i] :
( ~ ( rel_s4 @ SY1439 @ SY1441 )
| ~ ( ~ ( rel_s4 @ SY1441 @ ( sK14_SY342 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1438 @ SY1440 @ ( sK14_SY342 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) ) )
| ! [SY1442: $i] :
( ~ ( rel_s4 @ SY1441 @ SY1442 )
| ~ ( ~ ( rel_s4 @ SY1442 @ ( sK13_SY344 @ SY1442 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1440 @ SY1438 @ ( sK13_SY344 @ SY1442 @ SY1441 @ SY1440 @ SY1439 @ SY1438 @ SV26 @ SV12 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV27: $i,SV13: $i] :
( ( ( rel_s4 @ SV13 @ SV27 )
= $false )
| ( ( ! [SY1443: mu] :
( ~ ( exists_in_world @ SY1443 @ SV27 )
| ! [SY1444: $i] :
( ~ ( rel_s4 @ SV27 @ SY1444 )
| ! [SY1445: mu] :
( ~ ( exists_in_world @ SY1445 @ SY1444 )
| ! [SY1446: $i] :
( ~ ( rel_s4 @ SY1444 @ SY1446 )
| ~ ( ~ ( rel_s4 @ SY1446 @ ( sK21_SY796 @ SY1446 @ SY1445 @ SY1444 @ SY1443 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SY1443 @ SY1445 @ ( sK21_SY796 @ SY1446 @ SY1445 @ SY1444 @ SY1443 @ SV27 @ SV13 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1446 @ SX6 )
| ( qmltpeq @ ( singleton @ SY1443 ) @ ( singleton @ SY1445 ) @ SX6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(139,plain,
( ( ~ ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
| ~ ~ ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(140,plain,
! [SV28: $i,SV14: $i] :
( ( ( rel_s4 @ SV14 @ SV28 )
= $false )
| ( ( ! [SY1448: mu] :
( ~ ( exists_in_world @ SY1448 @ SV28 )
| ! [SY1449: $i] :
( ~ ( rel_s4 @ SV28 @ SY1449 )
| ~ ( ~ ! [SY1450: mu] :
( ~ ( exists_in_world @ SY1450 @ SY1449 )
| ! [SY1451: $i] :
( ~ ( rel_s4 @ SY1449 @ SY1451 )
| ~ ( ~ ( rel_s4 @ SY1451 @ ( sK12_SY238 @ SY1451 @ SY1450 @ SY1449 @ SY1448 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY1448 ) @ SY1450 ) @ empty_set @ ( sK12_SY238 @ SY1451 @ SY1450 @ SY1449 @ SY1448 @ SV28 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1451 @ SX6 )
| ( in @ SY1448 @ SY1450 @ SX6 ) ) ) )
| ~ ! [SY1453: mu] :
( ~ ( exists_in_world @ SY1453 @ SY1449 )
| ! [SY1454: $i] :
( ~ ( rel_s4 @ SY1449 @ SY1454 )
| ~ ( ~ ( rel_s4 @ SY1454 @ ( sK11_SY241 @ SY1454 @ SY1453 @ SY1449 @ SY1448 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SY1448 @ SY1453 @ ( sK11_SY241 @ SY1454 @ SY1453 @ SY1449 @ SY1448 @ SV28 @ SV14 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1454 @ SX6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY1448 ) @ SY1453 ) @ empty_set @ SX6 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(141,plain,
! [SV29: $i,SV15: $i] :
( ( ( rel_s4 @ SV15 @ SV29 )
= $false )
| ( ( ! [SY1456: mu] :
( ~ ( exists_in_world @ SY1456 @ SV29 )
| ! [SY1457: $i] :
( ~ ( rel_s4 @ SV29 @ SY1457 )
| ! [SY1458: mu] :
( ~ ( exists_in_world @ SY1458 @ SY1457 )
| ! [SY1459: $i] :
( ~ ( rel_s4 @ SY1457 @ SY1459 )
| ! [SY1460: mu] :
( ~ ( exists_in_world @ SY1460 @ SY1459 )
| ! [SY1461: $i] :
( ~ ( rel_s4 @ SY1459 @ SY1461 )
| ~ ( ~ ( rel_s4 @ SY1461 @ ( sK22_SY893 @ SY1461 @ SY1460 @ SY1459 @ SY1458 @ SY1457 @ SY1456 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SY1456 @ SY1458 @ ( sK22_SY893 @ SY1461 @ SY1460 @ SY1459 @ SY1458 @ SY1457 @ SY1456 @ SV29 @ SV15 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1461 @ SX8 )
| ( qmltpeq @ ( set_difference @ SY1460 @ SY1456 ) @ ( set_difference @ SY1460 @ SY1458 ) @ SX8 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(142,plain,
! [SV4: $i,SV18: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV18 )
| ! [SY1463: $i] :
( ~ ( rel_s4 @ SV18 @ SY1463 )
| ( qmltpeq @ SV31 @ SV31 @ SY1463 ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(143,plain,
! [SV6: $i,SV20: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV20 )
| ! [SY1464: $i] :
( ~ ( rel_s4 @ SV20 @ SY1464 )
| ! [SY1465: mu] :
( ~ ( exists_in_world @ SY1465 @ SY1464 )
| ! [SY1466: $i] :
( ~ ( rel_s4 @ SY1464 @ SY1466 )
| ! [SY1467: mu] :
( ~ ( exists_in_world @ SY1467 @ SY1466 )
| ! [SY1468: $i] :
( ~ ( rel_s4 @ SY1466 @ SY1468 )
| ~ ( ~ ( rel_s4 @ SY1468 @ ( sK16_SY471 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SY1465 @ ( sK16_SY471 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1468 @ ( sK15_SY472 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1467 @ SV32 @ ( sK15_SY472 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1468 @ SX8 )
| ( in @ SY1467 @ SY1465 @ SX8 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV7: $i,SV21: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV21 )
| ! [SY1470: $i] :
( ~ ( rel_s4 @ SV21 @ SY1470 )
| ! [SY1471: mu] :
( ~ ( exists_in_world @ SY1471 @ SY1470 )
| ! [SY1472: $i] :
( ~ ( rel_s4 @ SY1470 @ SY1472 )
| ~ ( ~ ( rel_s4 @ SY1472 @ ( sK20_SY718 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SY1471 @ ( sK20_SY718 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1472 @ ( sK19_SY719 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1472 @ SX6 )
| ( empty @ SY1471 @ SX6 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV8: $i,SV22: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV22 )
| ! [SY1474: $i] :
( ~ ( rel_s4 @ SV22 @ SY1474 )
| ! [SY1475: mu] :
( ~ ( exists_in_world @ SY1475 @ SY1474 )
| ! [SY1476: $i] :
( ~ ( rel_s4 @ SY1474 @ SY1476 )
| ! [SY1477: mu] :
( ~ ( exists_in_world @ SY1477 @ SY1476 )
| ! [SY1478: $i] :
( ~ ( rel_s4 @ SY1476 @ SY1478 )
| ~ ( ~ ( rel_s4 @ SY1478 @ ( sK18_SY608 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SY1475 @ ( sK18_SY608 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1478 @ ( sK17_SY609 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1477 @ ( sK17_SY609 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1478 @ SX8 )
| ( in @ SY1475 @ SY1477 @ SX8 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV9: $i,SV23: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV23 )
| ! [SY1480: $i] :
( ~ ( rel_s4 @ SV23 @ SY1480 )
| ! [SY1481: mu] :
( ~ ( exists_in_world @ SY1481 @ SY1480 )
| ! [SY1482: $i] :
( ~ ( rel_s4 @ SY1480 @ SY1482 )
| ! [SY1483: mu] :
( ~ ( exists_in_world @ SY1483 @ SY1482 )
| ! [SY1484: $i] :
( ~ ( rel_s4 @ SY1482 @ SY1484 )
| ~ ( ~ ( rel_s4 @ SY1484 @ ( sK23_SY998 @ SY1484 @ SY1483 @ SY1482 @ SY1481 @ SY1480 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SY1481 @ ( sK23_SY998 @ SY1484 @ SY1483 @ SY1482 @ SY1481 @ SY1480 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SY1484 @ SY1485 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1483 ) @ ( set_difference @ SY1481 @ SY1483 ) @ SY1485 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV10: $i,SV24: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV24 )
| ! [SY1486: $i] :
( ~ ( rel_s4 @ SV24 @ SY1486 )
| ! [SY1487: mu] :
( ~ ( exists_in_world @ SY1487 @ SY1486 )
| ! [SY1488: $i] :
( ~ ( rel_s4 @ SY1486 @ SY1488 )
| ~ ( ~ ( rel_s4 @ SY1488 @ ( sK26_SY1216 @ SY1488 @ SY1487 @ SY1486 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SY1487 @ ( sK26_SY1216 @ SY1488 @ SY1487 @ SY1486 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SY1488 @ SY1489 )
| ( qmltpeq @ SY1487 @ SV36 @ SY1489 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV11: $i,SV25: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV25 )
| ! [SY1490: $i] :
( ~ ( rel_s4 @ SV25 @ SY1490 )
| ! [SY1491: mu] :
( ~ ( exists_in_world @ SY1491 @ SY1490 )
| ! [SY1492: $i] :
( ~ ( rel_s4 @ SY1490 @ SY1492 )
| ! [SY1493: mu] :
( ~ ( exists_in_world @ SY1493 @ SY1492 )
| ! [SY1494: $i] :
( ~ ( rel_s4 @ SY1492 @ SY1494 )
| ~ ( ~ ( rel_s4 @ SY1494 @ ( sK25_SY1130 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SY1491 @ ( sK25_SY1130 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1494 @ ( sK24_SY1105 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1491 @ SY1493 @ ( sK24_SY1105 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1494 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1493 @ SY1495 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV12: $i,SV26: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV26 )
| ! [SY1496: $i] :
( ~ ( rel_s4 @ SV26 @ SY1496 )
| ! [SY1497: mu] :
( ~ ( exists_in_world @ SY1497 @ SY1496 )
| ! [SY1498: $i] :
( ~ ( rel_s4 @ SY1496 @ SY1498 )
| ~ ( ~ ( rel_s4 @ SY1498 @ ( sK14_SY342 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SY1497 @ ( sK14_SY342 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1499: $i] :
( ~ ( rel_s4 @ SY1498 @ SY1499 )
| ~ ( ~ ( rel_s4 @ SY1499 @ ( sK13_SY344 @ SY1499 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1497 @ SV38 @ ( sK13_SY344 @ SY1499 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV13: $i,SV27: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV27 )
| ! [SY1500: $i] :
( ~ ( rel_s4 @ SV27 @ SY1500 )
| ! [SY1501: mu] :
( ~ ( exists_in_world @ SY1501 @ SY1500 )
| ! [SY1502: $i] :
( ~ ( rel_s4 @ SY1500 @ SY1502 )
| ~ ( ~ ( rel_s4 @ SY1502 @ ( sK21_SY796 @ SY1502 @ SY1501 @ SY1500 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SY1501 @ ( sK21_SY796 @ SY1502 @ SY1501 @ SY1500 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SY1502 @ SY1503 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SY1501 ) @ SY1503 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
( ( ~ ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(152,plain,
( ( ~ ~ ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(153,plain,
! [SV14: $i,SV28: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV28 )
| ! [SY1504: $i] :
( ~ ( rel_s4 @ SV28 @ SY1504 )
| ~ ( ~ ! [SY1505: mu] :
( ~ ( exists_in_world @ SY1505 @ SY1504 )
| ! [SY1506: $i] :
( ~ ( rel_s4 @ SY1504 @ SY1506 )
| ~ ( ~ ( rel_s4 @ SY1506 @ ( sK12_SY238 @ SY1506 @ SY1505 @ SY1504 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1505 ) @ empty_set @ ( sK12_SY238 @ SY1506 @ SY1505 @ SY1504 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1506 @ SY1507 )
| ( in @ SV40 @ SY1505 @ SY1507 ) ) ) )
| ~ ! [SY1508: mu] :
( ~ ( exists_in_world @ SY1508 @ SY1504 )
| ! [SY1509: $i] :
( ~ ( rel_s4 @ SY1504 @ SY1509 )
| ~ ( ~ ( rel_s4 @ SY1509 @ ( sK11_SY241 @ SY1509 @ SY1508 @ SY1504 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1508 @ ( sK11_SY241 @ SY1509 @ SY1508 @ SY1504 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1509 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1508 ) @ empty_set @ SY1510 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV15: $i,SV29: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV29 )
| ! [SY1511: $i] :
( ~ ( rel_s4 @ SV29 @ SY1511 )
| ! [SY1512: mu] :
( ~ ( exists_in_world @ SY1512 @ SY1511 )
| ! [SY1513: $i] :
( ~ ( rel_s4 @ SY1511 @ SY1513 )
| ! [SY1514: mu] :
( ~ ( exists_in_world @ SY1514 @ SY1513 )
| ! [SY1515: $i] :
( ~ ( rel_s4 @ SY1513 @ SY1515 )
| ~ ( ~ ( rel_s4 @ SY1515 @ ( sK22_SY893 @ SY1515 @ SY1514 @ SY1513 @ SY1512 @ SY1511 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SY1512 @ ( sK22_SY893 @ SY1515 @ SY1514 @ SY1513 @ SY1512 @ SY1511 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1516: $i] :
( ~ ( rel_s4 @ SY1515 @ SY1516 )
| ( qmltpeq @ ( set_difference @ SY1514 @ SV41 ) @ ( set_difference @ SY1514 @ SY1512 ) @ SY1516 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV4: $i,SV18: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV18 ) )
= $true )
| ( ( ! [SY1463: $i] :
( ~ ( rel_s4 @ SV18 @ SY1463 )
| ( qmltpeq @ SV31 @ SV31 @ SY1463 ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(156,plain,
! [SV6: $i,SV20: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV20 ) )
= $true )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV20 @ SY1464 )
| ! [SY1465: mu] :
( ~ ( exists_in_world @ SY1465 @ SY1464 )
| ! [SY1466: $i] :
( ~ ( rel_s4 @ SY1464 @ SY1466 )
| ! [SY1467: mu] :
( ~ ( exists_in_world @ SY1467 @ SY1466 )
| ! [SY1468: $i] :
( ~ ( rel_s4 @ SY1466 @ SY1468 )
| ~ ( ~ ( rel_s4 @ SY1468 @ ( sK16_SY471 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SY1465 @ ( sK16_SY471 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1468 @ ( sK15_SY472 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1467 @ SV32 @ ( sK15_SY472 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1468 @ SX8 )
| ( in @ SY1467 @ SY1465 @ SX8 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(157,plain,
! [SV7: $i,SV21: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV21 ) )
= $true )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV21 @ SY1470 )
| ! [SY1471: mu] :
( ~ ( exists_in_world @ SY1471 @ SY1470 )
| ! [SY1472: $i] :
( ~ ( rel_s4 @ SY1470 @ SY1472 )
| ~ ( ~ ( rel_s4 @ SY1472 @ ( sK20_SY718 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SY1471 @ ( sK20_SY718 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1472 @ ( sK19_SY719 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1472 @ SX6 )
| ( empty @ SY1471 @ SX6 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV8: $i,SV22: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV22 ) )
= $true )
| ( ( ! [SY1474: $i] :
( ~ ( rel_s4 @ SV22 @ SY1474 )
| ! [SY1475: mu] :
( ~ ( exists_in_world @ SY1475 @ SY1474 )
| ! [SY1476: $i] :
( ~ ( rel_s4 @ SY1474 @ SY1476 )
| ! [SY1477: mu] :
( ~ ( exists_in_world @ SY1477 @ SY1476 )
| ! [SY1478: $i] :
( ~ ( rel_s4 @ SY1476 @ SY1478 )
| ~ ( ~ ( rel_s4 @ SY1478 @ ( sK18_SY608 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SY1475 @ ( sK18_SY608 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1478 @ ( sK17_SY609 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1477 @ ( sK17_SY609 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1478 @ SX8 )
| ( in @ SY1475 @ SY1477 @ SX8 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV9: $i,SV23: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV23 ) )
= $true )
| ( ( ! [SY1480: $i] :
( ~ ( rel_s4 @ SV23 @ SY1480 )
| ! [SY1481: mu] :
( ~ ( exists_in_world @ SY1481 @ SY1480 )
| ! [SY1482: $i] :
( ~ ( rel_s4 @ SY1480 @ SY1482 )
| ! [SY1483: mu] :
( ~ ( exists_in_world @ SY1483 @ SY1482 )
| ! [SY1484: $i] :
( ~ ( rel_s4 @ SY1482 @ SY1484 )
| ~ ( ~ ( rel_s4 @ SY1484 @ ( sK23_SY998 @ SY1484 @ SY1483 @ SY1482 @ SY1481 @ SY1480 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SY1481 @ ( sK23_SY998 @ SY1484 @ SY1483 @ SY1482 @ SY1481 @ SY1480 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SY1484 @ SY1485 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1483 ) @ ( set_difference @ SY1481 @ SY1483 ) @ SY1485 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV10: $i,SV24: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV24 ) )
= $true )
| ( ( ! [SY1486: $i] :
( ~ ( rel_s4 @ SV24 @ SY1486 )
| ! [SY1487: mu] :
( ~ ( exists_in_world @ SY1487 @ SY1486 )
| ! [SY1488: $i] :
( ~ ( rel_s4 @ SY1486 @ SY1488 )
| ~ ( ~ ( rel_s4 @ SY1488 @ ( sK26_SY1216 @ SY1488 @ SY1487 @ SY1486 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SY1487 @ ( sK26_SY1216 @ SY1488 @ SY1487 @ SY1486 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SY1488 @ SY1489 )
| ( qmltpeq @ SY1487 @ SV36 @ SY1489 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV11: $i,SV25: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV25 ) )
= $true )
| ( ( ! [SY1490: $i] :
( ~ ( rel_s4 @ SV25 @ SY1490 )
| ! [SY1491: mu] :
( ~ ( exists_in_world @ SY1491 @ SY1490 )
| ! [SY1492: $i] :
( ~ ( rel_s4 @ SY1490 @ SY1492 )
| ! [SY1493: mu] :
( ~ ( exists_in_world @ SY1493 @ SY1492 )
| ! [SY1494: $i] :
( ~ ( rel_s4 @ SY1492 @ SY1494 )
| ~ ( ~ ( rel_s4 @ SY1494 @ ( sK25_SY1130 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SY1491 @ ( sK25_SY1130 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1494 @ ( sK24_SY1105 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1491 @ SY1493 @ ( sK24_SY1105 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1494 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1493 @ SY1495 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV12: $i,SV26: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV26 ) )
= $true )
| ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV26 @ SY1496 )
| ! [SY1497: mu] :
( ~ ( exists_in_world @ SY1497 @ SY1496 )
| ! [SY1498: $i] :
( ~ ( rel_s4 @ SY1496 @ SY1498 )
| ~ ( ~ ( rel_s4 @ SY1498 @ ( sK14_SY342 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SY1497 @ ( sK14_SY342 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1499: $i] :
( ~ ( rel_s4 @ SY1498 @ SY1499 )
| ~ ( ~ ( rel_s4 @ SY1499 @ ( sK13_SY344 @ SY1499 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1497 @ SV38 @ ( sK13_SY344 @ SY1499 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV13: $i,SV27: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV27 ) )
= $true )
| ( ( ! [SY1500: $i] :
( ~ ( rel_s4 @ SV27 @ SY1500 )
| ! [SY1501: mu] :
( ~ ( exists_in_world @ SY1501 @ SY1500 )
| ! [SY1502: $i] :
( ~ ( rel_s4 @ SY1500 @ SY1502 )
| ~ ( ~ ( rel_s4 @ SY1502 @ ( sK21_SY796 @ SY1502 @ SY1501 @ SY1500 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SY1501 @ ( sK21_SY796 @ SY1502 @ SY1501 @ SY1500 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SY1502 @ SY1503 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SY1501 ) @ SY1503 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(164,plain,
( ( exists_in_world @ sK3_SY1283 @ sK2_SY1273 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(165,plain,
( ( ~ ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(166,plain,
! [SV14: $i,SV28: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV28 ) )
= $true )
| ( ( ! [SY1504: $i] :
( ~ ( rel_s4 @ SV28 @ SY1504 )
| ~ ( ~ ! [SY1505: mu] :
( ~ ( exists_in_world @ SY1505 @ SY1504 )
| ! [SY1506: $i] :
( ~ ( rel_s4 @ SY1504 @ SY1506 )
| ~ ( ~ ( rel_s4 @ SY1506 @ ( sK12_SY238 @ SY1506 @ SY1505 @ SY1504 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1505 ) @ empty_set @ ( sK12_SY238 @ SY1506 @ SY1505 @ SY1504 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1506 @ SY1507 )
| ( in @ SV40 @ SY1505 @ SY1507 ) ) ) )
| ~ ! [SY1508: mu] :
( ~ ( exists_in_world @ SY1508 @ SY1504 )
| ! [SY1509: $i] :
( ~ ( rel_s4 @ SY1504 @ SY1509 )
| ~ ( ~ ( rel_s4 @ SY1509 @ ( sK11_SY241 @ SY1509 @ SY1508 @ SY1504 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1508 @ ( sK11_SY241 @ SY1509 @ SY1508 @ SY1504 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1509 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1508 ) @ empty_set @ SY1510 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV15: $i,SV29: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV29 ) )
= $true )
| ( ( ! [SY1511: $i] :
( ~ ( rel_s4 @ SV29 @ SY1511 )
| ! [SY1512: mu] :
( ~ ( exists_in_world @ SY1512 @ SY1511 )
| ! [SY1513: $i] :
( ~ ( rel_s4 @ SY1511 @ SY1513 )
| ! [SY1514: mu] :
( ~ ( exists_in_world @ SY1514 @ SY1513 )
| ! [SY1515: $i] :
( ~ ( rel_s4 @ SY1513 @ SY1515 )
| ~ ( ~ ( rel_s4 @ SY1515 @ ( sK22_SY893 @ SY1515 @ SY1514 @ SY1513 @ SY1512 @ SY1511 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SY1512 @ ( sK22_SY893 @ SY1515 @ SY1514 @ SY1513 @ SY1512 @ SY1511 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1516: $i] :
( ~ ( rel_s4 @ SY1515 @ SY1516 )
| ( qmltpeq @ ( set_difference @ SY1514 @ SV41 ) @ ( set_difference @ SY1514 @ SY1512 ) @ SY1516 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV4: $i,SV18: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV18 )
= $false )
| ( ( ! [SY1463: $i] :
( ~ ( rel_s4 @ SV18 @ SY1463 )
| ( qmltpeq @ SV31 @ SV31 @ SY1463 ) ) )
= $true )
| ( ( rel_s4 @ SV4 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV6: $i,SV20: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( rel_s4 @ SV20 @ SY1464 )
| ! [SY1465: mu] :
( ~ ( exists_in_world @ SY1465 @ SY1464 )
| ! [SY1466: $i] :
( ~ ( rel_s4 @ SY1464 @ SY1466 )
| ! [SY1467: mu] :
( ~ ( exists_in_world @ SY1467 @ SY1466 )
| ! [SY1468: $i] :
( ~ ( rel_s4 @ SY1466 @ SY1468 )
| ~ ( ~ ( rel_s4 @ SY1468 @ ( sK16_SY471 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SY1465 @ ( sK16_SY471 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1468 @ ( sK15_SY472 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1467 @ SV32 @ ( sK15_SY472 @ SY1468 @ SY1467 @ SY1466 @ SY1465 @ SY1464 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1468 @ SX8 )
| ( in @ SY1467 @ SY1465 @ SX8 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV7: $i,SV21: $i,SV33: mu] :
( ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( ! [SY1470: $i] :
( ~ ( rel_s4 @ SV21 @ SY1470 )
| ! [SY1471: mu] :
( ~ ( exists_in_world @ SY1471 @ SY1470 )
| ! [SY1472: $i] :
( ~ ( rel_s4 @ SY1470 @ SY1472 )
| ~ ( ~ ( rel_s4 @ SY1472 @ ( sK20_SY718 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SY1471 @ ( sK20_SY718 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1472 @ ( sK19_SY719 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1472 @ SY1471 @ SY1470 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1472 @ SX6 )
| ( empty @ SY1471 @ SX6 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV8: $i,SV22: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( ! [SY1474: $i] :
( ~ ( rel_s4 @ SV22 @ SY1474 )
| ! [SY1475: mu] :
( ~ ( exists_in_world @ SY1475 @ SY1474 )
| ! [SY1476: $i] :
( ~ ( rel_s4 @ SY1474 @ SY1476 )
| ! [SY1477: mu] :
( ~ ( exists_in_world @ SY1477 @ SY1476 )
| ! [SY1478: $i] :
( ~ ( rel_s4 @ SY1476 @ SY1478 )
| ~ ( ~ ( rel_s4 @ SY1478 @ ( sK18_SY608 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SY1475 @ ( sK18_SY608 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1478 @ ( sK17_SY609 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1477 @ ( sK17_SY609 @ SY1478 @ SY1477 @ SY1476 @ SY1475 @ SY1474 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1478 @ SX8 )
| ( in @ SY1475 @ SY1477 @ SX8 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV9: $i,SV23: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( ! [SY1480: $i] :
( ~ ( rel_s4 @ SV23 @ SY1480 )
| ! [SY1481: mu] :
( ~ ( exists_in_world @ SY1481 @ SY1480 )
| ! [SY1482: $i] :
( ~ ( rel_s4 @ SY1480 @ SY1482 )
| ! [SY1483: mu] :
( ~ ( exists_in_world @ SY1483 @ SY1482 )
| ! [SY1484: $i] :
( ~ ( rel_s4 @ SY1482 @ SY1484 )
| ~ ( ~ ( rel_s4 @ SY1484 @ ( sK23_SY998 @ SY1484 @ SY1483 @ SY1482 @ SY1481 @ SY1480 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SY1481 @ ( sK23_SY998 @ SY1484 @ SY1483 @ SY1482 @ SY1481 @ SY1480 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SY1484 @ SY1485 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1483 ) @ ( set_difference @ SY1481 @ SY1483 ) @ SY1485 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV10: $i,SV24: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( ! [SY1486: $i] :
( ~ ( rel_s4 @ SV24 @ SY1486 )
| ! [SY1487: mu] :
( ~ ( exists_in_world @ SY1487 @ SY1486 )
| ! [SY1488: $i] :
( ~ ( rel_s4 @ SY1486 @ SY1488 )
| ~ ( ~ ( rel_s4 @ SY1488 @ ( sK26_SY1216 @ SY1488 @ SY1487 @ SY1486 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SY1487 @ ( sK26_SY1216 @ SY1488 @ SY1487 @ SY1486 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SY1488 @ SY1489 )
| ( qmltpeq @ SY1487 @ SV36 @ SY1489 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV11: $i,SV25: $i,SV37: mu] :
( ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( ! [SY1490: $i] :
( ~ ( rel_s4 @ SV25 @ SY1490 )
| ! [SY1491: mu] :
( ~ ( exists_in_world @ SY1491 @ SY1490 )
| ! [SY1492: $i] :
( ~ ( rel_s4 @ SY1490 @ SY1492 )
| ! [SY1493: mu] :
( ~ ( exists_in_world @ SY1493 @ SY1492 )
| ! [SY1494: $i] :
( ~ ( rel_s4 @ SY1492 @ SY1494 )
| ~ ( ~ ( rel_s4 @ SY1494 @ ( sK25_SY1130 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SY1491 @ ( sK25_SY1130 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1494 @ ( sK24_SY1105 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1491 @ SY1493 @ ( sK24_SY1105 @ SY1494 @ SY1493 @ SY1492 @ SY1491 @ SY1490 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1494 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1493 @ SY1495 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV12: $i,SV26: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( ! [SY1496: $i] :
( ~ ( rel_s4 @ SV26 @ SY1496 )
| ! [SY1497: mu] :
( ~ ( exists_in_world @ SY1497 @ SY1496 )
| ! [SY1498: $i] :
( ~ ( rel_s4 @ SY1496 @ SY1498 )
| ~ ( ~ ( rel_s4 @ SY1498 @ ( sK14_SY342 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SY1497 @ ( sK14_SY342 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1499: $i] :
( ~ ( rel_s4 @ SY1498 @ SY1499 )
| ~ ( ~ ( rel_s4 @ SY1499 @ ( sK13_SY344 @ SY1499 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1497 @ SV38 @ ( sK13_SY344 @ SY1499 @ SY1498 @ SY1497 @ SY1496 @ SV38 @ SV26 @ SV12 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV13: $i,SV27: $i,SV39: mu] :
( ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( ! [SY1500: $i] :
( ~ ( rel_s4 @ SV27 @ SY1500 )
| ! [SY1501: mu] :
( ~ ( exists_in_world @ SY1501 @ SY1500 )
| ! [SY1502: $i] :
( ~ ( rel_s4 @ SY1500 @ SY1502 )
| ~ ( ~ ( rel_s4 @ SY1502 @ ( sK21_SY796 @ SY1502 @ SY1501 @ SY1500 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SY1501 @ ( sK21_SY796 @ SY1502 @ SY1501 @ SY1500 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SY1502 @ SY1503 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SY1501 ) @ SY1503 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(177,plain,
( ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
| ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV14: $i,SV28: $i,SV40: mu] :
( ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( ! [SY1504: $i] :
( ~ ( rel_s4 @ SV28 @ SY1504 )
| ~ ( ~ ! [SY1505: mu] :
( ~ ( exists_in_world @ SY1505 @ SY1504 )
| ! [SY1506: $i] :
( ~ ( rel_s4 @ SY1504 @ SY1506 )
| ~ ( ~ ( rel_s4 @ SY1506 @ ( sK12_SY238 @ SY1506 @ SY1505 @ SY1504 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1505 ) @ empty_set @ ( sK12_SY238 @ SY1506 @ SY1505 @ SY1504 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1506 @ SY1507 )
| ( in @ SV40 @ SY1505 @ SY1507 ) ) ) )
| ~ ! [SY1508: mu] :
( ~ ( exists_in_world @ SY1508 @ SY1504 )
| ! [SY1509: $i] :
( ~ ( rel_s4 @ SY1504 @ SY1509 )
| ~ ( ~ ( rel_s4 @ SY1509 @ ( sK11_SY241 @ SY1509 @ SY1508 @ SY1504 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1508 @ ( sK11_SY241 @ SY1509 @ SY1508 @ SY1504 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1509 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1508 ) @ empty_set @ SY1510 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV15: $i,SV29: $i,SV41: mu] :
( ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( ! [SY1511: $i] :
( ~ ( rel_s4 @ SV29 @ SY1511 )
| ! [SY1512: mu] :
( ~ ( exists_in_world @ SY1512 @ SY1511 )
| ! [SY1513: $i] :
( ~ ( rel_s4 @ SY1511 @ SY1513 )
| ! [SY1514: mu] :
( ~ ( exists_in_world @ SY1514 @ SY1513 )
| ! [SY1515: $i] :
( ~ ( rel_s4 @ SY1513 @ SY1515 )
| ~ ( ~ ( rel_s4 @ SY1515 @ ( sK22_SY893 @ SY1515 @ SY1514 @ SY1513 @ SY1512 @ SY1511 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SY1512 @ ( sK22_SY893 @ SY1515 @ SY1514 @ SY1513 @ SY1512 @ SY1511 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1516: $i] :
( ~ ( rel_s4 @ SY1515 @ SY1516 )
| ( qmltpeq @ ( set_difference @ SY1514 @ SV41 ) @ ( set_difference @ SY1514 @ SY1512 ) @ SY1516 ) ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV4: $i,SV31: mu,SV42: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV42 )
| ( qmltpeq @ SV31 @ SV31 @ SV42 ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV18 )
= $false )
| ( ( rel_s4 @ SV4 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV6: $i,SV32: mu,SV43: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV43 )
| ! [SY1517: mu] :
( ~ ( exists_in_world @ SY1517 @ SV43 )
| ! [SY1518: $i] :
( ~ ( rel_s4 @ SV43 @ SY1518 )
| ! [SY1519: mu] :
( ~ ( exists_in_world @ SY1519 @ SY1518 )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SY1518 @ SY1520 )
| ~ ( ~ ( rel_s4 @ SY1520 @ ( sK16_SY471 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SY1517 @ ( sK16_SY471 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1520 @ ( sK15_SY472 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1519 @ SV32 @ ( sK15_SY472 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1520 @ SX8 )
| ( in @ SY1519 @ SY1517 @ SX8 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV7: $i,SV33: mu,SV44: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ SV44 )
| ! [SY1522: mu] :
( ~ ( exists_in_world @ SY1522 @ SV44 )
| ! [SY1523: $i] :
( ~ ( rel_s4 @ SV44 @ SY1523 )
| ~ ( ~ ( rel_s4 @ SY1523 @ ( sK20_SY718 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SY1522 @ ( sK20_SY718 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1523 @ ( sK19_SY719 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1523 @ SX6 )
| ( empty @ SY1522 @ SX6 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV8: $i,SV34: mu,SV45: $i,SV22: $i] :
( ( ( ~ ( rel_s4 @ SV22 @ SV45 )
| ! [SY1525: mu] :
( ~ ( exists_in_world @ SY1525 @ SV45 )
| ! [SY1526: $i] :
( ~ ( rel_s4 @ SV45 @ SY1526 )
| ! [SY1527: mu] :
( ~ ( exists_in_world @ SY1527 @ SY1526 )
| ! [SY1528: $i] :
( ~ ( rel_s4 @ SY1526 @ SY1528 )
| ~ ( ~ ( rel_s4 @ SY1528 @ ( sK18_SY608 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SY1525 @ ( sK18_SY608 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1528 @ ( sK17_SY609 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1527 @ ( sK17_SY609 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1528 @ SX8 )
| ( in @ SY1525 @ SY1527 @ SX8 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV9: $i,SV35: mu,SV46: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV46 )
| ! [SY1530: mu] :
( ~ ( exists_in_world @ SY1530 @ SV46 )
| ! [SY1531: $i] :
( ~ ( rel_s4 @ SV46 @ SY1531 )
| ! [SY1532: mu] :
( ~ ( exists_in_world @ SY1532 @ SY1531 )
| ! [SY1533: $i] :
( ~ ( rel_s4 @ SY1531 @ SY1533 )
| ~ ( ~ ( rel_s4 @ SY1533 @ ( sK23_SY998 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SY1530 @ ( sK23_SY998 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SY1533 @ SY1485 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1532 ) @ ( set_difference @ SY1530 @ SY1532 ) @ SY1485 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV10: $i,SV36: mu,SV47: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV47 )
| ! [SY1535: mu] :
( ~ ( exists_in_world @ SY1535 @ SV47 )
| ! [SY1536: $i] :
( ~ ( rel_s4 @ SV47 @ SY1536 )
| ~ ( ~ ( rel_s4 @ SY1536 @ ( sK26_SY1216 @ SY1536 @ SY1535 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SY1535 @ ( sK26_SY1216 @ SY1536 @ SY1535 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SY1536 @ SY1489 )
| ( qmltpeq @ SY1535 @ SV36 @ SY1489 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV11: $i,SV37: mu,SV48: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV48 )
| ! [SY1538: mu] :
( ~ ( exists_in_world @ SY1538 @ SV48 )
| ! [SY1539: $i] :
( ~ ( rel_s4 @ SV48 @ SY1539 )
| ! [SY1540: mu] :
( ~ ( exists_in_world @ SY1540 @ SY1539 )
| ! [SY1541: $i] :
( ~ ( rel_s4 @ SY1539 @ SY1541 )
| ~ ( ~ ( rel_s4 @ SY1541 @ ( sK25_SY1130 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SY1538 @ ( sK25_SY1130 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1541 @ ( sK24_SY1105 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1538 @ SY1540 @ ( sK24_SY1105 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1541 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1540 @ SY1495 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV12: $i,SV38: mu,SV49: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV49 )
| ! [SY1543: mu] :
( ~ ( exists_in_world @ SY1543 @ SV49 )
| ! [SY1544: $i] :
( ~ ( rel_s4 @ SV49 @ SY1544 )
| ~ ( ~ ( rel_s4 @ SY1544 @ ( sK14_SY342 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SY1543 @ ( sK14_SY342 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1545: $i] :
( ~ ( rel_s4 @ SY1544 @ SY1545 )
| ~ ( ~ ( rel_s4 @ SY1545 @ ( sK13_SY344 @ SY1545 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1543 @ SV38 @ ( sK13_SY344 @ SY1545 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV13: $i,SV39: mu,SV50: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV50 )
| ! [SY1546: mu] :
( ~ ( exists_in_world @ SY1546 @ SV50 )
| ! [SY1547: $i] :
( ~ ( rel_s4 @ SV50 @ SY1547 )
| ~ ( ~ ( rel_s4 @ SY1547 @ ( sK21_SY796 @ SY1547 @ SY1546 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SY1546 @ ( sK21_SY796 @ SY1547 @ SY1546 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SY1547 @ SY1503 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SY1546 ) @ SY1503 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(189,plain,
( ( ~ ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(190,plain,
( ( ~ ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(191,plain,
! [SV14: $i,SV40: mu,SV51: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV51 )
| ~ ( ~ ! [SY1549: mu] :
( ~ ( exists_in_world @ SY1549 @ SV51 )
| ! [SY1550: $i] :
( ~ ( rel_s4 @ SV51 @ SY1550 )
| ~ ( ~ ( rel_s4 @ SY1550 @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1549 ) @ empty_set @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1550 @ SY1507 )
| ( in @ SV40 @ SY1549 @ SY1507 ) ) ) )
| ~ ! [SY1552: mu] :
( ~ ( exists_in_world @ SY1552 @ SV51 )
| ! [SY1553: $i] :
( ~ ( rel_s4 @ SV51 @ SY1553 )
| ~ ( ~ ( rel_s4 @ SY1553 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1552 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1553 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1552 ) @ empty_set @ SY1510 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(192,plain,
! [SV15: $i,SV41: mu,SV52: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV52 )
| ! [SY1555: mu] :
( ~ ( exists_in_world @ SY1555 @ SV52 )
| ! [SY1556: $i] :
( ~ ( rel_s4 @ SV52 @ SY1556 )
| ! [SY1557: mu] :
( ~ ( exists_in_world @ SY1557 @ SY1556 )
| ! [SY1558: $i] :
( ~ ( rel_s4 @ SY1556 @ SY1558 )
| ~ ( ~ ( rel_s4 @ SY1558 @ ( sK22_SY893 @ SY1558 @ SY1557 @ SY1556 @ SY1555 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SY1555 @ ( sK22_SY893 @ SY1558 @ SY1557 @ SY1556 @ SY1555 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1516: $i] :
( ~ ( rel_s4 @ SY1558 @ SY1516 )
| ( qmltpeq @ ( set_difference @ SY1557 @ SV41 ) @ ( set_difference @ SY1557 @ SY1555 ) @ SY1516 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV4: $i,SV31: mu,SV42: $i,SV18: $i] :
( ( ( ~ ( rel_s4 @ SV18 @ SV42 ) )
= $true )
| ( ( qmltpeq @ SV31 @ SV31 @ SV42 )
= $true )
| ( ( exists_in_world @ SV31 @ SV18 )
= $false )
| ( ( rel_s4 @ SV4 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(194,plain,
! [SV6: $i,SV32: mu,SV43: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV43 ) )
= $true )
| ( ( ! [SY1517: mu] :
( ~ ( exists_in_world @ SY1517 @ SV43 )
| ! [SY1518: $i] :
( ~ ( rel_s4 @ SV43 @ SY1518 )
| ! [SY1519: mu] :
( ~ ( exists_in_world @ SY1519 @ SY1518 )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SY1518 @ SY1520 )
| ~ ( ~ ( rel_s4 @ SY1520 @ ( sK16_SY471 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SY1517 @ ( sK16_SY471 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1520 @ ( sK15_SY472 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1519 @ SV32 @ ( sK15_SY472 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1520 @ SX8 )
| ( in @ SY1519 @ SY1517 @ SX8 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(195,plain,
! [SV7: $i,SV33: mu,SV44: $i,SV21: $i] :
( ( ( ~ ( rel_s4 @ SV21 @ SV44 ) )
= $true )
| ( ( ! [SY1522: mu] :
( ~ ( exists_in_world @ SY1522 @ SV44 )
| ! [SY1523: $i] :
( ~ ( rel_s4 @ SV44 @ SY1523 )
| ~ ( ~ ( rel_s4 @ SY1523 @ ( sK20_SY718 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SY1522 @ ( sK20_SY718 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1523 @ ( sK19_SY719 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1523 @ SX6 )
| ( empty @ SY1522 @ SX6 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(196,plain,
! [SV8: $i,SV34: mu,SV45: $i,SV22: $i] :
( ( ( ~ ( rel_s4 @ SV22 @ SV45 ) )
= $true )
| ( ( ! [SY1525: mu] :
( ~ ( exists_in_world @ SY1525 @ SV45 )
| ! [SY1526: $i] :
( ~ ( rel_s4 @ SV45 @ SY1526 )
| ! [SY1527: mu] :
( ~ ( exists_in_world @ SY1527 @ SY1526 )
| ! [SY1528: $i] :
( ~ ( rel_s4 @ SY1526 @ SY1528 )
| ~ ( ~ ( rel_s4 @ SY1528 @ ( sK18_SY608 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SY1525 @ ( sK18_SY608 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1528 @ ( sK17_SY609 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1527 @ ( sK17_SY609 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1528 @ SX8 )
| ( in @ SY1525 @ SY1527 @ SX8 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(197,plain,
! [SV9: $i,SV35: mu,SV46: $i,SV23: $i] :
( ( ( ~ ( rel_s4 @ SV23 @ SV46 ) )
= $true )
| ( ( ! [SY1530: mu] :
( ~ ( exists_in_world @ SY1530 @ SV46 )
| ! [SY1531: $i] :
( ~ ( rel_s4 @ SV46 @ SY1531 )
| ! [SY1532: mu] :
( ~ ( exists_in_world @ SY1532 @ SY1531 )
| ! [SY1533: $i] :
( ~ ( rel_s4 @ SY1531 @ SY1533 )
| ~ ( ~ ( rel_s4 @ SY1533 @ ( sK23_SY998 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SY1530 @ ( sK23_SY998 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SY1533 @ SY1485 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1532 ) @ ( set_difference @ SY1530 @ SY1532 ) @ SY1485 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(198,plain,
! [SV10: $i,SV36: mu,SV47: $i,SV24: $i] :
( ( ( ~ ( rel_s4 @ SV24 @ SV47 ) )
= $true )
| ( ( ! [SY1535: mu] :
( ~ ( exists_in_world @ SY1535 @ SV47 )
| ! [SY1536: $i] :
( ~ ( rel_s4 @ SV47 @ SY1536 )
| ~ ( ~ ( rel_s4 @ SY1536 @ ( sK26_SY1216 @ SY1536 @ SY1535 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SY1535 @ ( sK26_SY1216 @ SY1536 @ SY1535 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SY1536 @ SY1489 )
| ( qmltpeq @ SY1535 @ SV36 @ SY1489 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(199,plain,
! [SV11: $i,SV37: mu,SV48: $i,SV25: $i] :
( ( ( ~ ( rel_s4 @ SV25 @ SV48 ) )
= $true )
| ( ( ! [SY1538: mu] :
( ~ ( exists_in_world @ SY1538 @ SV48 )
| ! [SY1539: $i] :
( ~ ( rel_s4 @ SV48 @ SY1539 )
| ! [SY1540: mu] :
( ~ ( exists_in_world @ SY1540 @ SY1539 )
| ! [SY1541: $i] :
( ~ ( rel_s4 @ SY1539 @ SY1541 )
| ~ ( ~ ( rel_s4 @ SY1541 @ ( sK25_SY1130 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SY1538 @ ( sK25_SY1130 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1541 @ ( sK24_SY1105 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1538 @ SY1540 @ ( sK24_SY1105 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1541 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1540 @ SY1495 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(200,plain,
! [SV12: $i,SV38: mu,SV49: $i,SV26: $i] :
( ( ( ~ ( rel_s4 @ SV26 @ SV49 ) )
= $true )
| ( ( ! [SY1543: mu] :
( ~ ( exists_in_world @ SY1543 @ SV49 )
| ! [SY1544: $i] :
( ~ ( rel_s4 @ SV49 @ SY1544 )
| ~ ( ~ ( rel_s4 @ SY1544 @ ( sK14_SY342 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SY1543 @ ( sK14_SY342 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1545: $i] :
( ~ ( rel_s4 @ SY1544 @ SY1545 )
| ~ ( ~ ( rel_s4 @ SY1545 @ ( sK13_SY344 @ SY1545 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1543 @ SV38 @ ( sK13_SY344 @ SY1545 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(201,plain,
! [SV13: $i,SV39: mu,SV50: $i,SV27: $i] :
( ( ( ~ ( rel_s4 @ SV27 @ SV50 ) )
= $true )
| ( ( ! [SY1546: mu] :
( ~ ( exists_in_world @ SY1546 @ SV50 )
| ! [SY1547: $i] :
( ~ ( rel_s4 @ SV50 @ SY1547 )
| ~ ( ~ ( rel_s4 @ SY1547 @ ( sK21_SY796 @ SY1547 @ SY1546 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SY1546 @ ( sK21_SY796 @ SY1547 @ SY1546 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SY1547 @ SY1503 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SY1546 ) @ SY1503 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(202,plain,
( ( rel_s4 @ sK2_SY1273 @ sK4_SY1292 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(203,plain,
( ( ~ ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(204,plain,
! [SV14: $i,SV40: mu,SV51: $i,SV28: $i] :
( ( ( ~ ( rel_s4 @ SV28 @ SV51 ) )
= $true )
| ( ( ~ ( ~ ! [SY1549: mu] :
( ~ ( exists_in_world @ SY1549 @ SV51 )
| ! [SY1550: $i] :
( ~ ( rel_s4 @ SV51 @ SY1550 )
| ~ ( ~ ( rel_s4 @ SY1550 @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1549 ) @ empty_set @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1550 @ SY1507 )
| ( in @ SV40 @ SY1549 @ SY1507 ) ) ) )
| ~ ! [SY1552: mu] :
( ~ ( exists_in_world @ SY1552 @ SV51 )
| ! [SY1553: $i] :
( ~ ( rel_s4 @ SV51 @ SY1553 )
| ~ ( ~ ( rel_s4 @ SY1553 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1552 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1553 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1552 ) @ empty_set @ SY1510 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV15: $i,SV41: mu,SV52: $i,SV29: $i] :
( ( ( ~ ( rel_s4 @ SV29 @ SV52 ) )
= $true )
| ( ( ! [SY1555: mu] :
( ~ ( exists_in_world @ SY1555 @ SV52 )
| ! [SY1556: $i] :
( ~ ( rel_s4 @ SV52 @ SY1556 )
| ! [SY1557: mu] :
( ~ ( exists_in_world @ SY1557 @ SY1556 )
| ! [SY1558: $i] :
( ~ ( rel_s4 @ SY1556 @ SY1558 )
| ~ ( ~ ( rel_s4 @ SY1558 @ ( sK22_SY893 @ SY1558 @ SY1557 @ SY1556 @ SY1555 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SY1555 @ ( sK22_SY893 @ SY1558 @ SY1557 @ SY1556 @ SY1555 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1516: $i] :
( ~ ( rel_s4 @ SY1558 @ SY1516 )
| ( qmltpeq @ ( set_difference @ SY1557 @ SV41 ) @ ( set_difference @ SY1557 @ SY1555 ) @ SY1516 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(206,plain,
! [SV4: $i,SV31: mu,SV42: $i,SV18: $i] :
( ( ( rel_s4 @ SV18 @ SV42 )
= $false )
| ( ( qmltpeq @ SV31 @ SV31 @ SV42 )
= $true )
| ( ( exists_in_world @ SV31 @ SV18 )
= $false )
| ( ( rel_s4 @ SV4 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV6: $i,SV32: mu,SV43: $i,SV20: $i] :
( ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( ! [SY1517: mu] :
( ~ ( exists_in_world @ SY1517 @ SV43 )
| ! [SY1518: $i] :
( ~ ( rel_s4 @ SV43 @ SY1518 )
| ! [SY1519: mu] :
( ~ ( exists_in_world @ SY1519 @ SY1518 )
| ! [SY1520: $i] :
( ~ ( rel_s4 @ SY1518 @ SY1520 )
| ~ ( ~ ( rel_s4 @ SY1520 @ ( sK16_SY471 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SY1517 @ ( sK16_SY471 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1520 @ ( sK15_SY472 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1519 @ SV32 @ ( sK15_SY472 @ SY1520 @ SY1519 @ SY1518 @ SY1517 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1520 @ SX8 )
| ( in @ SY1519 @ SY1517 @ SX8 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(208,plain,
! [SV7: $i,SV33: mu,SV44: $i,SV21: $i] :
( ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( ! [SY1522: mu] :
( ~ ( exists_in_world @ SY1522 @ SV44 )
| ! [SY1523: $i] :
( ~ ( rel_s4 @ SV44 @ SY1523 )
| ~ ( ~ ( rel_s4 @ SY1523 @ ( sK20_SY718 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SY1522 @ ( sK20_SY718 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1523 @ ( sK19_SY719 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1523 @ SY1522 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SX6: $i] :
( ~ ( rel_s4 @ SY1523 @ SX6 )
| ( empty @ SY1522 @ SX6 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(209,plain,
! [SV8: $i,SV34: mu,SV45: $i,SV22: $i] :
( ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( ! [SY1525: mu] :
( ~ ( exists_in_world @ SY1525 @ SV45 )
| ! [SY1526: $i] :
( ~ ( rel_s4 @ SV45 @ SY1526 )
| ! [SY1527: mu] :
( ~ ( exists_in_world @ SY1527 @ SY1526 )
| ! [SY1528: $i] :
( ~ ( rel_s4 @ SY1526 @ SY1528 )
| ~ ( ~ ( rel_s4 @ SY1528 @ ( sK18_SY608 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SY1525 @ ( sK18_SY608 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1528 @ ( sK17_SY609 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1527 @ ( sK17_SY609 @ SY1528 @ SY1527 @ SY1526 @ SY1525 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SX8: $i] :
( ~ ( rel_s4 @ SY1528 @ SX8 )
| ( in @ SY1525 @ SY1527 @ SX8 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(210,plain,
! [SV9: $i,SV35: mu,SV46: $i,SV23: $i] :
( ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( ! [SY1530: mu] :
( ~ ( exists_in_world @ SY1530 @ SV46 )
| ! [SY1531: $i] :
( ~ ( rel_s4 @ SV46 @ SY1531 )
| ! [SY1532: mu] :
( ~ ( exists_in_world @ SY1532 @ SY1531 )
| ! [SY1533: $i] :
( ~ ( rel_s4 @ SY1531 @ SY1533 )
| ~ ( ~ ( rel_s4 @ SY1533 @ ( sK23_SY998 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SY1530 @ ( sK23_SY998 @ SY1533 @ SY1532 @ SY1531 @ SY1530 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1485: $i] :
( ~ ( rel_s4 @ SY1533 @ SY1485 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1532 ) @ ( set_difference @ SY1530 @ SY1532 ) @ SY1485 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(211,plain,
! [SV10: $i,SV36: mu,SV47: $i,SV24: $i] :
( ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( ! [SY1535: mu] :
( ~ ( exists_in_world @ SY1535 @ SV47 )
| ! [SY1536: $i] :
( ~ ( rel_s4 @ SV47 @ SY1536 )
| ~ ( ~ ( rel_s4 @ SY1536 @ ( sK26_SY1216 @ SY1536 @ SY1535 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SY1535 @ ( sK26_SY1216 @ SY1536 @ SY1535 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1489: $i] :
( ~ ( rel_s4 @ SY1536 @ SY1489 )
| ( qmltpeq @ SY1535 @ SV36 @ SY1489 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(212,plain,
! [SV11: $i,SV37: mu,SV48: $i,SV25: $i] :
( ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( ! [SY1538: mu] :
( ~ ( exists_in_world @ SY1538 @ SV48 )
| ! [SY1539: $i] :
( ~ ( rel_s4 @ SV48 @ SY1539 )
| ! [SY1540: mu] :
( ~ ( exists_in_world @ SY1540 @ SY1539 )
| ! [SY1541: $i] :
( ~ ( rel_s4 @ SY1539 @ SY1541 )
| ~ ( ~ ( rel_s4 @ SY1541 @ ( sK25_SY1130 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SY1538 @ ( sK25_SY1130 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1541 @ ( sK24_SY1105 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SY1538 @ SY1540 @ ( sK24_SY1105 @ SY1541 @ SY1540 @ SY1539 @ SY1538 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1541 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1540 @ SY1495 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(213,plain,
! [SV12: $i,SV38: mu,SV49: $i,SV26: $i] :
( ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( ! [SY1543: mu] :
( ~ ( exists_in_world @ SY1543 @ SV49 )
| ! [SY1544: $i] :
( ~ ( rel_s4 @ SV49 @ SY1544 )
| ~ ( ~ ( rel_s4 @ SY1544 @ ( sK14_SY342 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SY1543 @ ( sK14_SY342 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1545: $i] :
( ~ ( rel_s4 @ SY1544 @ SY1545 )
| ~ ( ~ ( rel_s4 @ SY1545 @ ( sK13_SY344 @ SY1545 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SY1543 @ SV38 @ ( sK13_SY344 @ SY1545 @ SY1544 @ SY1543 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(214,plain,
! [SV13: $i,SV39: mu,SV50: $i,SV27: $i] :
( ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( ! [SY1546: mu] :
( ~ ( exists_in_world @ SY1546 @ SV50 )
| ! [SY1547: $i] :
( ~ ( rel_s4 @ SV50 @ SY1547 )
| ~ ( ~ ( rel_s4 @ SY1547 @ ( sK21_SY796 @ SY1547 @ SY1546 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SY1546 @ ( sK21_SY796 @ SY1547 @ SY1546 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1503: $i] :
( ~ ( rel_s4 @ SY1547 @ SY1503 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SY1546 ) @ SY1503 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(215,plain,
( ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
| ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(216,plain,
! [SV14: $i,SV40: mu,SV51: $i,SV28: $i] :
( ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( ~ ( ~ ! [SY1549: mu] :
( ~ ( exists_in_world @ SY1549 @ SV51 )
| ! [SY1550: $i] :
( ~ ( rel_s4 @ SV51 @ SY1550 )
| ~ ( ~ ( rel_s4 @ SY1550 @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1549 ) @ empty_set @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1550 @ SY1507 )
| ( in @ SV40 @ SY1549 @ SY1507 ) ) ) )
| ~ ! [SY1552: mu] :
( ~ ( exists_in_world @ SY1552 @ SV51 )
| ! [SY1553: $i] :
( ~ ( rel_s4 @ SV51 @ SY1553 )
| ~ ( ~ ( rel_s4 @ SY1553 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1552 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1553 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1552 ) @ empty_set @ SY1510 ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(217,plain,
! [SV15: $i,SV41: mu,SV52: $i,SV29: $i] :
( ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( ! [SY1555: mu] :
( ~ ( exists_in_world @ SY1555 @ SV52 )
| ! [SY1556: $i] :
( ~ ( rel_s4 @ SV52 @ SY1556 )
| ! [SY1557: mu] :
( ~ ( exists_in_world @ SY1557 @ SY1556 )
| ! [SY1558: $i] :
( ~ ( rel_s4 @ SY1556 @ SY1558 )
| ~ ( ~ ( rel_s4 @ SY1558 @ ( sK22_SY893 @ SY1558 @ SY1557 @ SY1556 @ SY1555 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SY1555 @ ( sK22_SY893 @ SY1558 @ SY1557 @ SY1556 @ SY1555 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1516: $i] :
( ~ ( rel_s4 @ SY1558 @ SY1516 )
| ( qmltpeq @ ( set_difference @ SY1557 @ SV41 ) @ ( set_difference @ SY1557 @ SY1555 ) @ SY1516 ) ) ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(218,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV43 )
| ! [SY1560: $i] :
( ~ ( rel_s4 @ SV43 @ SY1560 )
| ! [SY1561: mu] :
( ~ ( exists_in_world @ SY1561 @ SY1560 )
| ! [SY1562: $i] :
( ~ ( rel_s4 @ SY1560 @ SY1562 )
| ~ ( ~ ( rel_s4 @ SY1562 @ ( sK16_SY471 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1562 @ ( sK15_SY472 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1561 @ SV32 @ ( sK15_SY472 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1563: $i] :
( ~ ( rel_s4 @ SY1562 @ SY1563 )
| ( in @ SY1561 @ SV53 @ SY1563 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(219,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV44 )
| ! [SY1564: $i] :
( ~ ( rel_s4 @ SV44 @ SY1564 )
| ~ ( ~ ( rel_s4 @ SY1564 @ ( sK20_SY718 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1564 @ ( sK19_SY719 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SY1565: $i] :
( ~ ( rel_s4 @ SY1564 @ SY1565 )
| ( empty @ SV54 @ SY1565 ) ) ) )
= $true )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(220,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV45 )
| ! [SY1566: $i] :
( ~ ( rel_s4 @ SV45 @ SY1566 )
| ! [SY1567: mu] :
( ~ ( exists_in_world @ SY1567 @ SY1566 )
| ! [SY1568: $i] :
( ~ ( rel_s4 @ SY1566 @ SY1568 )
| ~ ( ~ ( rel_s4 @ SY1568 @ ( sK18_SY608 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1568 @ ( sK17_SY609 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1567 @ ( sK17_SY609 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1569: $i] :
( ~ ( rel_s4 @ SY1568 @ SY1569 )
| ( in @ SV55 @ SY1567 @ SY1569 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(221,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV46 )
| ! [SY1570: $i] :
( ~ ( rel_s4 @ SV46 @ SY1570 )
| ! [SY1571: mu] :
( ~ ( exists_in_world @ SY1571 @ SY1570 )
| ! [SY1572: $i] :
( ~ ( rel_s4 @ SY1570 @ SY1572 )
| ~ ( ~ ( rel_s4 @ SY1572 @ ( sK23_SY998 @ SY1572 @ SY1571 @ SY1570 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1572 @ SY1571 @ SY1570 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1573: $i] :
( ~ ( rel_s4 @ SY1572 @ SY1573 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1571 ) @ ( set_difference @ SV56 @ SY1571 ) @ SY1573 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV47: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV47 )
| ! [SY1574: $i] :
( ~ ( rel_s4 @ SV47 @ SY1574 )
| ~ ( ~ ( rel_s4 @ SY1574 @ ( sK26_SY1216 @ SY1574 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SY1574 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1575: $i] :
( ~ ( rel_s4 @ SY1574 @ SY1575 )
| ( qmltpeq @ SV57 @ SV36 @ SY1575 ) ) ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(223,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu] :
( ( ( ~ ( exists_in_world @ SV58 @ SV48 )
| ! [SY1576: $i] :
( ~ ( rel_s4 @ SV48 @ SY1576 )
| ! [SY1577: mu] :
( ~ ( exists_in_world @ SY1577 @ SY1576 )
| ! [SY1578: $i] :
( ~ ( rel_s4 @ SY1576 @ SY1578 )
| ~ ( ~ ( rel_s4 @ SY1578 @ ( sK25_SY1130 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1578 @ ( sK24_SY1105 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SY1577 @ ( sK24_SY1105 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1578 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1577 @ SY1495 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(224,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV49 )
| ! [SY1580: $i] :
( ~ ( rel_s4 @ SV49 @ SY1580 )
| ~ ( ~ ( rel_s4 @ SY1580 @ ( sK14_SY342 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1581: $i] :
( ~ ( rel_s4 @ SY1580 @ SY1581 )
| ~ ( ~ ( rel_s4 @ SY1581 @ ( sK13_SY344 @ SY1581 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1581 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(225,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV50: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV50 )
| ! [SY1582: $i] :
( ~ ( rel_s4 @ SV50 @ SY1582 )
| ~ ( ~ ( rel_s4 @ SY1582 @ ( sK21_SY796 @ SY1582 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SY1582 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1583: $i] :
( ~ ( rel_s4 @ SY1582 @ SY1583 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1583 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(226,plain,
( ( ~ ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(227,plain,
( ( ~ ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(228,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i] :
( ( ( ~ ! [SY1549: mu] :
( ~ ( exists_in_world @ SY1549 @ SV51 )
| ! [SY1550: $i] :
( ~ ( rel_s4 @ SV51 @ SY1550 )
| ~ ( ~ ( rel_s4 @ SY1550 @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1549 ) @ empty_set @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1550 @ SY1507 )
| ( in @ SV40 @ SY1549 @ SY1507 ) ) ) )
| ~ ! [SY1552: mu] :
( ~ ( exists_in_world @ SY1552 @ SV51 )
| ! [SY1553: $i] :
( ~ ( rel_s4 @ SV51 @ SY1553 )
| ~ ( ~ ( rel_s4 @ SY1553 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1552 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1553 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1552 ) @ empty_set @ SY1510 ) ) ) ) )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(229,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV52 )
| ! [SY1584: $i] :
( ~ ( rel_s4 @ SV52 @ SY1584 )
| ! [SY1585: mu] :
( ~ ( exists_in_world @ SY1585 @ SY1584 )
| ! [SY1586: $i] :
( ~ ( rel_s4 @ SY1584 @ SY1586 )
| ~ ( ~ ( rel_s4 @ SY1586 @ ( sK22_SY893 @ SY1586 @ SY1585 @ SY1584 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1586 @ SY1585 @ SY1584 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1587: $i] :
( ~ ( rel_s4 @ SY1586 @ SY1587 )
| ( qmltpeq @ ( set_difference @ SY1585 @ SV41 ) @ ( set_difference @ SY1585 @ SV61 ) @ SY1587 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(230,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV43 ) )
= $true )
| ( ( ! [SY1560: $i] :
( ~ ( rel_s4 @ SV43 @ SY1560 )
| ! [SY1561: mu] :
( ~ ( exists_in_world @ SY1561 @ SY1560 )
| ! [SY1562: $i] :
( ~ ( rel_s4 @ SY1560 @ SY1562 )
| ~ ( ~ ( rel_s4 @ SY1562 @ ( sK16_SY471 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1562 @ ( sK15_SY472 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1561 @ SV32 @ ( sK15_SY472 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1563: $i] :
( ~ ( rel_s4 @ SY1562 @ SY1563 )
| ( in @ SY1561 @ SV53 @ SY1563 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(231,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV44 ) )
= $true )
| ( ( ! [SY1564: $i] :
( ~ ( rel_s4 @ SV44 @ SY1564 )
| ~ ( ~ ( rel_s4 @ SY1564 @ ( sK20_SY718 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1564 @ ( sK19_SY719 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SY1565: $i] :
( ~ ( rel_s4 @ SY1564 @ SY1565 )
| ( empty @ SV54 @ SY1565 ) ) ) )
= $true )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(232,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV45 ) )
= $true )
| ( ( ! [SY1566: $i] :
( ~ ( rel_s4 @ SV45 @ SY1566 )
| ! [SY1567: mu] :
( ~ ( exists_in_world @ SY1567 @ SY1566 )
| ! [SY1568: $i] :
( ~ ( rel_s4 @ SY1566 @ SY1568 )
| ~ ( ~ ( rel_s4 @ SY1568 @ ( sK18_SY608 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1568 @ ( sK17_SY609 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1567 @ ( sK17_SY609 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1569: $i] :
( ~ ( rel_s4 @ SY1568 @ SY1569 )
| ( in @ SV55 @ SY1567 @ SY1569 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(233,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV46 ) )
= $true )
| ( ( ! [SY1570: $i] :
( ~ ( rel_s4 @ SV46 @ SY1570 )
| ! [SY1571: mu] :
( ~ ( exists_in_world @ SY1571 @ SY1570 )
| ! [SY1572: $i] :
( ~ ( rel_s4 @ SY1570 @ SY1572 )
| ~ ( ~ ( rel_s4 @ SY1572 @ ( sK23_SY998 @ SY1572 @ SY1571 @ SY1570 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1572 @ SY1571 @ SY1570 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1573: $i] :
( ~ ( rel_s4 @ SY1572 @ SY1573 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1571 ) @ ( set_difference @ SV56 @ SY1571 ) @ SY1573 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(234,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV47: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV47 ) )
= $true )
| ( ( ! [SY1574: $i] :
( ~ ( rel_s4 @ SV47 @ SY1574 )
| ~ ( ~ ( rel_s4 @ SY1574 @ ( sK26_SY1216 @ SY1574 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SY1574 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1575: $i] :
( ~ ( rel_s4 @ SY1574 @ SY1575 )
| ( qmltpeq @ SV57 @ SV36 @ SY1575 ) ) ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(235,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu] :
( ( ( ~ ( exists_in_world @ SV58 @ SV48 ) )
= $true )
| ( ( ! [SY1576: $i] :
( ~ ( rel_s4 @ SV48 @ SY1576 )
| ! [SY1577: mu] :
( ~ ( exists_in_world @ SY1577 @ SY1576 )
| ! [SY1578: $i] :
( ~ ( rel_s4 @ SY1576 @ SY1578 )
| ~ ( ~ ( rel_s4 @ SY1578 @ ( sK25_SY1130 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1578 @ ( sK24_SY1105 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SY1577 @ ( sK24_SY1105 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1578 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1577 @ SY1495 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(236,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu] :
( ( ( ~ ( exists_in_world @ SV59 @ SV49 ) )
= $true )
| ( ( ! [SY1580: $i] :
( ~ ( rel_s4 @ SV49 @ SY1580 )
| ~ ( ~ ( rel_s4 @ SY1580 @ ( sK14_SY342 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1581: $i] :
( ~ ( rel_s4 @ SY1580 @ SY1581 )
| ~ ( ~ ( rel_s4 @ SY1581 @ ( sK13_SY344 @ SY1581 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1581 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(237,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV50: $i,SV60: mu] :
( ( ( ~ ( exists_in_world @ SV60 @ SV50 ) )
= $true )
| ( ( ! [SY1582: $i] :
( ~ ( rel_s4 @ SV50 @ SY1582 )
| ~ ( ~ ( rel_s4 @ SY1582 @ ( sK21_SY796 @ SY1582 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SY1582 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1583: $i] :
( ~ ( rel_s4 @ SY1582 @ SY1583 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1583 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(238,plain,
( ( exists_in_world @ sK5_SY1300 @ sK4_SY1292 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(239,plain,
( ( ~ ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(240,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i] :
( ( ( ~ ! [SY1549: mu] :
( ~ ( exists_in_world @ SY1549 @ SV51 )
| ! [SY1550: $i] :
( ~ ( rel_s4 @ SV51 @ SY1550 )
| ~ ( ~ ( rel_s4 @ SY1550 @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1549 ) @ empty_set @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1550 @ SY1507 )
| ( in @ SV40 @ SY1549 @ SY1507 ) ) ) ) )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(241,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i] :
( ( ( ~ ! [SY1552: mu] :
( ~ ( exists_in_world @ SY1552 @ SV51 )
| ! [SY1553: $i] :
( ~ ( rel_s4 @ SV51 @ SY1553 )
| ~ ( ~ ( rel_s4 @ SY1553 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1552 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1553 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1552 ) @ empty_set @ SY1510 ) ) ) ) )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(242,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu] :
( ( ( ~ ( exists_in_world @ SV61 @ SV52 ) )
= $true )
| ( ( ! [SY1584: $i] :
( ~ ( rel_s4 @ SV52 @ SY1584 )
| ! [SY1585: mu] :
( ~ ( exists_in_world @ SY1585 @ SY1584 )
| ! [SY1586: $i] :
( ~ ( rel_s4 @ SY1584 @ SY1586 )
| ~ ( ~ ( rel_s4 @ SY1586 @ ( sK22_SY893 @ SY1586 @ SY1585 @ SY1584 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1586 @ SY1585 @ SY1584 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1587: $i] :
( ~ ( rel_s4 @ SY1586 @ SY1587 )
| ( qmltpeq @ ( set_difference @ SY1585 @ SV41 ) @ ( set_difference @ SY1585 @ SV61 ) @ SY1587 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(243,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu] :
( ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( ! [SY1560: $i] :
( ~ ( rel_s4 @ SV43 @ SY1560 )
| ! [SY1561: mu] :
( ~ ( exists_in_world @ SY1561 @ SY1560 )
| ! [SY1562: $i] :
( ~ ( rel_s4 @ SY1560 @ SY1562 )
| ~ ( ~ ( rel_s4 @ SY1562 @ ( sK16_SY471 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1562 @ ( sK15_SY472 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1561 @ SV32 @ ( sK15_SY472 @ SY1562 @ SY1561 @ SY1560 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1563: $i] :
( ~ ( rel_s4 @ SY1562 @ SY1563 )
| ( in @ SY1561 @ SV53 @ SY1563 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(244,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu] :
( ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( ! [SY1564: $i] :
( ~ ( rel_s4 @ SV44 @ SY1564 )
| ~ ( ~ ( rel_s4 @ SY1564 @ ( sK20_SY718 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SY1564 @ ( sK19_SY719 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SY1564 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SY1565: $i] :
( ~ ( rel_s4 @ SY1564 @ SY1565 )
| ( empty @ SV54 @ SY1565 ) ) ) )
= $true )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(245,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu] :
( ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( ! [SY1566: $i] :
( ~ ( rel_s4 @ SV45 @ SY1566 )
| ! [SY1567: mu] :
( ~ ( exists_in_world @ SY1567 @ SY1566 )
| ! [SY1568: $i] :
( ~ ( rel_s4 @ SY1566 @ SY1568 )
| ~ ( ~ ( rel_s4 @ SY1568 @ ( sK18_SY608 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1568 @ ( sK17_SY609 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1567 @ ( sK17_SY609 @ SY1568 @ SY1567 @ SY1566 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1569: $i] :
( ~ ( rel_s4 @ SY1568 @ SY1569 )
| ( in @ SV55 @ SY1567 @ SY1569 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(246,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu] :
( ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( ! [SY1570: $i] :
( ~ ( rel_s4 @ SV46 @ SY1570 )
| ! [SY1571: mu] :
( ~ ( exists_in_world @ SY1571 @ SY1570 )
| ! [SY1572: $i] :
( ~ ( rel_s4 @ SY1570 @ SY1572 )
| ~ ( ~ ( rel_s4 @ SY1572 @ ( sK23_SY998 @ SY1572 @ SY1571 @ SY1570 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1572 @ SY1571 @ SY1570 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1573: $i] :
( ~ ( rel_s4 @ SY1572 @ SY1573 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1571 ) @ ( set_difference @ SV56 @ SY1571 ) @ SY1573 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(247,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV47: $i,SV57: mu] :
( ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( ! [SY1574: $i] :
( ~ ( rel_s4 @ SV47 @ SY1574 )
| ~ ( ~ ( rel_s4 @ SY1574 @ ( sK26_SY1216 @ SY1574 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SY1574 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1575: $i] :
( ~ ( rel_s4 @ SY1574 @ SY1575 )
| ( qmltpeq @ SV57 @ SV36 @ SY1575 ) ) ) )
= $true )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(248,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu] :
( ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( ! [SY1576: $i] :
( ~ ( rel_s4 @ SV48 @ SY1576 )
| ! [SY1577: mu] :
( ~ ( exists_in_world @ SY1577 @ SY1576 )
| ! [SY1578: $i] :
( ~ ( rel_s4 @ SY1576 @ SY1578 )
| ~ ( ~ ( rel_s4 @ SY1578 @ ( sK25_SY1130 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1578 @ ( sK24_SY1105 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SY1577 @ ( sK24_SY1105 @ SY1578 @ SY1577 @ SY1576 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1578 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1577 @ SY1495 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(249,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu] :
( ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( ! [SY1580: $i] :
( ~ ( rel_s4 @ SV49 @ SY1580 )
| ~ ( ~ ( rel_s4 @ SY1580 @ ( sK14_SY342 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1581: $i] :
( ~ ( rel_s4 @ SY1580 @ SY1581 )
| ~ ( ~ ( rel_s4 @ SY1581 @ ( sK13_SY344 @ SY1581 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1581 @ SY1580 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(250,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV50: $i,SV60: mu] :
( ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( ! [SY1582: $i] :
( ~ ( rel_s4 @ SV50 @ SY1582 )
| ~ ( ~ ( rel_s4 @ SY1582 @ ( sK21_SY796 @ SY1582 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SY1582 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1583: $i] :
( ~ ( rel_s4 @ SY1582 @ SY1583 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1583 ) ) ) )
= $true )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(251,plain,
( ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
| ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(252,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i] :
( ( ( ! [SY1549: mu] :
( ~ ( exists_in_world @ SY1549 @ SV51 )
| ! [SY1550: $i] :
( ~ ( rel_s4 @ SV51 @ SY1550 )
| ~ ( ~ ( rel_s4 @ SY1550 @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1549 ) @ empty_set @ ( sK12_SY238 @ SY1550 @ SY1549 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1507: $i] :
( ~ ( rel_s4 @ SY1550 @ SY1507 )
| ( in @ SV40 @ SY1549 @ SY1507 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(253,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i] :
( ( ( ! [SY1552: mu] :
( ~ ( exists_in_world @ SY1552 @ SV51 )
| ! [SY1553: $i] :
( ~ ( rel_s4 @ SV51 @ SY1553 )
| ~ ( ~ ( rel_s4 @ SY1553 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SY1552 @ ( sK11_SY241 @ SY1553 @ SY1552 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1510: $i] :
( ~ ( rel_s4 @ SY1553 @ SY1510 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SY1552 ) @ empty_set @ SY1510 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(254,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu] :
( ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( ! [SY1584: $i] :
( ~ ( rel_s4 @ SV52 @ SY1584 )
| ! [SY1585: mu] :
( ~ ( exists_in_world @ SY1585 @ SY1584 )
| ! [SY1586: $i] :
( ~ ( rel_s4 @ SY1584 @ SY1586 )
| ~ ( ~ ( rel_s4 @ SY1586 @ ( sK22_SY893 @ SY1586 @ SY1585 @ SY1584 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1586 @ SY1585 @ SY1584 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1587: $i] :
( ~ ( rel_s4 @ SY1586 @ SY1587 )
| ( qmltpeq @ ( set_difference @ SY1585 @ SV41 ) @ ( set_difference @ SY1585 @ SV61 ) @ SY1587 ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(255,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV53: mu,SV62: $i,SV43: $i] :
( ( ( ~ ( rel_s4 @ SV43 @ SV62 )
| ! [SY1588: mu] :
( ~ ( exists_in_world @ SY1588 @ SV62 )
| ! [SY1589: $i] :
( ~ ( rel_s4 @ SV62 @ SY1589 )
| ~ ( ~ ( rel_s4 @ SY1589 @ ( sK16_SY471 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1589 @ ( sK15_SY472 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1588 @ SV32 @ ( sK15_SY472 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1563: $i] :
( ~ ( rel_s4 @ SY1589 @ SY1563 )
| ( in @ SY1588 @ SV53 @ SY1563 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(256,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV54: mu,SV63: $i,SV44: $i] :
( ( ( ~ ( rel_s4 @ SV44 @ SV63 )
| ~ ( ~ ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(257,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV55: mu,SV64: $i,SV45: $i] :
( ( ( ~ ( rel_s4 @ SV45 @ SV64 )
| ! [SY1592: mu] :
( ~ ( exists_in_world @ SY1592 @ SV64 )
| ! [SY1593: $i] :
( ~ ( rel_s4 @ SV64 @ SY1593 )
| ~ ( ~ ( rel_s4 @ SY1593 @ ( sK18_SY608 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1593 @ ( sK17_SY609 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1592 @ ( sK17_SY609 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1569: $i] :
( ~ ( rel_s4 @ SY1593 @ SY1569 )
| ( in @ SV55 @ SY1592 @ SY1569 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(258,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV56: mu,SV65: $i,SV46: $i] :
( ( ( ~ ( rel_s4 @ SV46 @ SV65 )
| ! [SY1595: mu] :
( ~ ( exists_in_world @ SY1595 @ SV65 )
| ! [SY1596: $i] :
( ~ ( rel_s4 @ SV65 @ SY1596 )
| ~ ( ~ ( rel_s4 @ SY1596 @ ( sK23_SY998 @ SY1596 @ SY1595 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1596 @ SY1595 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1573: $i] :
( ~ ( rel_s4 @ SY1596 @ SY1573 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1595 ) @ ( set_difference @ SV56 @ SY1595 ) @ SY1573 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(259,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV57: mu,SV66: $i,SV47: $i] :
( ( ( ~ ( rel_s4 @ SV47 @ SV66 )
| ~ ( ~ ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(260,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV58: mu,SV67: $i,SV48: $i] :
( ( ( ~ ( rel_s4 @ SV48 @ SV67 )
| ! [SY1599: mu] :
( ~ ( exists_in_world @ SY1599 @ SV67 )
| ! [SY1600: $i] :
( ~ ( rel_s4 @ SV67 @ SY1600 )
| ~ ( ~ ( rel_s4 @ SY1600 @ ( sK25_SY1130 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1600 @ ( sK24_SY1105 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SY1599 @ ( sK24_SY1105 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1600 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1599 @ SY1495 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV59: mu,SV68: $i,SV49: $i] :
( ( ( ~ ( rel_s4 @ SV49 @ SV68 )
| ~ ( ~ ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(262,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV60: mu,SV69: $i,SV50: $i] :
( ( ( ~ ( rel_s4 @ SV50 @ SV69 )
| ~ ( ~ ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(263,plain,
( ( ~ ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(264,plain,
( ( ~ ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(265,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV51 )
| ! [SY1604: $i] :
( ~ ( rel_s4 @ SV51 @ SY1604 )
| ~ ( ~ ( rel_s4 @ SY1604 @ ( sK12_SY238 @ SY1604 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SY1604 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1605: $i] :
( ~ ( rel_s4 @ SY1604 @ SY1605 )
| ( in @ SV40 @ SV70 @ SY1605 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(266,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV51 )
| ! [SY1606: $i] :
( ~ ( rel_s4 @ SV51 @ SY1606 )
| ~ ( ~ ( rel_s4 @ SY1606 @ ( sK11_SY241 @ SY1606 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SY1606 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1607: $i] :
( ~ ( rel_s4 @ SY1606 @ SY1607 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1607 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(267,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV61: mu,SV72: $i,SV52: $i] :
( ( ( ~ ( rel_s4 @ SV52 @ SV72 )
| ! [SY1608: mu] :
( ~ ( exists_in_world @ SY1608 @ SV72 )
| ! [SY1609: $i] :
( ~ ( rel_s4 @ SV72 @ SY1609 )
| ~ ( ~ ( rel_s4 @ SY1609 @ ( sK22_SY893 @ SY1609 @ SY1608 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1609 @ SY1608 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1587: $i] :
( ~ ( rel_s4 @ SY1609 @ SY1587 )
| ( qmltpeq @ ( set_difference @ SY1608 @ SV41 ) @ ( set_difference @ SY1608 @ SV61 ) @ SY1587 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(268,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV53: mu,SV62: $i,SV43: $i] :
( ( ( ~ ( rel_s4 @ SV43 @ SV62 ) )
= $true )
| ( ( ! [SY1588: mu] :
( ~ ( exists_in_world @ SY1588 @ SV62 )
| ! [SY1589: $i] :
( ~ ( rel_s4 @ SV62 @ SY1589 )
| ~ ( ~ ( rel_s4 @ SY1589 @ ( sK16_SY471 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1589 @ ( sK15_SY472 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1588 @ SV32 @ ( sK15_SY472 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1563: $i] :
( ~ ( rel_s4 @ SY1589 @ SY1563 )
| ( in @ SY1588 @ SV53 @ SY1563 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(269,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV54: mu,SV63: $i,SV44: $i] :
( ( ( ~ ( rel_s4 @ SV44 @ SV63 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(270,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV55: mu,SV64: $i,SV45: $i] :
( ( ( ~ ( rel_s4 @ SV45 @ SV64 ) )
= $true )
| ( ( ! [SY1592: mu] :
( ~ ( exists_in_world @ SY1592 @ SV64 )
| ! [SY1593: $i] :
( ~ ( rel_s4 @ SV64 @ SY1593 )
| ~ ( ~ ( rel_s4 @ SY1593 @ ( sK18_SY608 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1593 @ ( sK17_SY609 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1592 @ ( sK17_SY609 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1569: $i] :
( ~ ( rel_s4 @ SY1593 @ SY1569 )
| ( in @ SV55 @ SY1592 @ SY1569 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(271,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV56: mu,SV65: $i,SV46: $i] :
( ( ( ~ ( rel_s4 @ SV46 @ SV65 ) )
= $true )
| ( ( ! [SY1595: mu] :
( ~ ( exists_in_world @ SY1595 @ SV65 )
| ! [SY1596: $i] :
( ~ ( rel_s4 @ SV65 @ SY1596 )
| ~ ( ~ ( rel_s4 @ SY1596 @ ( sK23_SY998 @ SY1596 @ SY1595 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1596 @ SY1595 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1573: $i] :
( ~ ( rel_s4 @ SY1596 @ SY1573 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1595 ) @ ( set_difference @ SV56 @ SY1595 ) @ SY1573 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(272,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV57: mu,SV66: $i,SV47: $i] :
( ( ( ~ ( rel_s4 @ SV47 @ SV66 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(273,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV58: mu,SV67: $i,SV48: $i] :
( ( ( ~ ( rel_s4 @ SV48 @ SV67 ) )
= $true )
| ( ( ! [SY1599: mu] :
( ~ ( exists_in_world @ SY1599 @ SV67 )
| ! [SY1600: $i] :
( ~ ( rel_s4 @ SV67 @ SY1600 )
| ~ ( ~ ( rel_s4 @ SY1600 @ ( sK25_SY1130 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1600 @ ( sK24_SY1105 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SY1599 @ ( sK24_SY1105 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1600 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1599 @ SY1495 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(274,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV59: mu,SV68: $i,SV49: $i] :
( ( ( ~ ( rel_s4 @ SV49 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(275,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV60: mu,SV69: $i,SV50: $i] :
( ( ( ~ ( rel_s4 @ SV50 @ SV69 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(276,plain,
( ( sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(277,plain,
( ( ~ sK10_REN
| ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(278,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV70: mu] :
( ( ( ~ ( exists_in_world @ SV70 @ SV51 ) )
= $true )
| ( ( ! [SY1604: $i] :
( ~ ( rel_s4 @ SV51 @ SY1604 )
| ~ ( ~ ( rel_s4 @ SY1604 @ ( sK12_SY238 @ SY1604 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SY1604 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1605: $i] :
( ~ ( rel_s4 @ SY1604 @ SY1605 )
| ( in @ SV40 @ SV70 @ SY1605 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(279,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV71: mu] :
( ( ( ~ ( exists_in_world @ SV71 @ SV51 ) )
= $true )
| ( ( ! [SY1606: $i] :
( ~ ( rel_s4 @ SV51 @ SY1606 )
| ~ ( ~ ( rel_s4 @ SY1606 @ ( sK11_SY241 @ SY1606 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SY1606 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1607: $i] :
( ~ ( rel_s4 @ SY1606 @ SY1607 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1607 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(280,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV61: mu,SV72: $i,SV52: $i] :
( ( ( ~ ( rel_s4 @ SV52 @ SV72 ) )
= $true )
| ( ( ! [SY1608: mu] :
( ~ ( exists_in_world @ SY1608 @ SV72 )
| ! [SY1609: $i] :
( ~ ( rel_s4 @ SV72 @ SY1609 )
| ~ ( ~ ( rel_s4 @ SY1609 @ ( sK22_SY893 @ SY1609 @ SY1608 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1609 @ SY1608 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1587: $i] :
( ~ ( rel_s4 @ SY1609 @ SY1587 )
| ( qmltpeq @ ( set_difference @ SY1608 @ SV41 ) @ ( set_difference @ SY1608 @ SV61 ) @ SY1587 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(281,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV53: mu,SV62: $i,SV43: $i] :
( ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( ! [SY1588: mu] :
( ~ ( exists_in_world @ SY1588 @ SV62 )
| ! [SY1589: $i] :
( ~ ( rel_s4 @ SV62 @ SY1589 )
| ~ ( ~ ( rel_s4 @ SY1589 @ ( sK16_SY471 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1589 @ ( sK15_SY472 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SY1588 @ SV32 @ ( sK15_SY472 @ SY1589 @ SY1588 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1563: $i] :
( ~ ( rel_s4 @ SY1589 @ SY1563 )
| ( in @ SY1588 @ SV53 @ SY1563 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(282,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV54: mu,SV63: $i,SV44: $i] :
( ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(283,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV55: mu,SV64: $i,SV45: $i] :
( ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( ! [SY1592: mu] :
( ~ ( exists_in_world @ SY1592 @ SV64 )
| ! [SY1593: $i] :
( ~ ( rel_s4 @ SV64 @ SY1593 )
| ~ ( ~ ( rel_s4 @ SY1593 @ ( sK18_SY608 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1593 @ ( sK17_SY609 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SY1592 @ ( sK17_SY609 @ SY1593 @ SY1592 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1569: $i] :
( ~ ( rel_s4 @ SY1593 @ SY1569 )
| ( in @ SV55 @ SY1592 @ SY1569 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(284,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV56: mu,SV65: $i,SV46: $i] :
( ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( ! [SY1595: mu] :
( ~ ( exists_in_world @ SY1595 @ SV65 )
| ! [SY1596: $i] :
( ~ ( rel_s4 @ SV65 @ SY1596 )
| ~ ( ~ ( rel_s4 @ SY1596 @ ( sK23_SY998 @ SY1596 @ SY1595 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1596 @ SY1595 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1573: $i] :
( ~ ( rel_s4 @ SY1596 @ SY1573 )
| ( qmltpeq @ ( set_difference @ SV35 @ SY1595 ) @ ( set_difference @ SV56 @ SY1595 ) @ SY1573 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(285,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV57: mu,SV66: $i,SV47: $i] :
( ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
| ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(286,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV58: mu,SV67: $i,SV48: $i] :
( ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( ! [SY1599: mu] :
( ~ ( exists_in_world @ SY1599 @ SV67 )
| ! [SY1600: $i] :
( ~ ( rel_s4 @ SV67 @ SY1600 )
| ~ ( ~ ( rel_s4 @ SY1600 @ ( sK25_SY1130 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1600 @ ( sK24_SY1105 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SY1599 @ ( sK24_SY1105 @ SY1600 @ SY1599 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1495: $i] :
( ~ ( rel_s4 @ SY1600 @ SY1495 )
| ( qmltpeq @ SV37 @ SY1599 @ SY1495 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(287,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV59: mu,SV68: $i,SV49: $i] :
( ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
| ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(288,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV60: mu,SV69: $i,SV50: $i] :
( ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
| ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(289,plain,
( ( sK10_REN = $true )
| ( ( ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(290,plain,
( ( ( ~ sK10_REN ) = $true )
| ( ( ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(291,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV70: mu] :
( ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( ! [SY1604: $i] :
( ~ ( rel_s4 @ SV51 @ SY1604 )
| ~ ( ~ ( rel_s4 @ SY1604 @ ( sK12_SY238 @ SY1604 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SY1604 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1605: $i] :
( ~ ( rel_s4 @ SY1604 @ SY1605 )
| ( in @ SV40 @ SV70 @ SY1605 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(292,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV71: mu] :
( ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( ! [SY1606: $i] :
( ~ ( rel_s4 @ SV51 @ SY1606 )
| ~ ( ~ ( rel_s4 @ SY1606 @ ( sK11_SY241 @ SY1606 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SY1606 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1607: $i] :
( ~ ( rel_s4 @ SY1606 @ SY1607 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1607 ) ) ) )
= $true )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(293,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV61: mu,SV72: $i,SV52: $i] :
( ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( ! [SY1608: mu] :
( ~ ( exists_in_world @ SY1608 @ SV72 )
| ! [SY1609: $i] :
( ~ ( rel_s4 @ SV72 @ SY1609 )
| ~ ( ~ ( rel_s4 @ SY1609 @ ( sK22_SY893 @ SY1609 @ SY1608 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1609 @ SY1608 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1587: $i] :
( ~ ( rel_s4 @ SY1609 @ SY1587 )
| ( qmltpeq @ ( set_difference @ SY1608 @ SV41 ) @ ( set_difference @ SY1608 @ SV61 ) @ SY1587 ) ) ) ) )
= $true )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(294,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV62 )
| ! [SY1611: $i] :
( ~ ( rel_s4 @ SV62 @ SY1611 )
| ~ ( ~ ( rel_s4 @ SY1611 @ ( sK16_SY471 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1611 @ ( sK15_SY472 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1612: $i] :
( ~ ( rel_s4 @ SY1611 @ SY1612 )
| ( in @ SV73 @ SV53 @ SY1612 ) ) ) )
= $true )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(295,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
| ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(296,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV64 )
| ! [SY1613: $i] :
( ~ ( rel_s4 @ SV64 @ SY1613 )
| ~ ( ~ ( rel_s4 @ SY1613 @ ( sK18_SY608 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1613 @ ( sK17_SY609 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1614: $i] :
( ~ ( rel_s4 @ SY1613 @ SY1614 )
| ( in @ SV55 @ SV74 @ SY1614 ) ) ) )
= $true )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(297,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV65: $i,SV75: mu] :
( ( ( ~ ( exists_in_world @ SV75 @ SV65 )
| ! [SY1615: $i] :
( ~ ( rel_s4 @ SV65 @ SY1615 )
| ~ ( ~ ( rel_s4 @ SY1615 @ ( sK23_SY998 @ SY1615 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1615 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1616: $i] :
( ~ ( rel_s4 @ SY1615 @ SY1616 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1616 ) ) ) )
= $true )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(298,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV47: $i,SV57: mu,SV66: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) ) )
= $true )
| ( ( ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(299,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu] :
( ( ( ~ ( exists_in_world @ SV76 @ SV67 )
| ! [SY1617: $i] :
( ~ ( rel_s4 @ SV67 @ SY1617 )
| ~ ( ~ ( rel_s4 @ SY1617 @ ( sK25_SY1130 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1617 @ ( sK24_SY1105 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1618: $i] :
( ~ ( rel_s4 @ SY1617 @ SY1618 )
| ( qmltpeq @ SV37 @ SV76 @ SY1618 ) ) ) )
= $true )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(300,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) )
= $true )
| ( ( ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(301,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV50: $i,SV60: mu,SV69: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) ) )
= $true )
| ( ( ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(302,plain,
( ( ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(303,plain,
( ( sK10_REN = $false )
| ( ( ~ ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(304,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV70: mu,SV77: $i,SV51: $i] :
( ( ( ~ ( rel_s4 @ SV51 @ SV77 )
| ~ ( ~ ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(305,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV71: mu,SV78: $i,SV51: $i] :
( ( ( ~ ( rel_s4 @ SV51 @ SV78 )
| ~ ( ~ ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(306,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV72: $i,SV79: mu] :
( ( ( ~ ( exists_in_world @ SV79 @ SV72 )
| ! [SY1621: $i] :
( ~ ( rel_s4 @ SV72 @ SY1621 )
| ~ ( ~ ( rel_s4 @ SY1621 @ ( sK22_SY893 @ SY1621 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1621 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1622: $i] :
( ~ ( rel_s4 @ SY1621 @ SY1622 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1622 ) ) ) )
= $true )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(307,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu] :
( ( ( ~ ( exists_in_world @ SV73 @ SV62 ) )
= $true )
| ( ( ! [SY1611: $i] :
( ~ ( rel_s4 @ SV62 @ SY1611 )
| ~ ( ~ ( rel_s4 @ SY1611 @ ( sK16_SY471 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1611 @ ( sK15_SY472 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1612: $i] :
( ~ ( rel_s4 @ SY1611 @ SY1612 )
| ( in @ SV73 @ SV53 @ SY1612 ) ) ) )
= $true )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(308,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(309,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu] :
( ( ( ~ ( exists_in_world @ SV74 @ SV64 ) )
= $true )
| ( ( ! [SY1613: $i] :
( ~ ( rel_s4 @ SV64 @ SY1613 )
| ~ ( ~ ( rel_s4 @ SY1613 @ ( sK18_SY608 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1613 @ ( sK17_SY609 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1614: $i] :
( ~ ( rel_s4 @ SY1613 @ SY1614 )
| ( in @ SV55 @ SV74 @ SY1614 ) ) ) )
= $true )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(310,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV65: $i,SV75: mu] :
( ( ( ~ ( exists_in_world @ SV75 @ SV65 ) )
= $true )
| ( ( ! [SY1615: $i] :
( ~ ( rel_s4 @ SV65 @ SY1615 )
| ~ ( ~ ( rel_s4 @ SY1615 @ ( sK23_SY998 @ SY1615 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1615 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1616: $i] :
( ~ ( rel_s4 @ SY1615 @ SY1616 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1616 ) ) ) )
= $true )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(311,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV47: $i,SV57: mu,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
| ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
= $false )
| ( ( ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(312,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu] :
( ( ( ~ ( exists_in_world @ SV76 @ SV67 ) )
= $true )
| ( ( ! [SY1617: $i] :
( ~ ( rel_s4 @ SV67 @ SY1617 )
| ~ ( ~ ( rel_s4 @ SY1617 @ ( sK25_SY1130 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1617 @ ( sK24_SY1105 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1618: $i] :
( ~ ( rel_s4 @ SY1617 @ SY1618 )
| ( qmltpeq @ SV37 @ SV76 @ SY1618 ) ) ) )
= $true )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(313,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(314,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV50: $i,SV60: mu,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
| ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
= $false )
| ( ( ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(315,plain,
( ( ( ~ ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(316,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(317,plain,
( ( ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(318,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV70: mu,SV77: $i,SV51: $i] :
( ( ( ~ ( rel_s4 @ SV51 @ SV77 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(319,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV71: mu,SV78: $i,SV51: $i] :
( ( ( ~ ( rel_s4 @ SV51 @ SV78 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(320,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV72: $i,SV79: mu] :
( ( ( ~ ( exists_in_world @ SV79 @ SV72 ) )
= $true )
| ( ( ! [SY1621: $i] :
( ~ ( rel_s4 @ SV72 @ SY1621 )
| ~ ( ~ ( rel_s4 @ SY1621 @ ( sK22_SY893 @ SY1621 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1621 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1622: $i] :
( ~ ( rel_s4 @ SY1621 @ SY1622 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1622 ) ) ) )
= $true )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(321,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu] :
( ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( ! [SY1611: $i] :
( ~ ( rel_s4 @ SV62 @ SY1611 )
| ~ ( ~ ( rel_s4 @ SY1611 @ ( sK16_SY471 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SY1611 @ ( sK15_SY472 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SY1611 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1612: $i] :
( ~ ( rel_s4 @ SY1611 @ SY1612 )
| ( in @ SV73 @ SV53 @ SY1612 ) ) ) )
= $true )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(322,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(323,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu] :
( ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( ! [SY1613: $i] :
( ~ ( rel_s4 @ SV64 @ SY1613 )
| ~ ( ~ ( rel_s4 @ SY1613 @ ( sK18_SY608 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SY1613 @ ( sK17_SY609 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SY1613 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1614: $i] :
( ~ ( rel_s4 @ SY1613 @ SY1614 )
| ( in @ SV55 @ SV74 @ SY1614 ) ) ) )
= $true )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(324,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV65: $i,SV75: mu] :
( ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( ! [SY1615: $i] :
( ~ ( rel_s4 @ SV65 @ SY1615 )
| ~ ( ~ ( rel_s4 @ SY1615 @ ( sK23_SY998 @ SY1615 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SY1615 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1616: $i] :
( ~ ( rel_s4 @ SY1615 @ SY1616 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1616 ) ) ) )
= $true )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(325,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV47: $i,SV57: mu,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
= $false )
| ( ( ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(326,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV66: $i,SV57: mu,SV36: mu] :
( ( ( ~ ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
= $false )
| ( ( ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(327,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu] :
( ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( rel_s4 @ SV67 @ SY1617 )
| ~ ( ~ ( rel_s4 @ SY1617 @ ( sK25_SY1130 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SY1617 @ ( sK24_SY1105 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SY1617 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1618: $i] :
( ~ ( rel_s4 @ SY1617 @ SY1618 )
| ( qmltpeq @ SV37 @ SV76 @ SY1618 ) ) ) )
= $true )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(328,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(329,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV59: mu,SV38: mu] :
( ( ( ~ ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(330,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV50: $i,SV60: mu,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
= $false )
| ( ( ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(331,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV69: $i,SV60: mu,SV39: mu] :
( ( ( ~ ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
= $false )
| ( ( ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(332,plain,
( ( ( rel_s4 @ sK4_SY1292 @ sK6_SY1310 )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(333,plain,
( ( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) ) )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(334,plain,
( ( ( ~ ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(335,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(336,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV70: mu,SV77: $i,SV51: $i] :
( ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(337,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV71: mu,SV78: $i,SV51: $i] :
( ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
| ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(338,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV72: $i,SV79: mu] :
( ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( ! [SY1621: $i] :
( ~ ( rel_s4 @ SV72 @ SY1621 )
| ~ ( ~ ( rel_s4 @ SY1621 @ ( sK22_SY893 @ SY1621 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SY1621 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1622: $i] :
( ~ ( rel_s4 @ SY1621 @ SY1622 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1622 ) ) ) )
= $true )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(339,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV73: mu,SV80: $i,SV62: $i] :
( ( ( ~ ( rel_s4 @ SV62 @ SV80 )
| ~ ( ~ ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(340,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(341,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV63: $i,SV54: mu,SV33: mu] :
( ( ( ~ ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(342,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV74: mu,SV81: $i,SV64: $i] :
( ( ( ~ ( rel_s4 @ SV64 @ SV81 )
| ~ ( ~ ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(343,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV75: mu,SV82: $i,SV65: $i] :
( ( ( ~ ( rel_s4 @ SV65 @ SV82 )
| ~ ( ~ ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(344,plain,
! [SV10: $i,SV24: $i,SV36: mu,SV47: $i,SV57: mu,SV66: $i] :
( ( ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $true )
| ( ( ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(345,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV66: $i,SV57: mu,SV36: mu] :
( ( ( ~ ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) ) )
= $true )
| ( ( ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(346,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV76: mu,SV83: $i,SV67: $i] :
( ( ( ~ ( rel_s4 @ SV67 @ SV83 )
| ~ ( ~ ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(347,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i] :
( ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(348,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV59: mu,SV38: mu] :
( ( ( ~ ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $true )
| ( ( ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(349,plain,
! [SV13: $i,SV27: $i,SV39: mu,SV50: $i,SV60: mu,SV69: $i] :
( ( ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $true )
| ( ( ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(350,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV69: $i,SV60: mu,SV39: mu] :
( ( ( ~ ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) ) )
= $true )
| ( ( ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(351,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(352,plain,
( ( ( rel_s4 @ sK4_SY1292 @ sK8_SY1307 )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(353,plain,
( ( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) ) )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(354,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV70: mu,SV77: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) ) )
= $true )
| ( ( ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(355,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV71: mu,SV78: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) ) )
= $true )
| ( ( ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(356,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV79: mu,SV84: $i,SV72: $i] :
( ( ( ~ ( rel_s4 @ SV72 @ SV84 )
| ~ ( ~ ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(357,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV73: mu,SV80: $i,SV62: $i] :
( ( ( ~ ( rel_s4 @ SV62 @ SV80 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(358,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(359,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV63: $i,SV54: mu,SV33: mu] :
( ( ( ~ ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(360,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV74: mu,SV81: $i,SV64: $i] :
( ( ( ~ ( rel_s4 @ SV64 @ SV81 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(361,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV75: mu,SV82: $i,SV65: $i] :
( ( ( ~ ( rel_s4 @ SV65 @ SV82 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(362,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV36: mu,SV57: mu,SV85: $i,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ SV85 )
| ( qmltpeq @ SV57 @ SV36 @ SV85 ) )
= $true )
| ( ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(363,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV66: $i,SV57: mu,SV36: mu] :
( ( ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $false )
| ( ( ! [SY1598: $i] :
( ~ ( rel_s4 @ SV66 @ SY1598 )
| ( qmltpeq @ SV57 @ SV36 @ SY1598 ) ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(364,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV76: mu,SV83: $i,SV67: $i] :
( ( ( ~ ( rel_s4 @ SV67 @ SV83 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(365,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV86: $i,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ SV86 )
| ~ ( ~ ( rel_s4 @ SV86 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) )
= $true )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(366,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV59: mu,SV38: mu] :
( ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( ! [SY1602: $i] :
( ~ ( rel_s4 @ SV68 @ SY1602 )
| ~ ( ~ ( rel_s4 @ SY1602 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SY1602 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(367,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV60: mu,SV39: mu,SV87: $i,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ SV87 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SV87 ) )
= $true )
| ( ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(368,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV69: $i,SV60: mu,SV39: mu] :
( ( ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $false )
| ( ( ! [SY1603: $i] :
( ~ ( rel_s4 @ SV69 @ SY1603 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SY1603 ) ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(369,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(370,plain,
( ( ( ~ ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(371,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) )
| ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(372,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV70: mu,SV77: $i] :
( ( ( ~ ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $false )
| ( ( ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(373,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV71: mu,SV78: $i] :
( ( ( ~ ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
| ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $false )
| ( ( ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(374,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV79: mu,SV84: $i,SV72: $i] :
( ( ( ~ ( rel_s4 @ SV72 @ SV84 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(375,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV73: mu,SV80: $i,SV62: $i] :
( ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(376,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(377,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV63: $i,SV54: mu,SV33: mu] :
( ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(378,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV74: mu,SV81: $i,SV64: $i] :
( ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(379,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV75: mu,SV82: $i,SV65: $i] :
( ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
| ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(380,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV36: mu,SV57: mu,SV85: $i,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ SV85 ) )
= $true )
| ( ( qmltpeq @ SV57 @ SV36 @ SV85 )
= $true )
| ( ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(381,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV36: mu,SV57: mu,SV88: $i,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ SV88 )
| ( qmltpeq @ SV57 @ SV36 @ SV88 ) )
= $true )
| ( ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $false )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(382,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV76: mu,SV83: $i,SV67: $i] :
( ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(383,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV86: $i,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ SV86 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV86 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) )
= $true )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(384,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV89: $i,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ SV89 )
| ~ ( ~ ( rel_s4 @ SV89 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) )
= $true )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(385,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV60: mu,SV39: mu,SV87: $i,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ SV87 ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SV87 )
= $true )
| ( ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(386,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV60: mu,SV39: mu,SV90: $i,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ SV90 )
| ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SV90 ) )
= $true )
| ( ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $false )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(387,plain,
( ( ( ! [SX0: $i] :
( ~ ( rel_s4 @ sK6_SY1310 @ SX0 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SX0 ) ) )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(388,plain,
( ( ( ~ ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) ) )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(389,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(390,plain,
( ( ( ~ ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(391,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV70: mu,SV77: $i] :
( ( ( ~ ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $false )
| ( ( ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(392,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV77: $i,SV70: mu,SV40: mu] :
( ( ( ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $false )
| ( ( ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(393,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV71: mu,SV78: $i] :
( ( ( ~ ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $false )
| ( ( ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(394,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV78: $i,SV71: mu,SV40: mu] :
( ( ( ~ ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $false )
| ( ( ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[373]) ).
thf(395,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV79: mu,SV84: $i,SV72: $i] :
( ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
| ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(396,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
| ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(397,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(398,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV54: mu,SV63: $i,SV33: mu] :
( ( ( ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(399,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
| ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(400,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
| ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(401,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV65: $i,SV75: mu,SV82: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) ) )
= $true )
| ( ( ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(402,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV36: mu,SV57: mu,SV85: $i,SV66: $i] :
( ( ( rel_s4 @ SV66 @ SV85 )
= $false )
| ( ( qmltpeq @ SV57 @ SV36 @ SV85 )
= $true )
| ( ( rel_s4 @ SV66 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $true )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(403,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV36: mu,SV57: mu,SV88: $i,SV66: $i] :
( ( ( ~ ( rel_s4 @ SV66 @ SV88 ) )
= $true )
| ( ( qmltpeq @ SV57 @ SV36 @ SV88 )
= $true )
| ( ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $false )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(404,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
| ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(405,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV86: $i,SV68: $i] :
( ( ( rel_s4 @ SV68 @ SV86 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV86 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) )
= $true )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(406,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV89: $i,SV68: $i] :
( ( ( ~ ( rel_s4 @ SV68 @ SV89 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV89 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) )
= $true )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(407,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV60: mu,SV39: mu,SV87: $i,SV69: $i] :
( ( ( rel_s4 @ SV69 @ SV87 )
= $false )
| ( ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SV87 )
= $true )
| ( ( rel_s4 @ SV69 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $true )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(408,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV60: mu,SV39: mu,SV90: $i,SV69: $i] :
( ( ( ~ ( rel_s4 @ SV69 @ SV90 ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SV90 )
= $true )
| ( ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $false )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(409,plain,
! [SV91: $i] :
( ( ( ~ ( rel_s4 @ sK6_SY1310 @ SV91 )
| ( in @ sK3_SY1283 @ sK5_SY1300 @ SV91 ) )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(410,plain,
( ( ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
| ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(411,plain,
( ( ( ! [SX0: $i] :
( ~ ( rel_s4 @ sK8_SY1307 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SX0 ) ) )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(412,plain,
( ( ( ~ ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) ) )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(413,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV70: mu,SV77: $i] :
( ( ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(414,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV77: $i,SV70: mu,SV40: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $true )
| ( ( ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(415,plain,
! [SV14: $i,SV28: $i,SV40: mu,SV51: $i,SV71: mu,SV78: $i] :
( ( ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(416,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV78: $i,SV71: mu,SV40: mu] :
( ( ( ~ ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) ) )
= $true )
| ( ( ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(417,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV72: $i,SV79: mu,SV84: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) ) )
= $true )
| ( ( ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(418,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(419,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(420,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV54: mu,SV63: $i,SV33: mu] :
( ( ( ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(421,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(422,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV54: mu,SV63: $i,SV33: mu] :
( ( ( ~ ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $false )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(423,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(424,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV65: $i,SV75: mu,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
| ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
= $false )
| ( ( ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(425,plain,
! [SV10: $i,SV24: $i,SV47: $i,SV36: mu,SV57: mu,SV88: $i,SV66: $i] :
( ( ( rel_s4 @ SV66 @ SV88 )
= $false )
| ( ( qmltpeq @ SV57 @ SV36 @ SV88 )
= $true )
| ( ( qmltpeq @ SV36 @ SV57 @ ( sK26_SY1216 @ SV66 @ SV57 @ SV47 @ SV36 @ SV24 @ SV10 ) )
= $false )
| ( ( rel_s4 @ SV47 @ SV66 )
= $false )
| ( ( exists_in_world @ SV57 @ SV47 )
= $false )
| ( ( rel_s4 @ SV24 @ SV47 )
= $false )
| ( ( exists_in_world @ SV36 @ SV24 )
= $false )
| ( ( rel_s4 @ SV10 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(426,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(427,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i,SV86: $i] :
( ( ( ~ ( rel_s4 @ SV86 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV86 )
= $false )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(428,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV89: $i,SV68: $i] :
( ( ( rel_s4 @ SV68 @ SV89 )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV89 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) ) )
= $true )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(429,plain,
! [SV13: $i,SV27: $i,SV50: $i,SV60: mu,SV39: mu,SV90: $i,SV69: $i] :
( ( ( rel_s4 @ SV69 @ SV90 )
= $false )
| ( ( qmltpeq @ ( singleton @ SV39 ) @ ( singleton @ SV60 ) @ SV90 )
= $true )
| ( ( qmltpeq @ SV39 @ SV60 @ ( sK21_SY796 @ SV69 @ SV60 @ SV50 @ SV39 @ SV27 @ SV13 ) )
= $false )
| ( ( rel_s4 @ SV50 @ SV69 )
= $false )
| ( ( exists_in_world @ SV60 @ SV50 )
= $false )
| ( ( rel_s4 @ SV27 @ SV50 )
= $false )
| ( ( exists_in_world @ SV39 @ SV27 )
= $false )
| ( ( rel_s4 @ SV13 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(430,plain,
! [SV91: $i] :
( ( ( ~ ( rel_s4 @ sK6_SY1310 @ SV91 ) )
= $true )
| ( ( in @ sK3_SY1283 @ sK5_SY1300 @ SV91 )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(431,plain,
( ( ( ~ ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(432,plain,
( ( ( ~ ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(433,plain,
! [SV92: $i] :
( ( ( ~ ( rel_s4 @ sK8_SY1307 @ SV92 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SV92 ) )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(434,plain,
( ( ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
| ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(435,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV70: mu,SV40: mu,SV93: $i,SV77: $i] :
( ( ( ~ ( rel_s4 @ SV77 @ SV93 )
| ( in @ SV40 @ SV70 @ SV93 ) )
= $true )
| ( ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(436,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV77: $i,SV70: mu,SV40: mu] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( ! [SY1619: $i] :
( ~ ( rel_s4 @ SV77 @ SY1619 )
| ( in @ SV40 @ SV70 @ SY1619 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(437,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV71: mu,SV40: mu,SV94: $i,SV78: $i] :
( ( ( ~ ( rel_s4 @ SV78 @ SV94 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SV94 ) )
= $true )
| ( ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(438,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV78: $i,SV71: mu,SV40: mu] :
( ( ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( ! [SY1620: $i] :
( ~ ( rel_s4 @ SV78 @ SY1620 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SY1620 ) ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(439,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV72: $i,SV79: mu,SV84: $i] :
( ( ( ~ ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
| ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
= $false )
| ( ( ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(440,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(441,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV95: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV95 )
| ( empty @ SV54 @ SV95 ) )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(442,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV54: mu,SV63: $i,SV33: mu] :
( ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(443,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV63: $i] :
( ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(444,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV54: mu,SV63: $i,SV33: mu] :
( ( ( ~ ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(445,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(446,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV65: $i,SV75: mu,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
= $false )
| ( ( ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(447,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV75: mu,SV82: $i,SV56: mu,SV35: mu] :
( ( ( ~ ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
= $false )
| ( ( ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(448,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(449,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i,SV86: $i] :
( ( ( ~ ( rel_s4 @ SV86 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV86 )
= $false )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(450,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV86: $i,SV38: mu,SV59: mu] :
( ( ( ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV86 )
= $false )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(451,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i,SV89: $i] :
( ( ( ~ ( rel_s4 @ SV89 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
| ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV89 )
= $false )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(452,plain,
! [SV91: $i] :
( ( ( rel_s4 @ sK6_SY1310 @ SV91 )
= $false )
| ( ( in @ sK3_SY1283 @ sK5_SY1300 @ SV91 )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(453,plain,
( ( ( rel_s4 @ sK6_SY1310 @ sK7_SY1314 )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(454,plain,
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 ) )
= $true )
| ( sK10_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(455,plain,
! [SV92: $i] :
( ( ( ~ ( rel_s4 @ sK8_SY1307 @ SV92 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SV92 )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(456,plain,
( ( ( ~ ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(457,plain,
( ( ( ~ ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(458,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV70: mu,SV40: mu,SV93: $i,SV77: $i] :
( ( ( ~ ( rel_s4 @ SV77 @ SV93 ) )
= $true )
| ( ( in @ SV40 @ SV70 @ SV93 )
= $true )
| ( ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(459,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV70: mu,SV40: mu,SV96: $i,SV77: $i] :
( ( ( ~ ( rel_s4 @ SV77 @ SV96 )
| ( in @ SV40 @ SV70 @ SV96 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(460,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV71: mu,SV40: mu,SV94: $i,SV78: $i] :
( ( ( ~ ( rel_s4 @ SV78 @ SV94 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SV94 )
= $true )
| ( ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(461,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV71: mu,SV40: mu,SV97: $i,SV78: $i] :
( ( ( ~ ( rel_s4 @ SV78 @ SV97 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SV97 ) )
= $true )
| ( ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(462,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV72: $i,SV79: mu,SV84: $i] :
( ( ( ~ ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
= $false )
| ( ( ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(463,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV79: mu,SV84: $i,SV61: mu,SV41: mu] :
( ( ( ~ ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
= $false )
| ( ( ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(464,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(465,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV73: mu,SV80: $i,SV53: mu,SV32: mu] :
( ( ( ~ ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(466,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV95: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV95 ) )
= $true )
| ( ( empty @ SV54 @ SV95 )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(467,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV98: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV98 )
| ( empty @ SV54 @ SV98 ) )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(468,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV33: mu,SV54: mu,SV99: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV99 )
| ( empty @ SV54 @ SV99 ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(469,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV54: mu,SV63: $i,SV33: mu] :
( ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( ! [SY1591: $i] :
( ~ ( rel_s4 @ SV63 @ SY1591 )
| ( empty @ SV54 @ SY1591 ) ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(470,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(471,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV74: mu,SV81: $i,SV55: mu,SV34: mu] :
( ( ( ~ ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(472,plain,
! [SV9: $i,SV23: $i,SV35: mu,SV46: $i,SV56: mu,SV65: $i,SV75: mu,SV82: $i] :
( ( ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $true )
| ( ( ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(473,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV75: mu,SV82: $i,SV56: mu,SV35: mu] :
( ( ( ~ ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) ) )
= $true )
| ( ( ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(474,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(475,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV76: mu,SV83: $i,SV58: mu,SV37: mu] :
( ( ( ~ ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(476,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i,SV86: $i] :
( ( ( rel_s4 @ SV86 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV68 @ SV86 )
= $false )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(477,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV86: $i,SV38: mu,SV59: mu] :
( ( ( ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $true )
| ( ( rel_s4 @ SV68 @ SV86 )
= $false )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(478,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i,SV89: $i] :
( ( ( ~ ( rel_s4 @ SV89 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV89 )
= $false )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(479,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV89: $i,SV38: mu,SV59: mu] :
( ( ( ~ ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV89 )
= $false )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(480,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ sK7_SY1314 )
= $false )
| ( sK10_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(481,plain,
! [SV92: $i] :
( ( ( rel_s4 @ sK8_SY1307 @ SV92 )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3_SY1283 ) @ sK5_SY1300 ) @ empty_set @ SV92 )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(482,plain,
( ( ( rel_s4 @ sK8_SY1307 @ sK9_SY1316 )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(483,plain,
( ( ( ~ ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 ) )
= $true )
| ( sK10_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(484,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV70: mu,SV40: mu,SV93: $i,SV77: $i] :
( ( ( rel_s4 @ SV77 @ SV93 )
= $false )
| ( ( in @ SV40 @ SV70 @ SV93 )
= $true )
| ( ( rel_s4 @ SV77 @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(485,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV70: mu,SV40: mu,SV96: $i,SV77: $i] :
( ( ( ~ ( rel_s4 @ SV77 @ SV96 ) )
= $true )
| ( ( in @ SV40 @ SV70 @ SV96 )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(486,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV71: mu,SV40: mu,SV94: $i,SV78: $i] :
( ( ( rel_s4 @ SV78 @ SV94 )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SV94 )
= $true )
| ( ( rel_s4 @ SV78 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $true )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(487,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV71: mu,SV40: mu,SV97: $i,SV78: $i] :
( ( ( ~ ( rel_s4 @ SV78 @ SV97 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SV97 )
= $true )
| ( ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(488,plain,
! [SV15: $i,SV29: $i,SV41: mu,SV52: $i,SV61: mu,SV72: $i,SV79: mu,SV84: $i] :
( ( ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $true )
| ( ( ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(489,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV79: mu,SV84: $i,SV61: mu,SV41: mu] :
( ( ( ~ ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) ) )
= $true )
| ( ( ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(490,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(491,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV73: mu,SV80: $i,SV53: mu,SV32: mu] :
( ( ( ~ ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(492,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV95: $i,SV63: $i] :
( ( ( rel_s4 @ SV63 @ SV95 )
= $false )
| ( ( empty @ SV54 @ SV95 )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(493,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV98: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV98 ) )
= $true )
| ( ( empty @ SV54 @ SV98 )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(494,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV33: mu,SV54: mu,SV99: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV99 ) )
= $true )
| ( ( empty @ SV54 @ SV99 )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(495,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV33: mu,SV54: mu,SV100: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV100 )
| ( empty @ SV54 @ SV100 ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(496,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(497,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV74: mu,SV81: $i,SV55: mu,SV34: mu] :
( ( ( ~ ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(498,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV56: mu,SV75: mu,SV35: mu,SV101: $i,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ SV101 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SV101 ) )
= $true )
| ( ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(499,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV75: mu,SV82: $i,SV56: mu,SV35: mu] :
( ( ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $false )
| ( ( ! [SY1625: $i] :
( ~ ( rel_s4 @ SV82 @ SY1625 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SY1625 ) ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(500,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(501,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV76: mu,SV83: $i,SV58: mu,SV37: mu] :
( ( ( ~ ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $true )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(502,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV86: $i,SV38: mu,SV59: mu] :
( ( ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV86 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV86 )
= $false )
| ( ( rel_s4 @ SV68 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(503,plain,
! [SV12: $i,SV26: $i,SV38: mu,SV49: $i,SV59: mu,SV68: $i,SV89: $i] :
( ( ( rel_s4 @ SV89 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $true )
| ( ( rel_s4 @ SV68 @ SV89 )
= $false )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(504,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV89: $i,SV38: mu,SV59: mu] :
( ( ( ~ ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) ) )
= $true )
| ( ( rel_s4 @ SV68 @ SV89 )
= $false )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(505,plain,
( ( ( in @ sK3_SY1283 @ sK5_SY1300 @ sK9_SY1316 )
= $false )
| ( sK10_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(506,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV70: mu,SV40: mu,SV96: $i,SV77: $i] :
( ( ( rel_s4 @ SV77 @ SV96 )
= $false )
| ( ( in @ SV40 @ SV70 @ SV96 )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV70 ) @ empty_set @ ( sK12_SY238 @ SV77 @ SV70 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( rel_s4 @ SV51 @ SV77 )
= $false )
| ( ( exists_in_world @ SV70 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(507,plain,
! [SV14: $i,SV28: $i,SV51: $i,SV71: mu,SV40: mu,SV97: $i,SV78: $i] :
( ( ( rel_s4 @ SV78 @ SV97 )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV40 ) @ SV71 ) @ empty_set @ SV97 )
= $true )
| ( ( in @ SV40 @ SV71 @ ( sK11_SY241 @ SV78 @ SV71 @ SV51 @ SV40 @ SV28 @ SV14 ) )
= $false )
| ( ( rel_s4 @ SV51 @ SV78 )
= $false )
| ( ( exists_in_world @ SV71 @ SV51 )
= $false )
| ( ( rel_s4 @ SV28 @ SV51 )
= $false )
| ( ( exists_in_world @ SV40 @ SV28 )
= $false )
| ( ( rel_s4 @ SV14 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(508,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV61: mu,SV41: mu,SV79: mu,SV102: $i,SV84: $i] :
( ( ( ~ ( rel_s4 @ SV84 @ SV102 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SV102 ) )
= $true )
| ( ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(509,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV79: mu,SV84: $i,SV61: mu,SV41: mu] :
( ( ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $false )
| ( ( ! [SY1627: $i] :
( ~ ( rel_s4 @ SV84 @ SY1627 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SY1627 ) ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(510,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(511,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV73: mu,SV80: $i,SV53: mu,SV32: mu] :
( ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(512,plain,
! [SV7: $i,SV21: $i,SV33: mu,SV44: $i,SV54: mu,SV98: $i,SV63: $i] :
( ( ( rel_s4 @ SV63 @ SV98 )
= $false )
| ( ( empty @ SV54 @ SV98 )
= $true )
| ( ( rel_s4 @ SV63 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(513,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV33: mu,SV54: mu,SV99: $i,SV63: $i] :
( ( ( rel_s4 @ SV63 @ SV99 )
= $false )
| ( ( empty @ SV54 @ SV99 )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV63 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $true )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(514,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV33: mu,SV54: mu,SV100: $i,SV63: $i] :
( ( ( ~ ( rel_s4 @ SV63 @ SV100 ) )
= $true )
| ( ( empty @ SV54 @ SV100 )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(515,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(516,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV74: mu,SV81: $i,SV55: mu,SV34: mu] :
( ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(517,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV56: mu,SV75: mu,SV35: mu,SV101: $i,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ SV101 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SV101 )
= $true )
| ( ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(518,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV56: mu,SV75: mu,SV35: mu,SV103: $i,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ SV103 )
| ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SV103 ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(519,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(520,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV76: mu,SV83: $i,SV58: mu,SV37: mu] :
( ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( ~ ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(521,plain,
! [SV12: $i,SV26: $i,SV49: $i,SV68: $i,SV89: $i,SV38: mu,SV59: mu] :
( ( ( in @ SV59 @ SV38 @ ( sK13_SY344 @ SV89 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV68 @ SV89 )
= $false )
| ( ( in @ SV38 @ SV59 @ ( sK14_SY342 @ SV68 @ SV59 @ SV49 @ SV38 @ SV26 @ SV12 ) )
= $false )
| ( ( rel_s4 @ SV49 @ SV68 )
= $false )
| ( ( exists_in_world @ SV59 @ SV49 )
= $false )
| ( ( rel_s4 @ SV26 @ SV49 )
= $false )
| ( ( exists_in_world @ SV38 @ SV26 )
= $false )
| ( ( rel_s4 @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(522,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV61: mu,SV41: mu,SV79: mu,SV102: $i,SV84: $i] :
( ( ( ~ ( rel_s4 @ SV84 @ SV102 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SV102 )
= $true )
| ( ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(523,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV61: mu,SV41: mu,SV79: mu,SV104: $i,SV84: $i] :
( ( ( ~ ( rel_s4 @ SV84 @ SV104 )
| ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SV104 ) )
= $true )
| ( ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $false )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(524,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(525,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV53: mu,SV62: $i,SV80: $i,SV32: mu,SV73: mu] :
( ( ( ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(526,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
| ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(527,plain,
! [SV7: $i,SV21: $i,SV44: $i,SV33: mu,SV54: mu,SV100: $i,SV63: $i] :
( ( ( rel_s4 @ SV63 @ SV100 )
= $false )
| ( ( empty @ SV54 @ SV100 )
= $true )
| ( ( qmltpeq @ SV33 @ SV54 @ ( sK20_SY718 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( empty @ SV33 @ ( sK19_SY719 @ SV63 @ SV54 @ SV44 @ SV33 @ SV21 @ SV7 ) )
= $false )
| ( ( rel_s4 @ SV44 @ SV63 )
= $false )
| ( ( exists_in_world @ SV54 @ SV44 )
= $false )
| ( ( rel_s4 @ SV21 @ SV44 )
= $false )
| ( ( exists_in_world @ SV33 @ SV21 )
= $false )
| ( ( rel_s4 @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(528,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(529,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV55: mu,SV64: $i,SV81: $i,SV74: mu,SV34: mu] :
( ( ( ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(530,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
| ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(531,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV56: mu,SV75: mu,SV35: mu,SV101: $i,SV82: $i] :
( ( ( rel_s4 @ SV82 @ SV101 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SV101 )
= $true )
| ( ( rel_s4 @ SV82 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $true )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(532,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV56: mu,SV75: mu,SV35: mu,SV103: $i,SV82: $i] :
( ( ( ~ ( rel_s4 @ SV82 @ SV103 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SV103 )
= $true )
| ( ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(533,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(534,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV67: $i,SV83: $i,SV76: mu,SV58: mu] :
( ( ( ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(535,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
| ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(536,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV61: mu,SV41: mu,SV79: mu,SV102: $i,SV84: $i] :
( ( ( rel_s4 @ SV84 @ SV102 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SV102 )
= $true )
| ( ( rel_s4 @ SV84 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $true )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(537,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV61: mu,SV41: mu,SV79: mu,SV104: $i,SV84: $i] :
( ( ( ~ ( rel_s4 @ SV84 @ SV104 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SV104 )
= $true )
| ( ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $false )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(538,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(539,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV53: mu,SV62: $i,SV80: $i,SV32: mu,SV73: mu] :
( ( ( ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(540,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(541,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV53: mu,SV62: $i,SV80: $i,SV32: mu,SV73: mu] :
( ( ( ~ ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $false )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(542,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(543,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV55: mu,SV64: $i,SV81: $i,SV74: mu,SV34: mu] :
( ( ( ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(544,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(545,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV55: mu,SV64: $i,SV81: $i,SV74: mu,SV34: mu] :
( ( ( ~ ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $false )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(546,plain,
! [SV9: $i,SV23: $i,SV46: $i,SV65: $i,SV56: mu,SV75: mu,SV35: mu,SV103: $i,SV82: $i] :
( ( ( rel_s4 @ SV82 @ SV103 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV35 @ SV75 ) @ ( set_difference @ SV56 @ SV75 ) @ SV103 )
= $true )
| ( ( qmltpeq @ SV35 @ SV56 @ ( sK23_SY998 @ SV82 @ SV75 @ SV65 @ SV56 @ SV46 @ SV35 @ SV23 @ SV9 ) )
= $false )
| ( ( rel_s4 @ SV65 @ SV82 )
= $false )
| ( ( exists_in_world @ SV75 @ SV65 )
= $false )
| ( ( rel_s4 @ SV46 @ SV65 )
= $false )
| ( ( exists_in_world @ SV56 @ SV46 )
= $false )
| ( ( rel_s4 @ SV23 @ SV46 )
= $false )
| ( ( exists_in_world @ SV35 @ SV23 )
= $false )
| ( ( rel_s4 @ SV9 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(547,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(548,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV67: $i,SV83: $i,SV76: mu,SV58: mu] :
( ( ( ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(549,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(550,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV67: $i,SV83: $i,SV76: mu,SV58: mu] :
( ( ( ~ ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $false )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(551,plain,
! [SV15: $i,SV29: $i,SV52: $i,SV72: $i,SV61: mu,SV41: mu,SV79: mu,SV104: $i,SV84: $i] :
( ( ( rel_s4 @ SV84 @ SV104 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV79 @ SV41 ) @ ( set_difference @ SV79 @ SV61 ) @ SV104 )
= $true )
| ( ( qmltpeq @ SV41 @ SV61 @ ( sK22_SY893 @ SV84 @ SV79 @ SV72 @ SV61 @ SV52 @ SV41 @ SV29 @ SV15 ) )
= $false )
| ( ( rel_s4 @ SV72 @ SV84 )
= $false )
| ( ( exists_in_world @ SV79 @ SV72 )
= $false )
| ( ( rel_s4 @ SV52 @ SV72 )
= $false )
| ( ( exists_in_world @ SV61 @ SV52 )
= $false )
| ( ( rel_s4 @ SV29 @ SV52 )
= $false )
| ( ( exists_in_world @ SV41 @ SV29 )
= $false )
| ( ( rel_s4 @ SV15 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(552,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV62: $i,SV53: mu,SV73: mu,SV105: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV105 )
| ( in @ SV73 @ SV53 @ SV105 ) )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(553,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV53: mu,SV62: $i,SV80: $i,SV32: mu,SV73: mu] :
( ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(554,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV53: mu,SV62: $i,SV73: mu,SV80: $i] :
( ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(555,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV53: mu,SV62: $i,SV80: $i,SV32: mu,SV73: mu] :
( ( ( ~ ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) ) )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(556,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV64: $i,SV74: mu,SV55: mu,SV106: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV106 )
| ( in @ SV55 @ SV74 @ SV106 ) )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(557,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV55: mu,SV64: $i,SV81: $i,SV74: mu,SV34: mu] :
( ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(558,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV55: mu,SV64: $i,SV74: mu,SV81: $i] :
( ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(559,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV55: mu,SV64: $i,SV81: $i,SV74: mu,SV34: mu] :
( ( ( ~ ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) ) )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(560,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV37: mu,SV107: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV107 )
| ( qmltpeq @ SV37 @ SV76 @ SV107 ) )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(561,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV67: $i,SV83: $i,SV76: mu,SV58: mu] :
( ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(562,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV83: $i] :
( ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(563,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV67: $i,SV83: $i,SV76: mu,SV58: mu] :
( ( ( ~ ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(564,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV62: $i,SV53: mu,SV73: mu,SV105: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV105 ) )
= $true )
| ( ( in @ SV73 @ SV53 @ SV105 )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(565,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV62: $i,SV53: mu,SV73: mu,SV108: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV108 )
| ( in @ SV73 @ SV53 @ SV108 ) )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(566,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV32: mu,SV53: mu,SV73: mu,SV109: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV109 )
| ( in @ SV73 @ SV53 @ SV109 ) )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(567,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV53: mu,SV62: $i,SV80: $i,SV32: mu,SV73: mu] :
( ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( ! [SY1623: $i] :
( ~ ( rel_s4 @ SV80 @ SY1623 )
| ( in @ SV73 @ SV53 @ SY1623 ) ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(568,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV64: $i,SV74: mu,SV55: mu,SV106: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV106 ) )
= $true )
| ( ( in @ SV55 @ SV74 @ SV106 )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(569,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV64: $i,SV74: mu,SV55: mu,SV110: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV110 )
| ( in @ SV55 @ SV74 @ SV110 ) )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(570,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV34: mu,SV74: mu,SV55: mu,SV111: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV111 )
| ( in @ SV55 @ SV74 @ SV111 ) )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(571,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV55: mu,SV64: $i,SV81: $i,SV74: mu,SV34: mu] :
( ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( rel_s4 @ SV81 @ SY1624 )
| ( in @ SV55 @ SV74 @ SY1624 ) ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(572,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV37: mu,SV107: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV107 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV76 @ SV107 )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(573,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV37: mu,SV112: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV112 )
| ( qmltpeq @ SV37 @ SV76 @ SV112 ) )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(574,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV58: mu,SV76: mu,SV37: mu,SV113: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV113 )
| ( qmltpeq @ SV37 @ SV76 @ SV113 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(575,plain,
! [SV11: $i,SV25: $i,SV37: mu,SV48: $i,SV67: $i,SV83: $i,SV76: mu,SV58: mu] :
( ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( ! [SY1626: $i] :
( ~ ( rel_s4 @ SV83 @ SY1626 )
| ( qmltpeq @ SV37 @ SV76 @ SY1626 ) ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(576,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV62: $i,SV53: mu,SV73: mu,SV105: $i,SV80: $i] :
( ( ( rel_s4 @ SV80 @ SV105 )
= $false )
| ( ( in @ SV73 @ SV53 @ SV105 )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(577,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV62: $i,SV53: mu,SV73: mu,SV108: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV108 ) )
= $true )
| ( ( in @ SV73 @ SV53 @ SV108 )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(578,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV32: mu,SV53: mu,SV73: mu,SV109: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV109 ) )
= $true )
| ( ( in @ SV73 @ SV53 @ SV109 )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(579,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV32: mu,SV53: mu,SV73: mu,SV114: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV114 )
| ( in @ SV73 @ SV53 @ SV114 ) )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(580,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV64: $i,SV74: mu,SV55: mu,SV106: $i,SV81: $i] :
( ( ( rel_s4 @ SV81 @ SV106 )
= $false )
| ( ( in @ SV55 @ SV74 @ SV106 )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(581,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV64: $i,SV74: mu,SV55: mu,SV110: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV110 ) )
= $true )
| ( ( in @ SV55 @ SV74 @ SV110 )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(582,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV34: mu,SV74: mu,SV55: mu,SV111: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV111 ) )
= $true )
| ( ( in @ SV55 @ SV74 @ SV111 )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(583,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV34: mu,SV74: mu,SV55: mu,SV115: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV115 )
| ( in @ SV55 @ SV74 @ SV115 ) )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(584,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV37: mu,SV107: $i,SV83: $i] :
( ( ( rel_s4 @ SV83 @ SV107 )
= $false )
| ( ( qmltpeq @ SV37 @ SV76 @ SV107 )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(585,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV37: mu,SV112: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV112 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV76 @ SV112 )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(586,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV58: mu,SV76: mu,SV37: mu,SV113: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV113 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV76 @ SV113 )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(587,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV58: mu,SV76: mu,SV37: mu,SV116: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV116 )
| ( qmltpeq @ SV37 @ SV76 @ SV116 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(588,plain,
! [SV6: $i,SV20: $i,SV32: mu,SV43: $i,SV62: $i,SV53: mu,SV73: mu,SV108: $i,SV80: $i] :
( ( ( rel_s4 @ SV80 @ SV108 )
= $false )
| ( ( in @ SV73 @ SV53 @ SV108 )
= $true )
| ( ( rel_s4 @ SV80 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(589,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV32: mu,SV53: mu,SV73: mu,SV109: $i,SV80: $i] :
( ( ( rel_s4 @ SV80 @ SV109 )
= $false )
| ( ( in @ SV73 @ SV53 @ SV109 )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV80 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $true )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(590,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV32: mu,SV53: mu,SV73: mu,SV114: $i,SV80: $i] :
( ( ( ~ ( rel_s4 @ SV80 @ SV114 ) )
= $true )
| ( ( in @ SV73 @ SV53 @ SV114 )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(591,plain,
! [SV8: $i,SV22: $i,SV34: mu,SV45: $i,SV64: $i,SV74: mu,SV55: mu,SV110: $i,SV81: $i] :
( ( ( rel_s4 @ SV81 @ SV110 )
= $false )
| ( ( in @ SV55 @ SV74 @ SV110 )
= $true )
| ( ( rel_s4 @ SV81 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(592,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV34: mu,SV74: mu,SV55: mu,SV111: $i,SV81: $i] :
( ( ( rel_s4 @ SV81 @ SV111 )
= $false )
| ( ( in @ SV55 @ SV74 @ SV111 )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV81 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $true )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(593,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV34: mu,SV74: mu,SV55: mu,SV115: $i,SV81: $i] :
( ( ( ~ ( rel_s4 @ SV81 @ SV115 ) )
= $true )
| ( ( in @ SV55 @ SV74 @ SV115 )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(594,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV58: mu,SV67: $i,SV76: mu,SV37: mu,SV112: $i,SV83: $i] :
( ( ( rel_s4 @ SV83 @ SV112 )
= $false )
| ( ( qmltpeq @ SV37 @ SV76 @ SV112 )
= $true )
| ( ( rel_s4 @ SV83 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(595,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV58: mu,SV76: mu,SV37: mu,SV113: $i,SV83: $i] :
( ( ( rel_s4 @ SV83 @ SV113 )
= $false )
| ( ( qmltpeq @ SV37 @ SV76 @ SV113 )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV83 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $true )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(596,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV58: mu,SV76: mu,SV37: mu,SV116: $i,SV83: $i] :
( ( ( ~ ( rel_s4 @ SV83 @ SV116 ) )
= $true )
| ( ( qmltpeq @ SV37 @ SV76 @ SV116 )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(597,plain,
! [SV6: $i,SV20: $i,SV43: $i,SV62: $i,SV32: mu,SV53: mu,SV73: mu,SV114: $i,SV80: $i] :
( ( ( rel_s4 @ SV80 @ SV114 )
= $false )
| ( ( in @ SV73 @ SV53 @ SV114 )
= $true )
| ( ( qmltpeq @ SV32 @ SV53 @ ( sK16_SY471 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( in @ SV73 @ SV32 @ ( sK15_SY472 @ SV80 @ SV73 @ SV62 @ SV53 @ SV43 @ SV32 @ SV20 @ SV6 ) )
= $false )
| ( ( rel_s4 @ SV62 @ SV80 )
= $false )
| ( ( exists_in_world @ SV73 @ SV62 )
= $false )
| ( ( rel_s4 @ SV43 @ SV62 )
= $false )
| ( ( exists_in_world @ SV53 @ SV43 )
= $false )
| ( ( rel_s4 @ SV20 @ SV43 )
= $false )
| ( ( exists_in_world @ SV32 @ SV20 )
= $false )
| ( ( rel_s4 @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(598,plain,
! [SV8: $i,SV22: $i,SV45: $i,SV64: $i,SV34: mu,SV74: mu,SV55: mu,SV115: $i,SV81: $i] :
( ( ( rel_s4 @ SV81 @ SV115 )
= $false )
| ( ( in @ SV55 @ SV74 @ SV115 )
= $true )
| ( ( qmltpeq @ SV34 @ SV55 @ ( sK18_SY608 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( in @ SV34 @ SV74 @ ( sK17_SY609 @ SV81 @ SV74 @ SV64 @ SV55 @ SV45 @ SV34 @ SV22 @ SV8 ) )
= $false )
| ( ( rel_s4 @ SV64 @ SV81 )
= $false )
| ( ( exists_in_world @ SV74 @ SV64 )
= $false )
| ( ( rel_s4 @ SV45 @ SV64 )
= $false )
| ( ( exists_in_world @ SV55 @ SV45 )
= $false )
| ( ( rel_s4 @ SV22 @ SV45 )
= $false )
| ( ( exists_in_world @ SV34 @ SV22 )
= $false )
| ( ( rel_s4 @ SV8 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(599,plain,
! [SV11: $i,SV25: $i,SV48: $i,SV67: $i,SV58: mu,SV76: mu,SV37: mu,SV116: $i,SV83: $i] :
( ( ( rel_s4 @ SV83 @ SV116 )
= $false )
| ( ( qmltpeq @ SV37 @ SV76 @ SV116 )
= $true )
| ( ( qmltpeq @ SV37 @ SV58 @ ( sK25_SY1130 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( qmltpeq @ SV58 @ SV76 @ ( sK24_SY1105 @ SV83 @ SV76 @ SV67 @ SV58 @ SV48 @ SV37 @ SV25 @ SV11 ) )
= $false )
| ( ( rel_s4 @ SV67 @ SV83 )
= $false )
| ( ( exists_in_world @ SV76 @ SV67 )
= $false )
| ( ( rel_s4 @ SV48 @ SV67 )
= $false )
| ( ( exists_in_world @ SV58 @ SV48 )
= $false )
| ( ( rel_s4 @ SV25 @ SV48 )
= $false )
| ( ( exists_in_world @ SV37 @ SV25 )
= $false )
| ( ( rel_s4 @ SV11 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(600,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[82,599,598,597,595,594,592,591,589,588,584,580,576,551,546,536,531,527,521,513,512,507,506,505,503,502,492,486,484,482,481,480,476,453,452,429,425,407,402,352,332,238,206,202,164,130,125,114,98]) ).
thf(601,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET925^7 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 14:51:31 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.97/1.22
% 5.97/1.22 No.of.Axioms: 21
% 5.97/1.22
% 5.97/1.22 Length.of.Defs: 5508
% 5.97/1.22
% 5.97/1.22 Contains.Choice.Funs: false
% 5.97/1.22 .............................................................
% 5.97/1.22
% 5.97/1.22 ********************************
% 5.97/1.22 * All subproblems solved! *
% 5.97/1.22 ********************************
% 5.97/1.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:600,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 5.97/1.22
% 5.97/1.22 %**** Beginning of derivation protocol ****
% 5.97/1.22 % SZS output start CNFRefutation
% See solution above
% 5.97/1.23
% 5.97/1.23 %**** End of derivation protocol ****
% 5.97/1.23 %**** no. of clauses in derivation: 595 ****
% 5.97/1.23 %**** clause counter: 600 ****
% 5.97/1.23
% 5.97/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:600,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------