TSTP Solution File: SET926^7 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET926^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:06:20 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 102
% Syntax : Number of formulae : 352 ( 149 unt; 47 typ; 32 def)
% Number of atoms : 2419 ( 609 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 4610 ( 671 ~; 725 |; 9 &;3195 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 191 ( 191 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 6 con; 0-3 aty)
% Number of variables : 842 ( 117 ^ 718 !; 7 ?; 842 :)
% 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_sK1_X,type,
sK1_X: $i > mu ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY28,type,
sK3_SY28: $i > mu ).
thf(tp_sK4_SY34,type,
sK4_SY34: $i > mu ).
thf(tp_sK5_SY56,type,
sK5_SY56: mu ).
thf(tp_sK6_SY58,type,
sK6_SY58: mu ).
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
@ ( mexists_ind
@ ^ [A: mu] : ( mnot @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( empty @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(4,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(5,axiom,
mvalid @ ( empty @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(6,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(7,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_2) ).
thf(8,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_1) ).
thf(9,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_substitution_1) ).
thf(10,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(11,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_substitution_2) ).
thf(12,axiom,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_substitution_1) ).
thf(13,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(14,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(15,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(16,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(17,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_singleton_ax) ).
thf(18,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(19,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax) ).
thf(20,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(21,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(22,axiom,
! [V: $i] :
? [X: mu] : ( exists_in_world @ X @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(23,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_zfmisc_1) ).
thf(24,negated_conjecture,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[23]) ).
thf(25,plain,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(26,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(27,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(28,plain,
( ( ! [V: $i] : ( exists_in_world @ ( sK1_X @ V ) @ V ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(29,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(30,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(31,plain,
( ( ! [X: mu,V: $i,W: $i] :
( ~ ( exists_in_world @ X @ V )
| ~ ( rel_s4 @ V @ W )
| ( exists_in_world @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(32,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(33,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(34,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(35,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(36,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(37,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [X: mu] :
( mforall_ind
@ ^ [Y: mu] :
( mforall_ind
@ ^ [Z: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(38,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(39,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(40,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(41,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(42,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(43,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(44,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(45,plain,
( ( mvalid @ ( empty @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(46,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(47,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(48,plain,
( ( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( empty @ A ) ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(49,plain,
( ( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( mnot @ ( empty @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(50,plain,
( ( ~ ( mvalid
@ ( mforall_ind
@ ^ [A: mu] :
( mforall_ind
@ ^ [B: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( in @ SX3 @ SX1 @ SX0 ) )
| ( in @ SX3 @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(52,plain,
( ( ! [SX0: $i] : ( rel_s4 @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[29,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( set_difference @ SX3 @ SX1 ) @ ( set_difference @ SX3 @ SX2 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ ( singleton @ SX1 ) @ SX0 )
| ~ ( in @ SX1 @ SX2 @ SX0 ) )
| ~ ( ~ ~ ( in @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ ( singleton @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(56,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( empty @ SX1 @ SX0 ) )
| ( empty @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ~ ( ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX2 @ SX3 @ SX0 ) )
| ( qmltpeq @ SX1 @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(60,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ empty_set @ SX0 )
| ( in @ SX1 @ SX2 @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ empty_set @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(62,plain,
( ( ! [SX0: $i] : ( empty @ empty_set @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[45,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(63,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ( empty @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(64,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ! [SX3: mu] :
( ~ ( exists_in_world @ SX3 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( set_difference @ SX1 @ SX3 ) @ ( set_difference @ SX2 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(65,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( rel_s4 @ SX0 @ SX1 )
| ~ ( rel_s4 @ SX1 @ SX2 ) )
| ( rel_s4 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(66,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ~ ( empty @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ~ ( qmltpeq @ SX1 @ SX2 @ SX0 )
| ( qmltpeq @ ( singleton @ SX1 ) @ ( singleton @ SX2 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(68,plain,
( ( ~ ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ empty_set @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ ( singleton @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(69,plain,
! [SV1: $i] :
( ( exists_in_world @ ( sK1_X @ SV1 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(70,plain,
! [SV2: mu] :
( ( ! [SY0: $i,SY1: $i] :
( ~ ( exists_in_world @ SV2 @ SY0 )
| ~ ( rel_s4 @ SY0 @ SY1 )
| ( exists_in_world @ SV2 @ SY1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(71,plain,
! [SV3: $i] :
( ( exists_in_world @ empty_set @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(72,plain,
! [SV4: $i] :
( ( ! [SY2: mu] : ( exists_in_world @ ( singleton @ SY2 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(73,plain,
! [SV5: $i] :
( ( ! [SY3: mu,SY4: mu] : ( exists_in_world @ ( set_difference @ SY3 @ SY4 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(74,plain,
! [SV6: $i] :
( ( ! [SY5: mu] :
( ~ ( exists_in_world @ SY5 @ SV6 )
| ! [SY6: mu] :
( ~ ( exists_in_world @ SY6 @ SV6 )
| ! [SY7: mu] :
( ~ ( exists_in_world @ SY7 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SY5 @ SY6 @ SV6 )
| ~ ( in @ SY7 @ SY5 @ SV6 ) )
| ( in @ SY7 @ SY6 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(75,plain,
! [SV7: $i] :
( ( rel_s4 @ SV7 @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(76,plain,
! [SV8: $i] :
( ( ! [SY8: mu] :
( ~ ( exists_in_world @ SY8 @ SV8 )
| ( qmltpeq @ SY8 @ SY8 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(77,plain,
! [SV9: $i] :
( ( ! [SY9: mu] :
( ~ ( exists_in_world @ SY9 @ SV9 )
| ! [SY10: mu] :
( ~ ( exists_in_world @ SY10 @ SV9 )
| ! [SY11: mu] :
( ~ ( exists_in_world @ SY11 @ SV9 )
| ~ ( qmltpeq @ SY9 @ SY10 @ SV9 )
| ( qmltpeq @ ( set_difference @ SY11 @ SY9 ) @ ( set_difference @ SY11 @ SY10 ) @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(78,plain,
! [SV10: $i] :
( ( ! [SY12: mu] :
( ~ ( exists_in_world @ SY12 @ SV10 )
| ! [SY13: mu] :
( ~ ( exists_in_world @ SY13 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY12 ) @ SY13 ) @ ( singleton @ SY12 ) @ SV10 )
| ~ ( in @ SY12 @ SY13 @ SV10 ) )
| ~ ( ~ ~ ( in @ SY12 @ SY13 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY12 ) @ SY13 ) @ ( singleton @ SY12 ) @ SV10 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(79,plain,
! [SV11: $i] :
( ( ! [SY14: mu] :
( ~ ( exists_in_world @ SY14 @ SV11 )
| ! [SY15: mu] :
( ~ ( exists_in_world @ SY15 @ SV11 )
| ! [SY16: mu] :
( ~ ( exists_in_world @ SY16 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SY14 @ SY15 @ SV11 )
| ~ ( in @ SY14 @ SY16 @ SV11 ) )
| ( in @ SY15 @ SY16 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(80,plain,
! [SV12: $i] :
( ( ! [SY17: mu] :
( ~ ( exists_in_world @ SY17 @ SV12 )
| ! [SY18: mu] :
( ~ ( exists_in_world @ SY18 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SY17 @ SY18 @ SV12 )
| ~ ( empty @ SY17 @ SV12 ) )
| ( empty @ SY18 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(81,plain,
! [SV13: $i] :
( ( ! [SY19: mu] :
( ~ ( exists_in_world @ SY19 @ SV13 )
| ! [SY20: mu] :
( ~ ( exists_in_world @ SY20 @ SV13 )
| ~ ( qmltpeq @ SY19 @ SY20 @ SV13 )
| ( qmltpeq @ SY20 @ SY19 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(82,plain,
! [SV14: $i] :
( ( ! [SY21: mu] :
( ~ ( exists_in_world @ SY21 @ SV14 )
| ! [SY22: mu] :
( ~ ( exists_in_world @ SY22 @ SV14 )
| ! [SY23: mu] :
( ~ ( exists_in_world @ SY23 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SY21 @ SY22 @ SV14 )
| ~ ( qmltpeq @ SY22 @ SY23 @ SV14 ) )
| ( qmltpeq @ SY21 @ SY23 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(83,plain,
! [SV15: $i] :
( ( ! [SY24: mu] :
( ~ ( exists_in_world @ SY24 @ SV15 )
| ! [SY25: mu] :
( ~ ( exists_in_world @ SY25 @ SV15 )
| ~ ( in @ SY24 @ SY25 @ SV15 )
| ~ ( in @ SY25 @ SY24 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(84,plain,
! [SV16: $i] :
( ( ! [SY26: mu] :
( ~ ( exists_in_world @ SY26 @ SV16 )
| ! [SY27: mu] :
( ~ ( exists_in_world @ SY27 @ SV16 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY26 ) @ SY27 ) @ empty_set @ SV16 )
| ( in @ SY26 @ SY27 @ SV16 ) )
| ~ ( ~ ( in @ SY26 @ SY27 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY26 ) @ SY27 ) @ empty_set @ SV16 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(85,plain,
! [SV17: $i] :
( ( empty @ empty_set @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(86,plain,
! [SV18: $i] :
( ( ~ ! [SY28: mu] :
( ~ ( exists_in_world @ SY28 @ SV18 )
| ~ ( empty @ SY28 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(87,plain,
! [SV19: $i] :
( ( ! [SY29: mu] :
( ~ ( exists_in_world @ SY29 @ SV19 )
| ! [SY30: mu] :
( ~ ( exists_in_world @ SY30 @ SV19 )
| ! [SY31: mu] :
( ~ ( exists_in_world @ SY31 @ SV19 )
| ~ ( qmltpeq @ SY29 @ SY30 @ SV19 )
| ( qmltpeq @ ( set_difference @ SY29 @ SY31 ) @ ( set_difference @ SY30 @ SY31 ) @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(88,plain,
! [SV20: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV20 @ SY32 )
| ~ ( rel_s4 @ SY32 @ SY33 ) )
| ( rel_s4 @ SV20 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(89,plain,
! [SV21: $i] :
( ( ~ ! [SY34: mu] :
( ~ ( exists_in_world @ SY34 @ SV21 )
| ~ ~ ( empty @ SY34 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(90,plain,
! [SV22: $i] :
( ( ! [SY35: mu] :
( ~ ( exists_in_world @ SY35 @ SV22 )
| ! [SY36: mu] :
( ~ ( exists_in_world @ SY36 @ SV22 )
| ~ ( qmltpeq @ SY35 @ SY36 @ SV22 )
| ( qmltpeq @ ( singleton @ SY35 ) @ ( singleton @ SY36 ) @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ! [SX2: mu] :
( ~ ( exists_in_world @ SX2 @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ empty_set @ SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SX1 ) @ SX2 ) @ ( singleton @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(92,plain,
! [SV23: $i,SV2: mu] :
( ( ! [SY37: $i] :
( ~ ( exists_in_world @ SV2 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SY37 )
| ( exists_in_world @ SV2 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(93,plain,
! [SV4: $i,SV24: mu] :
( ( exists_in_world @ ( singleton @ SV24 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV5: $i,SV25: mu] :
( ( ! [SY38: mu] : ( exists_in_world @ ( set_difference @ SV25 @ SY38 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV6: $i,SV26: mu] :
( ( ~ ( exists_in_world @ SV26 @ SV6 )
| ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV6 )
| ! [SY40: mu] :
( ~ ( exists_in_world @ SY40 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY39 @ SV6 )
| ~ ( in @ SY40 @ SV26 @ SV6 ) )
| ( in @ SY40 @ SY39 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV8: $i,SV27: mu] :
( ( ~ ( exists_in_world @ SV27 @ SV8 )
| ( qmltpeq @ SV27 @ SV27 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(97,plain,
! [SV9: $i,SV28: mu] :
( ( ~ ( exists_in_world @ SV28 @ SV9 )
| ! [SY41: mu] :
( ~ ( exists_in_world @ SY41 @ SV9 )
| ! [SY42: mu] :
( ~ ( exists_in_world @ SY42 @ SV9 )
| ~ ( qmltpeq @ SV28 @ SY41 @ SV9 )
| ( qmltpeq @ ( set_difference @ SY42 @ SV28 ) @ ( set_difference @ SY42 @ SY41 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(98,plain,
! [SV10: $i,SV29: mu] :
( ( ~ ( exists_in_world @ SV29 @ SV10 )
| ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SY43 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SY43 @ SV10 ) )
| ~ ( ~ ~ ( in @ SV29 @ SY43 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SY43 ) @ ( singleton @ SV29 ) @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(99,plain,
! [SV11: $i,SV30: mu] :
( ( ~ ( exists_in_world @ SV30 @ SV11 )
| ! [SY44: mu] :
( ~ ( exists_in_world @ SY44 @ SV11 )
| ! [SY45: mu] :
( ~ ( exists_in_world @ SY45 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY44 @ SV11 )
| ~ ( in @ SV30 @ SY45 @ SV11 ) )
| ( in @ SY44 @ SY45 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(100,plain,
! [SV12: $i,SV31: mu] :
( ( ~ ( exists_in_world @ SV31 @ SV12 )
| ! [SY46: mu] :
( ~ ( exists_in_world @ SY46 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SY46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) )
| ( empty @ SY46 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(101,plain,
! [SV13: $i,SV32: mu] :
( ( ~ ( exists_in_world @ SV32 @ SV13 )
| ! [SY47: mu] :
( ~ ( exists_in_world @ SY47 @ SV13 )
| ~ ( qmltpeq @ SV32 @ SY47 @ SV13 )
| ( qmltpeq @ SY47 @ SV32 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(102,plain,
! [SV14: $i,SV33: mu] :
( ( ~ ( exists_in_world @ SV33 @ SV14 )
| ! [SY48: mu] :
( ~ ( exists_in_world @ SY48 @ SV14 )
| ! [SY49: mu] :
( ~ ( exists_in_world @ SY49 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV33 @ SY48 @ SV14 )
| ~ ( qmltpeq @ SY48 @ SY49 @ SV14 ) )
| ( qmltpeq @ SV33 @ SY49 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(103,plain,
! [SV15: $i,SV34: mu] :
( ( ~ ( exists_in_world @ SV34 @ SV15 )
| ! [SY50: mu] :
( ~ ( exists_in_world @ SY50 @ SV15 )
| ~ ( in @ SV34 @ SY50 @ SV15 )
| ~ ( in @ SY50 @ SV34 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(104,plain,
! [SV16: $i,SV35: mu] :
( ( ~ ( exists_in_world @ SV35 @ SV16 )
| ! [SY51: mu] :
( ~ ( exists_in_world @ SY51 @ SV16 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SY51 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SY51 @ SV16 ) )
| ~ ( ~ ( in @ SV35 @ SY51 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SY51 ) @ empty_set @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(105,plain,
! [SV18: $i] :
( ( ! [SY28: mu] :
( ~ ( exists_in_world @ SY28 @ SV18 )
| ~ ( empty @ SY28 @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(106,plain,
! [SV19: $i,SV36: mu] :
( ( ~ ( exists_in_world @ SV36 @ SV19 )
| ! [SY52: mu] :
( ~ ( exists_in_world @ SY52 @ SV19 )
| ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV19 )
| ~ ( qmltpeq @ SV36 @ SY52 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SY53 ) @ ( set_difference @ SY52 @ SY53 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(107,plain,
! [SV37: $i,SV20: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ( rel_s4 @ SV20 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SY54 ) )
| ( rel_s4 @ SV20 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
! [SV21: $i] :
( ( ! [SY34: mu] :
( ~ ( exists_in_world @ SY34 @ SV21 )
| ~ ~ ( empty @ SY34 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(109,plain,
! [SV22: $i,SV38: mu] :
( ( ~ ( exists_in_world @ SV38 @ SV22 )
| ! [SY55: mu] :
( ~ ( exists_in_world @ SY55 @ SV22 )
| ~ ( qmltpeq @ SV38 @ SY55 @ SV22 )
| ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SY55 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(110,plain,
( ( ! [SY56: mu] :
( ~ ( exists_in_world @ SY56 @ sK2_SX0 )
| ! [SY57: mu] :
( ~ ( exists_in_world @ SY57 @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY56 ) @ SY57 ) @ empty_set @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY56 ) @ SY57 ) @ ( singleton @ SY56 ) @ sK2_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(111,plain,
! [SV39: $i,SV23: $i,SV2: mu] :
( ( ~ ( exists_in_world @ SV2 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SV39 )
| ( exists_in_world @ SV2 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(112,plain,
! [SV5: $i,SV40: mu,SV25: mu] :
( ( exists_in_world @ ( set_difference @ SV25 @ SV40 ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV6: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV6 ) )
= $true )
| ( ( ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV6 )
| ! [SY40: mu] :
( ~ ( exists_in_world @ SY40 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY39 @ SV6 )
| ~ ( in @ SY40 @ SV26 @ SV6 ) )
| ( in @ SY40 @ SY39 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(114,plain,
! [SV8: $i,SV27: mu] :
( ( ( ~ ( exists_in_world @ SV27 @ SV8 ) )
= $true )
| ( ( qmltpeq @ SV27 @ SV27 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV9: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV9 ) )
= $true )
| ( ( ! [SY41: mu] :
( ~ ( exists_in_world @ SY41 @ SV9 )
| ! [SY42: mu] :
( ~ ( exists_in_world @ SY42 @ SV9 )
| ~ ( qmltpeq @ SV28 @ SY41 @ SV9 )
| ( qmltpeq @ ( set_difference @ SY42 @ SV28 ) @ ( set_difference @ SY42 @ SY41 ) @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV10: $i,SV29: mu] :
( ( ( ~ ( exists_in_world @ SV29 @ SV10 ) )
= $true )
| ( ( ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SY43 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SY43 @ SV10 ) )
| ~ ( ~ ~ ( in @ SV29 @ SY43 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SY43 ) @ ( singleton @ SV29 ) @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV11: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV11 ) )
= $true )
| ( ( ! [SY44: mu] :
( ~ ( exists_in_world @ SY44 @ SV11 )
| ! [SY45: mu] :
( ~ ( exists_in_world @ SY45 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY44 @ SV11 )
| ~ ( in @ SV30 @ SY45 @ SV11 ) )
| ( in @ SY44 @ SY45 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV12: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV12 ) )
= $true )
| ( ( ! [SY46: mu] :
( ~ ( exists_in_world @ SY46 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SY46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) )
| ( empty @ SY46 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV13: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV13 ) )
= $true )
| ( ( ! [SY47: mu] :
( ~ ( exists_in_world @ SY47 @ SV13 )
| ~ ( qmltpeq @ SV32 @ SY47 @ SV13 )
| ( qmltpeq @ SY47 @ SV32 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV14: $i,SV33: mu] :
( ( ( ~ ( exists_in_world @ SV33 @ SV14 ) )
= $true )
| ( ( ! [SY48: mu] :
( ~ ( exists_in_world @ SY48 @ SV14 )
| ! [SY49: mu] :
( ~ ( exists_in_world @ SY49 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV33 @ SY48 @ SV14 )
| ~ ( qmltpeq @ SY48 @ SY49 @ SV14 ) )
| ( qmltpeq @ SV33 @ SY49 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV15: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV15 ) )
= $true )
| ( ( ! [SY50: mu] :
( ~ ( exists_in_world @ SY50 @ SV15 )
| ~ ( in @ SV34 @ SY50 @ SV15 )
| ~ ( in @ SY50 @ SV34 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV16: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV16 ) )
= $true )
| ( ( ! [SY51: mu] :
( ~ ( exists_in_world @ SY51 @ SV16 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SY51 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SY51 @ SV16 ) )
| ~ ( ~ ( in @ SV35 @ SY51 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SY51 ) @ empty_set @ SV16 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV18: $i] :
( ( ~ ( exists_in_world @ ( sK3_SY28 @ SV18 ) @ SV18 )
| ~ ( empty @ ( sK3_SY28 @ SV18 ) @ SV18 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(124,plain,
! [SV19: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV19 ) )
= $true )
| ( ( ! [SY52: mu] :
( ~ ( exists_in_world @ SY52 @ SV19 )
| ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV19 )
| ~ ( qmltpeq @ SV36 @ SY52 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SY53 ) @ ( set_difference @ SY52 @ SY53 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV41: $i,SV37: $i,SV20: $i] :
( ( ~ ~ ( ~ ( rel_s4 @ SV20 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV41 ) )
| ( rel_s4 @ SV20 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV21: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY34 @ SV21 ) @ SV21 )
| ~ ~ ( empty @ ( sK4_SY34 @ SV21 ) @ SV21 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(127,plain,
! [SV22: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV22 ) )
= $true )
| ( ( ! [SY55: mu] :
( ~ ( exists_in_world @ SY55 @ SV22 )
| ~ ( qmltpeq @ SV38 @ SY55 @ SV22 )
| ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SY55 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(128,plain,
( ( ~ ( exists_in_world @ sK5_SY56 @ sK2_SX0 )
| ! [SY58: mu] :
( ~ ( exists_in_world @ SY58 @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ SY58 ) @ empty_set @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ SY58 ) @ ( singleton @ sK5_SY56 ) @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(129,plain,
! [SV39: $i,SV23: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV23 )
| ~ ( rel_s4 @ SV23 @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV6: $i,SV26: mu] :
( ( ( exists_in_world @ SV26 @ SV6 )
= $false )
| ( ( ! [SY39: mu] :
( ~ ( exists_in_world @ SY39 @ SV6 )
| ! [SY40: mu] :
( ~ ( exists_in_world @ SY40 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY39 @ SV6 )
| ~ ( in @ SY40 @ SV26 @ SV6 ) )
| ( in @ SY40 @ SY39 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(131,plain,
! [SV8: $i,SV27: mu] :
( ( ( exists_in_world @ SV27 @ SV8 )
= $false )
| ( ( qmltpeq @ SV27 @ SV27 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(132,plain,
! [SV9: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV9 )
= $false )
| ( ( ! [SY41: mu] :
( ~ ( exists_in_world @ SY41 @ SV9 )
| ! [SY42: mu] :
( ~ ( exists_in_world @ SY42 @ SV9 )
| ~ ( qmltpeq @ SV28 @ SY41 @ SV9 )
| ( qmltpeq @ ( set_difference @ SY42 @ SV28 ) @ ( set_difference @ SY42 @ SY41 ) @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV10: $i,SV29: mu] :
( ( ( exists_in_world @ SV29 @ SV10 )
= $false )
| ( ( ! [SY43: mu] :
( ~ ( exists_in_world @ SY43 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SY43 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SY43 @ SV10 ) )
| ~ ( ~ ~ ( in @ SV29 @ SY43 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SY43 ) @ ( singleton @ SV29 ) @ SV10 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV11: $i,SV30: mu] :
( ( ( exists_in_world @ SV30 @ SV11 )
= $false )
| ( ( ! [SY44: mu] :
( ~ ( exists_in_world @ SY44 @ SV11 )
| ! [SY45: mu] :
( ~ ( exists_in_world @ SY45 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY44 @ SV11 )
| ~ ( in @ SV30 @ SY45 @ SV11 ) )
| ( in @ SY44 @ SY45 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV12: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV12 )
= $false )
| ( ( ! [SY46: mu] :
( ~ ( exists_in_world @ SY46 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SY46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) )
| ( empty @ SY46 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV13: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV13 )
= $false )
| ( ( ! [SY47: mu] :
( ~ ( exists_in_world @ SY47 @ SV13 )
| ~ ( qmltpeq @ SV32 @ SY47 @ SV13 )
| ( qmltpeq @ SY47 @ SV32 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV14: $i,SV33: mu] :
( ( ( exists_in_world @ SV33 @ SV14 )
= $false )
| ( ( ! [SY48: mu] :
( ~ ( exists_in_world @ SY48 @ SV14 )
| ! [SY49: mu] :
( ~ ( exists_in_world @ SY49 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV33 @ SY48 @ SV14 )
| ~ ( qmltpeq @ SY48 @ SY49 @ SV14 ) )
| ( qmltpeq @ SV33 @ SY49 @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV15: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV15 )
= $false )
| ( ( ! [SY50: mu] :
( ~ ( exists_in_world @ SY50 @ SV15 )
| ~ ( in @ SV34 @ SY50 @ SV15 )
| ~ ( in @ SY50 @ SV34 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV16: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV16 )
= $false )
| ( ( ! [SY51: mu] :
( ~ ( exists_in_world @ SY51 @ SV16 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SY51 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SY51 @ SV16 ) )
| ~ ( ~ ( in @ SV35 @ SY51 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SY51 ) @ empty_set @ SV16 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV18: $i] :
( ( ~ ( exists_in_world @ ( sK3_SY28 @ SV18 ) @ SV18 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(141,plain,
! [SV18: $i] :
( ( ~ ( empty @ ( sK3_SY28 @ SV18 ) @ SV18 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(142,plain,
! [SV19: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV19 )
= $false )
| ( ( ! [SY52: mu] :
( ~ ( exists_in_world @ SY52 @ SV19 )
| ! [SY53: mu] :
( ~ ( exists_in_world @ SY53 @ SV19 )
| ~ ( qmltpeq @ SV36 @ SY52 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SY53 ) @ ( set_difference @ SY52 @ SY53 ) @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV41: $i,SV37: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( rel_s4 @ SV20 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV41 ) ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(144,plain,
! [SV21: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY34 @ SV21 ) @ SV21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(145,plain,
! [SV21: $i] :
( ( ~ ~ ( empty @ ( sK4_SY34 @ SV21 ) @ SV21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(146,plain,
! [SV22: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV22 )
= $false )
| ( ( ! [SY55: mu] :
( ~ ( exists_in_world @ SY55 @ SV22 )
| ~ ( qmltpeq @ SV38 @ SY55 @ SV22 )
| ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SY55 ) @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(147,plain,
( ( ~ ( exists_in_world @ sK5_SY56 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(148,plain,
( ( ! [SY58: mu] :
( ~ ( exists_in_world @ SY58 @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ SY58 ) @ empty_set @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ SY58 ) @ ( singleton @ sK5_SY56 ) @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(149,plain,
! [SV39: $i,SV23: $i,SV2: mu] :
( ( ( ~ ( exists_in_world @ SV2 @ SV23 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV23 @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(150,plain,
! [SV26: mu,SV6: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV6 )
| ! [SY59: mu] :
( ~ ( exists_in_world @ SY59 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SY59 @ SV26 @ SV6 ) )
| ( in @ SY59 @ SV42 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(151,plain,
! [SV28: mu,SV9: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV9 )
| ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ SV9 )
| ~ ( qmltpeq @ SV28 @ SV43 @ SV9 )
| ( qmltpeq @ ( set_difference @ SY60 @ SV28 ) @ ( set_difference @ SY60 @ SV43 ) @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(152,plain,
! [SV29: mu,SV10: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV10 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SV44 @ SV10 ) )
| ~ ( ~ ~ ( in @ SV29 @ SV44 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 ) ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(153,plain,
! [SV30: mu,SV11: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV11 )
| ! [SY61: mu] :
( ~ ( exists_in_world @ SY61 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SY61 @ SV11 ) )
| ( in @ SV45 @ SY61 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV31: mu,SV12: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV31 @ SV46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) )
| ( empty @ SV46 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV32: mu,SV13: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV13 )
| ~ ( qmltpeq @ SV32 @ SV47 @ SV13 )
| ( qmltpeq @ SV47 @ SV32 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV33: mu,SV14: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV14 )
| ! [SY62: mu] :
( ~ ( exists_in_world @ SY62 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SY62 @ SV14 ) )
| ( qmltpeq @ SV33 @ SY62 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV34: mu,SV15: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV15 )
| ~ ( in @ SV34 @ SV49 @ SV15 )
| ~ ( in @ SV49 @ SV34 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV35: mu,SV16: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV16 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SV50 @ SV16 ) )
| ~ ( ~ ( in @ SV35 @ SV50 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV18: $i] :
( ( exists_in_world @ ( sK3_SY28 @ SV18 ) @ SV18 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(160,plain,
! [SV18: $i] :
( ( empty @ ( sK3_SY28 @ SV18 ) @ SV18 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(161,plain,
! [SV36: mu,SV19: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV19 )
| ! [SY63: mu] :
( ~ ( exists_in_world @ SY63 @ SV19 )
| ~ ( qmltpeq @ SV36 @ SV51 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SY63 ) @ ( set_difference @ SV51 @ SY63 ) @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(162,plain,
! [SV41: $i,SV37: $i,SV20: $i] :
( ( ( ~ ( ~ ( rel_s4 @ SV20 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV41 ) ) )
= $false )
| ( ( rel_s4 @ SV20 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV21: $i] :
( ( exists_in_world @ ( sK4_SY34 @ SV21 ) @ SV21 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(164,plain,
! [SV21: $i] :
( ( ~ ( empty @ ( sK4_SY34 @ SV21 ) @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(165,plain,
! [SV38: mu,SV22: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV22 )
| ~ ( qmltpeq @ SV38 @ SV52 @ SV22 )
| ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SV52 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(166,plain,
( ( exists_in_world @ sK5_SY56 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(167,plain,
( ( ~ ( exists_in_world @ sK6_SY58 @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ sK6_SY58 ) @ empty_set @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ sK6_SY58 ) @ ( singleton @ sK5_SY56 ) @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[148]) ).
thf(168,plain,
! [SV39: $i,SV23: $i,SV2: mu] :
( ( ( exists_in_world @ SV2 @ SV23 )
= $false )
| ( ( ~ ( rel_s4 @ SV23 @ SV39 ) )
= $true )
| ( ( exists_in_world @ SV2 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV26: mu,SV6: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV6 ) )
= $true )
| ( ( ! [SY59: mu] :
( ~ ( exists_in_world @ SY59 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SY59 @ SV26 @ SV6 ) )
| ( in @ SY59 @ SV42 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV28: mu,SV9: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV9 ) )
= $true )
| ( ( ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ SV9 )
| ~ ( qmltpeq @ SV28 @ SV43 @ SV9 )
| ( qmltpeq @ ( set_difference @ SY60 @ SV28 ) @ ( set_difference @ SY60 @ SV43 ) @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(171,plain,
! [SV29: mu,SV10: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SV44 @ SV10 ) )
| ~ ( ~ ~ ( in @ SV29 @ SV44 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 ) ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(172,plain,
! [SV30: mu,SV11: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV11 ) )
= $true )
| ( ( ! [SY61: mu] :
( ~ ( exists_in_world @ SY61 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SY61 @ SV11 ) )
| ( in @ SV45 @ SY61 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV31: mu,SV12: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV31 @ SV46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) )
| ( empty @ SV46 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV32: mu,SV13: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV13 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV32 @ SV47 @ SV13 )
| ( qmltpeq @ SV47 @ SV32 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV33: mu,SV14: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV14 ) )
= $true )
| ( ( ! [SY62: mu] :
( ~ ( exists_in_world @ SY62 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SY62 @ SV14 ) )
| ( qmltpeq @ SV33 @ SY62 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV34: mu,SV15: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV34 @ SV49 @ SV15 )
| ~ ( in @ SV49 @ SV34 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV35: mu,SV16: $i,SV50: mu] :
( ( ( ~ ( exists_in_world @ SV50 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SV50 @ SV16 ) )
| ~ ( ~ ( in @ SV35 @ SV50 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV36: mu,SV19: $i,SV51: mu] :
( ( ( ~ ( exists_in_world @ SV51 @ SV19 ) )
= $true )
| ( ( ! [SY63: mu] :
( ~ ( exists_in_world @ SY63 @ SV19 )
| ~ ( qmltpeq @ SV36 @ SV51 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SY63 ) @ ( set_difference @ SV51 @ SY63 ) @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV41: $i,SV37: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV37 )
| ~ ( rel_s4 @ SV37 @ SV41 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(180,plain,
! [SV21: $i] :
( ( empty @ ( sK4_SY34 @ SV21 ) @ SV21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV38: mu,SV22: $i,SV52: mu] :
( ( ( ~ ( exists_in_world @ SV52 @ SV22 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV38 @ SV52 @ SV22 )
| ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SV52 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(182,plain,
( ( ~ ( exists_in_world @ sK6_SY58 @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(183,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ sK6_SY58 ) @ empty_set @ sK2_SX0 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ sK6_SY58 ) @ ( singleton @ sK5_SY56 ) @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(184,plain,
! [SV2: mu,SV39: $i,SV23: $i] :
( ( ( rel_s4 @ SV23 @ SV39 )
= $false )
| ( ( exists_in_world @ SV2 @ SV23 )
= $false )
| ( ( exists_in_world @ SV2 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(185,plain,
! [SV26: mu,SV6: $i,SV42: mu] :
( ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( ! [SY59: mu] :
( ~ ( exists_in_world @ SY59 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SY59 @ SV26 @ SV6 ) )
| ( in @ SY59 @ SV42 @ SV6 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(186,plain,
! [SV28: mu,SV9: $i,SV43: mu] :
( ( ( exists_in_world @ SV43 @ SV9 )
= $false )
| ( ( ! [SY60: mu] :
( ~ ( exists_in_world @ SY60 @ SV9 )
| ~ ( qmltpeq @ SV28 @ SV43 @ SV9 )
| ( qmltpeq @ ( set_difference @ SY60 @ SV28 ) @ ( set_difference @ SY60 @ SV43 ) @ SV9 ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(187,plain,
! [SV29: mu,SV10: $i,SV44: mu] :
( ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SV44 @ SV10 ) )
| ~ ( ~ ~ ( in @ SV29 @ SV44 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 ) ) ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(188,plain,
! [SV30: mu,SV11: $i,SV45: mu] :
( ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( ! [SY61: mu] :
( ~ ( exists_in_world @ SY61 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SY61 @ SV11 ) )
| ( in @ SV45 @ SY61 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV31: mu,SV12: $i,SV46: mu] :
( ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV31 @ SV46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) )
| ( empty @ SV46 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV32: mu,SV13: $i,SV47: mu] :
( ( ( exists_in_world @ SV47 @ SV13 )
= $false )
| ( ( ~ ( qmltpeq @ SV32 @ SV47 @ SV13 )
| ( qmltpeq @ SV47 @ SV32 @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV32 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV33: mu,SV14: $i,SV48: mu] :
( ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( ! [SY62: mu] :
( ~ ( exists_in_world @ SY62 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SY62 @ SV14 ) )
| ( qmltpeq @ SV33 @ SY62 @ SV14 ) ) )
= $true )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV34: mu,SV15: $i,SV49: mu] :
( ( ( exists_in_world @ SV49 @ SV15 )
= $false )
| ( ( ~ ( in @ SV34 @ SV49 @ SV15 )
| ~ ( in @ SV49 @ SV34 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV35: mu,SV16: $i,SV50: mu] :
( ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SV50 @ SV16 ) )
| ~ ( ~ ( in @ SV35 @ SV50 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 ) ) ) )
= $true )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV36: mu,SV19: $i,SV51: mu] :
( ( ( exists_in_world @ SV51 @ SV19 )
= $false )
| ( ( ! [SY63: mu] :
( ~ ( exists_in_world @ SY63 @ SV19 )
| ~ ( qmltpeq @ SV36 @ SV51 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SY63 ) @ ( set_difference @ SV51 @ SY63 ) @ SV19 ) ) )
= $true )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV41: $i,SV37: $i,SV20: $i] :
( ( ( ~ ( rel_s4 @ SV20 @ SV37 ) )
= $true )
| ( ( ~ ( rel_s4 @ SV37 @ SV41 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV38: mu,SV22: $i,SV52: mu] :
( ( ( exists_in_world @ SV52 @ SV22 )
= $false )
| ( ( ~ ( qmltpeq @ SV38 @ SV52 @ SV22 )
| ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SV52 ) @ SV22 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(197,plain,
( ( exists_in_world @ sK6_SY58 @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(198,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ sK6_SY58 ) @ empty_set @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(199,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK5_SY56 ) @ sK6_SY58 ) @ ( singleton @ sK5_SY56 ) @ sK2_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(200,plain,
! [SV42: mu,SV26: mu,SV6: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV6 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SV53 @ SV26 @ SV6 ) )
| ( in @ SV53 @ SV42 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(201,plain,
! [SV43: mu,SV28: mu,SV9: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV9 )
| ~ ( qmltpeq @ SV28 @ SV43 @ SV9 )
| ( qmltpeq @ ( set_difference @ SV54 @ SV28 ) @ ( set_difference @ SV54 @ SV43 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV9 )
= $false )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(202,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SV44 @ SV10 ) )
| ~ ( ~ ~ ( in @ SV29 @ SV44 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 ) ) )
= $false )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(203,plain,
! [SV45: mu,SV30: mu,SV11: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SV55 @ SV11 ) )
| ( in @ SV45 @ SV55 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(204,plain,
! [SV12: $i,SV46: mu,SV31: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV31 @ SV46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) ) )
= $true )
| ( ( empty @ SV46 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(205,plain,
! [SV13: $i,SV47: mu,SV32: mu] :
( ( ( ~ ( qmltpeq @ SV32 @ SV47 @ SV13 ) )
= $true )
| ( ( qmltpeq @ SV47 @ SV32 @ SV13 )
= $true )
| ( ( exists_in_world @ SV47 @ SV13 )
= $false )
| ( ( exists_in_world @ SV32 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(206,plain,
! [SV48: mu,SV33: mu,SV14: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV14 )
| ~ ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) )
| ( qmltpeq @ SV33 @ SV56 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(207,plain,
! [SV15: $i,SV49: mu,SV34: mu] :
( ( ( ~ ( in @ SV34 @ SV49 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV49 @ SV34 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV15 )
= $false )
| ( ( exists_in_world @ SV34 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(208,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SV50 @ SV16 ) )
| ~ ( ~ ( in @ SV35 @ SV50 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 ) ) )
= $false )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(209,plain,
! [SV51: mu,SV36: mu,SV19: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV19 )
| ~ ( qmltpeq @ SV36 @ SV51 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SV57 ) @ ( set_difference @ SV51 @ SV57 ) @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV19 )
= $false )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(210,plain,
! [SV41: $i,SV37: $i,SV20: $i] :
( ( ( rel_s4 @ SV20 @ SV37 )
= $false )
| ( ( ~ ( rel_s4 @ SV37 @ SV41 ) )
= $true )
| ( ( rel_s4 @ SV20 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(211,plain,
! [SV22: $i,SV52: mu,SV38: mu] :
( ( ( ~ ( qmltpeq @ SV38 @ SV52 @ SV22 ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SV52 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV52 @ SV22 )
= $false )
| ( ( exists_in_world @ SV38 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(212,plain,
! [SV42: mu,SV26: mu,SV6: $i,SV53: mu] :
( ( ( ~ ( exists_in_world @ SV53 @ SV6 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SV53 @ SV26 @ SV6 ) )
| ( in @ SV53 @ SV42 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(213,plain,
! [SV43: mu,SV28: mu,SV9: $i,SV54: mu] :
( ( ( ~ ( exists_in_world @ SV54 @ SV9 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV28 @ SV43 @ SV9 )
| ( qmltpeq @ ( set_difference @ SV54 @ SV28 ) @ ( set_difference @ SV54 @ SV43 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV9 )
= $false )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(214,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SV44 @ SV10 ) ) )
= $false )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(215,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ( ~ ~ ( in @ SV29 @ SV44 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 ) ) )
= $false )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(216,plain,
! [SV45: mu,SV30: mu,SV11: $i,SV55: mu] :
( ( ( ~ ( exists_in_world @ SV55 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SV55 @ SV11 ) )
| ( in @ SV45 @ SV55 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(217,plain,
! [SV12: $i,SV46: mu,SV31: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV31 @ SV46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) ) )
= $false )
| ( ( empty @ SV46 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(218,plain,
! [SV13: $i,SV47: mu,SV32: mu] :
( ( ( qmltpeq @ SV32 @ SV47 @ SV13 )
= $false )
| ( ( qmltpeq @ SV47 @ SV32 @ SV13 )
= $true )
| ( ( exists_in_world @ SV47 @ SV13 )
= $false )
| ( ( exists_in_world @ SV32 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(219,plain,
! [SV48: mu,SV33: mu,SV14: $i,SV56: mu] :
( ( ( ~ ( exists_in_world @ SV56 @ SV14 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) )
| ( qmltpeq @ SV33 @ SV56 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(220,plain,
! [SV15: $i,SV49: mu,SV34: mu] :
( ( ( in @ SV34 @ SV49 @ SV15 )
= $false )
| ( ( ~ ( in @ SV49 @ SV34 @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV49 @ SV15 )
= $false )
| ( ( exists_in_world @ SV34 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(221,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SV50 @ SV16 ) ) )
= $false )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(222,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( ~ ( ~ ( in @ SV35 @ SV50 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 ) ) )
= $false )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(223,plain,
! [SV51: mu,SV36: mu,SV19: $i,SV57: mu] :
( ( ( ~ ( exists_in_world @ SV57 @ SV19 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV36 @ SV51 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SV57 ) @ ( set_difference @ SV51 @ SV57 ) @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV19 )
= $false )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(224,plain,
! [SV20: $i,SV41: $i,SV37: $i] :
( ( ( rel_s4 @ SV37 @ SV41 )
= $false )
| ( ( rel_s4 @ SV20 @ SV37 )
= $false )
| ( ( rel_s4 @ SV20 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(225,plain,
! [SV22: $i,SV52: mu,SV38: mu] :
( ( ( qmltpeq @ SV38 @ SV52 @ SV22 )
= $false )
| ( ( qmltpeq @ ( singleton @ SV38 ) @ ( singleton @ SV52 ) @ SV22 )
= $true )
| ( ( exists_in_world @ SV52 @ SV22 )
= $false )
| ( ( exists_in_world @ SV38 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(226,plain,
! [SV42: mu,SV26: mu,SV6: $i,SV53: mu] :
( ( ( exists_in_world @ SV53 @ SV6 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SV53 @ SV26 @ SV6 ) )
| ( in @ SV53 @ SV42 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(227,plain,
! [SV43: mu,SV28: mu,SV9: $i,SV54: mu] :
( ( ( exists_in_world @ SV54 @ SV9 )
= $false )
| ( ( ~ ( qmltpeq @ SV28 @ SV43 @ SV9 )
| ( qmltpeq @ ( set_difference @ SV54 @ SV28 ) @ ( set_difference @ SV54 @ SV43 ) @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV9 )
= $false )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(228,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
| ~ ( in @ SV29 @ SV44 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(229,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ~ ( in @ SV29 @ SV44 @ SV10 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(230,plain,
! [SV45: mu,SV30: mu,SV11: $i,SV55: mu] :
( ( ( exists_in_world @ SV55 @ SV11 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SV55 @ SV11 ) )
| ( in @ SV45 @ SV55 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(231,plain,
! [SV12: $i,SV46: mu,SV31: mu] :
( ( ( ~ ( qmltpeq @ SV31 @ SV46 @ SV12 )
| ~ ( empty @ SV31 @ SV12 ) )
= $true )
| ( ( empty @ SV46 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(232,plain,
! [SV48: mu,SV33: mu,SV14: $i,SV56: mu] :
( ( ( exists_in_world @ SV56 @ SV14 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) )
| ( qmltpeq @ SV33 @ SV56 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(233,plain,
! [SV15: $i,SV34: mu,SV49: mu] :
( ( ( in @ SV49 @ SV34 @ SV15 )
= $false )
| ( ( in @ SV34 @ SV49 @ SV15 )
= $false )
| ( ( exists_in_world @ SV49 @ SV15 )
= $false )
| ( ( exists_in_world @ SV34 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(234,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
| ( in @ SV35 @ SV50 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(235,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( ~ ( in @ SV35 @ SV50 @ SV16 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(236,plain,
! [SV51: mu,SV36: mu,SV19: $i,SV57: mu] :
( ( ( exists_in_world @ SV57 @ SV19 )
= $false )
| ( ( ~ ( qmltpeq @ SV36 @ SV51 @ SV19 )
| ( qmltpeq @ ( set_difference @ SV36 @ SV57 ) @ ( set_difference @ SV51 @ SV57 ) @ SV19 ) )
= $true )
| ( ( exists_in_world @ SV51 @ SV19 )
= $false )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(237,plain,
! [SV53: mu,SV6: $i,SV42: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SV53 @ SV26 @ SV6 ) ) )
= $true )
| ( ( in @ SV53 @ SV42 @ SV6 )
= $true )
| ( ( exists_in_world @ SV53 @ SV6 )
= $false )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV54: mu,SV9: $i,SV43: mu,SV28: mu] :
( ( ( ~ ( qmltpeq @ SV28 @ SV43 @ SV9 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV54 @ SV28 ) @ ( set_difference @ SV54 @ SV43 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV54 @ SV9 )
= $false )
| ( ( exists_in_world @ SV43 @ SV9 )
= $false )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(239,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 ) )
= $true )
| ( ( ~ ( in @ SV29 @ SV44 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(240,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ~ ( in @ SV29 @ SV44 @ SV10 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV55: mu,SV11: $i,SV45: mu,SV30: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SV55 @ SV11 ) ) )
= $true )
| ( ( in @ SV45 @ SV55 @ SV11 )
= $true )
| ( ( exists_in_world @ SV55 @ SV11 )
= $false )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV12: $i,SV46: mu,SV31: mu] :
( ( ( ~ ( qmltpeq @ SV31 @ SV46 @ SV12 ) )
= $true )
| ( ( ~ ( empty @ SV31 @ SV12 ) )
= $true )
| ( ( empty @ SV46 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV56: mu,SV14: $i,SV48: mu,SV33: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV56 @ SV14 )
= $true )
| ( ( exists_in_world @ SV56 @ SV14 )
= $false )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 ) )
= $true )
| ( ( in @ SV35 @ SV50 @ SV16 )
= $true )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( ~ ( in @ SV35 @ SV50 @ SV16 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
= $true )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(246,plain,
! [SV57: mu,SV19: $i,SV51: mu,SV36: mu] :
( ( ( ~ ( qmltpeq @ SV36 @ SV51 @ SV19 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV36 @ SV57 ) @ ( set_difference @ SV51 @ SV57 ) @ SV19 )
= $true )
| ( ( exists_in_world @ SV57 @ SV19 )
= $false )
| ( ( exists_in_world @ SV51 @ SV19 )
= $false )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV53: mu,SV6: $i,SV42: mu,SV26: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SV53 @ SV26 @ SV6 ) ) )
= $false )
| ( ( in @ SV53 @ SV42 @ SV6 )
= $true )
| ( ( exists_in_world @ SV53 @ SV6 )
= $false )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV54: mu,SV9: $i,SV43: mu,SV28: mu] :
( ( ( qmltpeq @ SV28 @ SV43 @ SV9 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV54 @ SV28 ) @ ( set_difference @ SV54 @ SV43 ) @ SV9 )
= $true )
| ( ( exists_in_world @ SV54 @ SV9 )
= $false )
| ( ( exists_in_world @ SV43 @ SV9 )
= $false )
| ( ( exists_in_world @ SV28 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
= $false )
| ( ( ~ ( in @ SV29 @ SV44 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(250,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( ~ ( in @ SV29 @ SV44 @ SV10 ) )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(251,plain,
! [SV55: mu,SV11: $i,SV45: mu,SV30: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SV55 @ SV11 ) ) )
= $false )
| ( ( in @ SV45 @ SV55 @ SV11 )
= $true )
| ( ( exists_in_world @ SV55 @ SV11 )
= $false )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(252,plain,
! [SV12: $i,SV46: mu,SV31: mu] :
( ( ( qmltpeq @ SV31 @ SV46 @ SV12 )
= $false )
| ( ( ~ ( empty @ SV31 @ SV12 ) )
= $true )
| ( ( empty @ SV46 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(253,plain,
! [SV56: mu,SV14: $i,SV48: mu,SV33: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) ) )
= $false )
| ( ( qmltpeq @ SV33 @ SV56 @ SV14 )
= $true )
| ( ( exists_in_world @ SV56 @ SV14 )
= $false )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(254,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
= $false )
| ( ( in @ SV35 @ SV50 @ SV16 )
= $true )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(255,plain,
! [SV16: $i,SV50: mu,SV35: mu] :
( ( ( in @ SV35 @ SV50 @ SV16 )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV35 ) @ SV50 ) @ empty_set @ SV16 )
= $true )
| ( ( exists_in_world @ SV50 @ SV16 )
= $false )
| ( ( exists_in_world @ SV35 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(256,plain,
! [SV57: mu,SV19: $i,SV51: mu,SV36: mu] :
( ( ( qmltpeq @ SV36 @ SV51 @ SV19 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV36 @ SV57 ) @ ( set_difference @ SV51 @ SV57 ) @ SV19 )
= $true )
| ( ( exists_in_world @ SV57 @ SV19 )
= $false )
| ( ( exists_in_world @ SV51 @ SV19 )
= $false )
| ( ( exists_in_world @ SV36 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(257,plain,
! [SV53: mu,SV6: $i,SV42: mu,SV26: mu] :
( ( ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 )
| ~ ( in @ SV53 @ SV26 @ SV6 ) )
= $true )
| ( ( in @ SV53 @ SV42 @ SV6 )
= $true )
| ( ( exists_in_world @ SV53 @ SV6 )
= $false )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(258,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( in @ SV29 @ SV44 @ SV10 )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
= $false )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(259,plain,
! [SV10: $i,SV44: mu,SV29: mu] :
( ( ( in @ SV29 @ SV44 @ SV10 )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV29 ) @ SV44 ) @ ( singleton @ SV29 ) @ SV10 )
= $true )
| ( ( exists_in_world @ SV44 @ SV10 )
= $false )
| ( ( exists_in_world @ SV29 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(260,plain,
! [SV55: mu,SV11: $i,SV45: mu,SV30: mu] :
( ( ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 )
| ~ ( in @ SV30 @ SV55 @ SV11 ) )
= $true )
| ( ( in @ SV45 @ SV55 @ SV11 )
= $true )
| ( ( exists_in_world @ SV55 @ SV11 )
= $false )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(261,plain,
! [SV46: mu,SV12: $i,SV31: mu] :
( ( ( empty @ SV31 @ SV12 )
= $false )
| ( ( qmltpeq @ SV31 @ SV46 @ SV12 )
= $false )
| ( ( empty @ SV46 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV31 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(262,plain,
! [SV56: mu,SV14: $i,SV48: mu,SV33: mu] :
( ( ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 )
| ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV56 @ SV14 )
= $true )
| ( ( exists_in_world @ SV56 @ SV14 )
= $false )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(263,plain,
! [SV53: mu,SV6: $i,SV42: mu,SV26: mu] :
( ( ( ~ ( qmltpeq @ SV26 @ SV42 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV53 @ SV26 @ SV6 ) )
= $true )
| ( ( in @ SV53 @ SV42 @ SV6 )
= $true )
| ( ( exists_in_world @ SV53 @ SV6 )
= $false )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(264,plain,
! [SV55: mu,SV11: $i,SV45: mu,SV30: mu] :
( ( ( ~ ( qmltpeq @ SV30 @ SV45 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV30 @ SV55 @ SV11 ) )
= $true )
| ( ( in @ SV45 @ SV55 @ SV11 )
= $true )
| ( ( exists_in_world @ SV55 @ SV11 )
= $false )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(265,plain,
! [SV56: mu,SV14: $i,SV48: mu,SV33: mu] :
( ( ( ~ ( qmltpeq @ SV33 @ SV48 @ SV14 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV56 @ SV14 )
= $true )
| ( ( exists_in_world @ SV56 @ SV14 )
= $false )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(266,plain,
! [SV53: mu,SV6: $i,SV42: mu,SV26: mu] :
( ( ( qmltpeq @ SV26 @ SV42 @ SV6 )
= $false )
| ( ( ~ ( in @ SV53 @ SV26 @ SV6 ) )
= $true )
| ( ( in @ SV53 @ SV42 @ SV6 )
= $true )
| ( ( exists_in_world @ SV53 @ SV6 )
= $false )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(267,plain,
! [SV55: mu,SV11: $i,SV45: mu,SV30: mu] :
( ( ( qmltpeq @ SV30 @ SV45 @ SV11 )
= $false )
| ( ( ~ ( in @ SV30 @ SV55 @ SV11 ) )
= $true )
| ( ( in @ SV45 @ SV55 @ SV11 )
= $true )
| ( ( exists_in_world @ SV55 @ SV11 )
= $false )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(268,plain,
! [SV56: mu,SV14: $i,SV48: mu,SV33: mu] :
( ( ( qmltpeq @ SV33 @ SV48 @ SV14 )
= $false )
| ( ( ~ ( qmltpeq @ SV48 @ SV56 @ SV14 ) )
= $true )
| ( ( qmltpeq @ SV33 @ SV56 @ SV14 )
= $true )
| ( ( exists_in_world @ SV56 @ SV14 )
= $false )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(269,plain,
! [SV42: mu,SV6: $i,SV26: mu,SV53: mu] :
( ( ( in @ SV53 @ SV26 @ SV6 )
= $false )
| ( ( qmltpeq @ SV26 @ SV42 @ SV6 )
= $false )
| ( ( in @ SV53 @ SV42 @ SV6 )
= $true )
| ( ( exists_in_world @ SV53 @ SV6 )
= $false )
| ( ( exists_in_world @ SV42 @ SV6 )
= $false )
| ( ( exists_in_world @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(270,plain,
! [SV45: mu,SV11: $i,SV55: mu,SV30: mu] :
( ( ( in @ SV30 @ SV55 @ SV11 )
= $false )
| ( ( qmltpeq @ SV30 @ SV45 @ SV11 )
= $false )
| ( ( in @ SV45 @ SV55 @ SV11 )
= $true )
| ( ( exists_in_world @ SV55 @ SV11 )
= $false )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV30 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(271,plain,
! [SV33: mu,SV14: $i,SV56: mu,SV48: mu] :
( ( ( qmltpeq @ SV48 @ SV56 @ SV14 )
= $false )
| ( ( qmltpeq @ SV33 @ SV48 @ SV14 )
= $false )
| ( ( qmltpeq @ SV33 @ SV56 @ SV14 )
= $true )
| ( ( exists_in_world @ SV56 @ SV14 )
= $false )
| ( ( exists_in_world @ SV48 @ SV14 )
= $false )
| ( ( exists_in_world @ SV33 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(272,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[69,271,270,269,261,259,258,256,255,254,248,233,225,224,218,199,198,197,184,180,166,163,160,159,131,112,93,85,75,71]) ).
thf(273,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET926^7 : TPTP v8.1.0. Released v5.5.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 08:54:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36
% 0.12/0.36 No.of.Axioms: 22
% 0.12/0.36
% 0.12/0.36 Length.of.Defs: 5508
% 0.12/0.36
% 0.12/0.36 Contains.Choice.Funs: false
% 0.12/0.37 (rf:0,axioms:22,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:24,loop_count:0,foatp_calls:0,translation:fof_full)...............
% 0.19/0.54
% 0.19/0.54 ********************************
% 0.19/0.54 * All subproblems solved! *
% 0.19/0.54 ********************************
% 0.19/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:272,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.57
% 0.19/0.57 %**** Beginning of derivation protocol ****
% 0.19/0.57 % SZS output start CNFRefutation
% See solution above
% 0.19/0.57
% 0.19/0.57 %**** End of derivation protocol ****
% 0.19/0.57 %**** no. of clauses in derivation: 273 ****
% 0.19/0.57 %**** clause counter: 272 ****
% 0.19/0.57
% 0.19/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:272,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------