%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET926^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:42:35 AM UTC 2026
% Result : Theorem 0.62s 0.36s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 51
% Syntax : Number of formulae : 293 ( 150 unt; 0 typ; 32 def)
% Number of atoms : 2330 ( 585 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 4791 ( 698 ~; 721 |; 8 &;3286 @)
% ( 0 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 6 con; 0-3 aty)
% Number of variables : 837 ( 83 ^; 748 !; 6 ?; 837 :)
% 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_SY13,type,
sK1_SY13: $i ).
thf(tp_sK2_SY418,type,
sK2_SY418: mu ).
thf(tp_sK3_SX0,type,
sK3_SX0: mu ).
thf(tp_sK4_SY424,type,
sK4_SY424: $i > mu ).
thf(tp_sK5_SY427,type,
sK5_SY427: $i > 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/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mbox_s4,definition,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( rel_s4 @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4) ).
thf(mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mcountersatisfiable) ).
thf(mdia,definition,
( mdia
= ( ^ [R: $i > $i > $o,Phi: $i > $o] : ( mnot @ ( mbox @ R @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mdia_s4,definition,
( mdia_s4
= ( ^ [Phi: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Phi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4) ).
thf(meq_prop,definition,
( meq_prop
= ( ^ [X: $i > $o,Y: $i > $o,W: $i] :
( ( X @ W )
= ( Y @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meq_prop) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(meuclidean,definition,
( meuclidean
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( R @ T @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [P: $i > $o] : ( mnot @ ( Phi @ P ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop) ).
thf(mfunctional,definition,
( mfunctional
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] :
( ( R @ S @ T )
& ! [U: $i] :
( ( R @ S @ U )
=> ( T = U ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mfunctional) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Psi ) @ Phi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(mpartially_functional,definition,
( mpartially_functional
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( T = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional) ).
thf(mreflexive,definition,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive) ).
thf(msatisfiable,definition,
( msatisfiable
= ( ^ [Phi: $i > $o] :
? [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msatisfiable) ).
thf(mserial,definition,
( mserial
= ( ^ [R: $i > $i > $o] :
! [S: $i] :
? [T: $i] : ( R @ S @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric) ).
thf(mtransitive,definition,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid) ).
thf(mweakly_connected,definition,
( mweakly_connected
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ( ( R @ T @ U )
| ( T = U )
| ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_connected) ).
thf(mweakly_dense,definition,
( mweakly_dense
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( R @ S @ T )
=> ? [U: $i] :
( ( R @ S @ U )
& ( R @ U @ T ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_dense) ).
thf(mweakly_directed,definition,
( mweakly_directed
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ S @ U ) )
=> ? [V: $i] :
( ( R @ T @ V )
& ( R @ U @ V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mweakly_directed) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mequiv @ Phi @ Psi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mxor) ).
thf(1,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( mnot @ ( empty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] : ( empty @ A ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(5,axiom,
mvalid @ ( empty @ empty_set ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(15,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( qmltpeq @ X @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(16,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_set_difference_ax) ).
thf(17,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_singleton_ax) ).
thf(18,axiom,
! [V: $i] : ( exists_in_world @ empty_set @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_empty_set_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/sandbox2/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,
( ( ! [SY13: $i,SY14: mu] :
( ( exists_in_world @ SY14 @ SY13 )
=> ! [SY15: mu] :
( ( exists_in_world @ SY15 @ SY13 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ SY14 ) @ SY15 ) @ empty_set @ SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY14 ) @ SY15 ) @ ( singleton @ SY14 ) @ SY13 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[24,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(26,plain,
( ( ! [SY29: $i] :
~ ! [SY30: mu] :
( ( exists_in_world @ SY30 @ SY29 )
=> ~ ~ ( empty @ SY30 @ SY29 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(27,plain,
( ( ! [SY41: $i] :
~ ! [SY42: mu] :
( ( exists_in_world @ SY42 @ SY41 )
=> ~ ( empty @ SY42 @ SY41 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(28,plain,
( ( ! [SY77: $i,SY78: mu] :
( ( exists_in_world @ SY78 @ SY77 )
=> ! [SY79: mu] :
( ( exists_in_world @ SY79 @ SY77 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY78 ) @ SY79 ) @ empty_set @ SY77 )
| ( in @ SY78 @ SY79 @ SY77 ) )
| ~ ( ~ ( in @ SY78 @ SY79 @ SY77 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY78 ) @ SY79 ) @ empty_set @ SY77 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(29,plain,
( ( ! [SY116: $i,SY117: mu] :
( ( exists_in_world @ SY117 @ SY116 )
=> ! [SY118: mu] :
( ( exists_in_world @ SY118 @ SY116 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY117 ) @ SY118 ) @ ( singleton @ SY117 ) @ SY116 )
| ~ ( in @ SY117 @ SY118 @ SY116 ) )
| ~ ( ~ ~ ( in @ SY117 @ SY118 @ SY116 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY117 ) @ SY118 ) @ ( singleton @ SY117 ) @ SY116 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(30,plain,
( ( ! [SY122: $i] : ( empty @ empty_set @ SY122 ) )
= $true ),
inference(unfold_def,[status(thm)],[5,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(31,plain,
( ( ! [SY141: $i,SY142: mu] :
( ( exists_in_world @ SY142 @ SY141 )
=> ! [SY143: mu] :
( ( exists_in_world @ SY143 @ SY141 )
=> ( ~ ( in @ SY142 @ SY143 @ SY141 )
| ~ ( in @ SY143 @ SY142 @ SY141 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(32,plain,
( ( ! [SY179: $i,SY180: mu] :
( ( exists_in_world @ SY180 @ SY179 )
=> ! [SY181: mu] :
( ( exists_in_world @ SY181 @ SY179 )
=> ! [SY182: mu] :
( ( exists_in_world @ SY182 @ SY179 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY180 @ SY181 @ SY179 )
| ~ ( in @ SY182 @ SY180 @ SY179 ) )
| ( in @ SY182 @ SY181 @ SY179 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(33,plain,
( ( ! [SY219: $i,SY220: mu] :
( ( exists_in_world @ SY220 @ SY219 )
=> ! [SY221: mu] :
( ( exists_in_world @ SY221 @ SY219 )
=> ! [SY222: mu] :
( ( exists_in_world @ SY222 @ SY219 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY220 @ SY221 @ SY219 )
| ~ ( in @ SY220 @ SY222 @ SY219 ) )
| ( in @ SY221 @ SY222 @ SY219 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(34,plain,
( ( ! [SY251: $i,SY252: mu] :
( ( exists_in_world @ SY252 @ SY251 )
=> ! [SY253: mu] :
( ( exists_in_world @ SY253 @ SY251 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY252 @ SY253 @ SY251 )
| ~ ( empty @ SY252 @ SY251 ) )
| ( empty @ SY253 @ SY251 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(35,plain,
( ( ! [SY273: $i,SY274: mu] :
( ( exists_in_world @ SY274 @ SY273 )
=> ! [SY275: mu] :
( ( exists_in_world @ SY275 @ SY273 )
=> ( ~ ( qmltpeq @ SY274 @ SY275 @ SY273 )
| ( qmltpeq @ ( singleton @ SY274 ) @ ( singleton @ SY275 ) @ SY273 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(36,plain,
( ( ! [SY303: $i,SY304: mu] :
( ( exists_in_world @ SY304 @ SY303 )
=> ! [SY305: mu] :
( ( exists_in_world @ SY305 @ SY303 )
=> ! [SY306: mu] :
( ( exists_in_world @ SY306 @ SY303 )
=> ( ~ ( qmltpeq @ SY304 @ SY305 @ SY303 )
| ( qmltpeq @ ( set_difference @ SY306 @ SY304 ) @ ( set_difference @ SY306 @ SY305 ) @ SY303 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(37,plain,
( ( ! [SY335: $i,SY336: mu] :
( ( exists_in_world @ SY336 @ SY335 )
=> ! [SY337: mu] :
( ( exists_in_world @ SY337 @ SY335 )
=> ! [SY338: mu] :
( ( exists_in_world @ SY338 @ SY335 )
=> ( ~ ( qmltpeq @ SY336 @ SY337 @ SY335 )
| ( qmltpeq @ ( set_difference @ SY336 @ SY338 ) @ ( set_difference @ SY337 @ SY338 ) @ SY335 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(38,plain,
( ( ! [SY375: $i,SY376: mu] :
( ( exists_in_world @ SY376 @ SY375 )
=> ! [SY377: mu] :
( ( exists_in_world @ SY377 @ SY375 )
=> ! [SY378: mu] :
( ( exists_in_world @ SY378 @ SY375 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY376 @ SY377 @ SY375 )
| ~ ( qmltpeq @ SY377 @ SY378 @ SY375 ) )
| ( qmltpeq @ SY376 @ SY378 @ SY375 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(39,plain,
( ( ! [SY399: $i,SY400: mu] :
( ( exists_in_world @ SY400 @ SY399 )
=> ! [SY401: mu] :
( ( exists_in_world @ SY401 @ SY399 )
=> ( ~ ( qmltpeq @ SY400 @ SY401 @ SY399 )
| ( qmltpeq @ SY401 @ SY400 @ SY399 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(40,plain,
( ( ! [SY408: $i,SY409: mu] :
( ( exists_in_world @ SY409 @ SY408 )
=> ( qmltpeq @ SY409 @ SY409 @ SY408 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(41,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[16,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(42,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[17,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(43,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[18,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(44,plain,
( ( ! [SY418: mu] :
( ( exists_in_world @ SY418 @ sK1_SY13 )
=> ! [SY419: mu] :
( ( exists_in_world @ SY419 @ sK1_SY13 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ SY418 ) @ SY419 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY418 ) @ SY419 ) @ ( singleton @ SY418 ) @ sK1_SY13 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(45,plain,
( ( ( exists_in_world @ sK2_SY418 @ sK1_SY13 )
=> ! [SY420: mu] :
( ( exists_in_world @ SY420 @ sK1_SY13 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(46,plain,
( ( exists_in_world @ sK2_SY418 @ sK1_SY13 )
= $true ),
inference(standard_cnf,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [SY420: mu] :
( ( exists_in_world @ SY420 @ sK1_SY13 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ! [SY420: mu] :
( ( exists_in_world @ SY420 @ sK1_SY13 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [V: $i] : ( exists_in_world @ empty_set @ V ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [V: $i,V1: mu] : ( exists_in_world @ ( singleton @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(51,plain,
( ( ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( set_difference @ V2 @ V1 ) @ V ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [SY408: $i,SY409: mu] :
( ( exists_in_world @ SY409 @ SY408 )
=> ( qmltpeq @ SY409 @ SY409 @ SY408 ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(53,plain,
( ( ! [SY399: $i,SY400: mu] :
( ( exists_in_world @ SY400 @ SY399 )
=> ! [SY401: mu] :
( ( exists_in_world @ SY401 @ SY399 )
=> ( ~ ( qmltpeq @ SY400 @ SY401 @ SY399 )
| ( qmltpeq @ SY401 @ SY400 @ SY399 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(54,plain,
( ( ! [SY375: $i,SY376: mu] :
( ( exists_in_world @ SY376 @ SY375 )
=> ! [SY377: mu] :
( ( exists_in_world @ SY377 @ SY375 )
=> ! [SY378: mu] :
( ( exists_in_world @ SY378 @ SY375 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY376 @ SY377 @ SY375 )
| ~ ( qmltpeq @ SY377 @ SY378 @ SY375 ) )
| ( qmltpeq @ SY376 @ SY378 @ SY375 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(55,plain,
( ( ! [SY335: $i,SY336: mu] :
( ( exists_in_world @ SY336 @ SY335 )
=> ! [SY337: mu] :
( ( exists_in_world @ SY337 @ SY335 )
=> ! [SY338: mu] :
( ( exists_in_world @ SY338 @ SY335 )
=> ( ~ ( qmltpeq @ SY336 @ SY337 @ SY335 )
| ( qmltpeq @ ( set_difference @ SY336 @ SY338 ) @ ( set_difference @ SY337 @ SY338 ) @ SY335 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(56,plain,
( ( ! [SY303: $i,SY304: mu] :
( ( exists_in_world @ SY304 @ SY303 )
=> ! [SY305: mu] :
( ( exists_in_world @ SY305 @ SY303 )
=> ! [SY306: mu] :
( ( exists_in_world @ SY306 @ SY303 )
=> ( ~ ( qmltpeq @ SY304 @ SY305 @ SY303 )
| ( qmltpeq @ ( set_difference @ SY306 @ SY304 ) @ ( set_difference @ SY306 @ SY305 ) @ SY303 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(57,plain,
( ( ! [SY273: $i,SY274: mu] :
( ( exists_in_world @ SY274 @ SY273 )
=> ! [SY275: mu] :
( ( exists_in_world @ SY275 @ SY273 )
=> ( ~ ( qmltpeq @ SY274 @ SY275 @ SY273 )
| ( qmltpeq @ ( singleton @ SY274 ) @ ( singleton @ SY275 ) @ SY273 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(58,plain,
( ( ! [SY251: $i,SY252: mu] :
( ( exists_in_world @ SY252 @ SY251 )
=> ! [SY253: mu] :
( ( exists_in_world @ SY253 @ SY251 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY252 @ SY253 @ SY251 )
| ~ ( empty @ SY252 @ SY251 ) )
| ( empty @ SY253 @ SY251 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(59,plain,
( ( ! [SY219: $i,SY220: mu] :
( ( exists_in_world @ SY220 @ SY219 )
=> ! [SY221: mu] :
( ( exists_in_world @ SY221 @ SY219 )
=> ! [SY222: mu] :
( ( exists_in_world @ SY222 @ SY219 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY220 @ SY221 @ SY219 )
| ~ ( in @ SY220 @ SY222 @ SY219 ) )
| ( in @ SY221 @ SY222 @ SY219 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(60,plain,
( ( ! [SY179: $i,SY180: mu] :
( ( exists_in_world @ SY180 @ SY179 )
=> ! [SY181: mu] :
( ( exists_in_world @ SY181 @ SY179 )
=> ! [SY182: mu] :
( ( exists_in_world @ SY182 @ SY179 )
=> ( ~ ~ ( ~ ( qmltpeq @ SY180 @ SY181 @ SY179 )
| ~ ( in @ SY182 @ SY180 @ SY179 ) )
| ( in @ SY182 @ SY181 @ SY179 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(61,plain,
( ( ! [SY141: $i,SY142: mu] :
( ( exists_in_world @ SY142 @ SY141 )
=> ! [SY143: mu] :
( ( exists_in_world @ SY143 @ SY141 )
=> ( ~ ( in @ SY142 @ SY143 @ SY141 )
| ~ ( in @ SY143 @ SY142 @ SY141 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(62,plain,
( ( ! [SY122: $i] : ( empty @ empty_set @ SY122 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(63,plain,
( ( ! [SY116: $i,SY117: mu] :
( ( exists_in_world @ SY117 @ SY116 )
=> ! [SY118: mu] :
( ( exists_in_world @ SY118 @ SY116 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY117 ) @ SY118 ) @ ( singleton @ SY117 ) @ SY116 )
| ~ ( in @ SY117 @ SY118 @ SY116 ) )
| ~ ( ~ ~ ( in @ SY117 @ SY118 @ SY116 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY117 ) @ SY118 ) @ ( singleton @ SY117 ) @ SY116 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(64,plain,
( ( ! [SY77: $i,SY78: mu] :
( ( exists_in_world @ SY78 @ SY77 )
=> ! [SY79: mu] :
( ( exists_in_world @ SY79 @ SY77 )
=> ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY78 ) @ SY79 ) @ empty_set @ SY77 )
| ( in @ SY78 @ SY79 @ SY77 ) )
| ~ ( ~ ( in @ SY78 @ SY79 @ SY77 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY78 ) @ SY79 ) @ empty_set @ SY77 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(65,plain,
( ( ! [SY41: $i] :
~ ! [SY42: mu] :
( ( exists_in_world @ SY42 @ SY41 )
=> ~ ( empty @ SY42 @ SY41 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(66,plain,
( ( ! [SY29: $i] :
~ ! [SY30: mu] :
( ( exists_in_world @ SY30 @ SY29 )
=> ~ ~ ( empty @ SY30 @ SY29 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(67,plain,
( ( exists_in_world @ sK2_SY418 @ sK1_SY13 )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(68,plain,
( ( ~ ! [SY420: mu] :
( ( exists_in_world @ SY420 @ sK1_SY13 )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SY420 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ~ ( empty @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(70,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)],[64,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(71,plain,
( ( ! [SX0: $i] :
~ ! [SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ~ ( empty @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(72,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)],[53,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: 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)],[58,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: 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)],[61,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: 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)],[59,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: 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)],[60,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: 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)],[55,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: 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)],[63,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(79,plain,
( ( ! [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)],[57,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(80,plain,
( ( ~ ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SX0 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SX0 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: 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)],[54,mand,mbox,mbox_s4,mcountersatisfiable,mdia,mdia_s4,meq_prop,mequiv,meuclidean,mexists_ind,mexists_prop,mfalse,mforall_ind,mforall_prop,mfunctional,mimplied,mimplies,minvalid,mnot,mor,mpartially_functional,mreflexive,msatisfiable,mserial,msymmetric,mtransitive,mtrue,mvalid,mweakly_connected,mweakly_dense,mweakly_directed,mxor]) ).
thf(82,plain,
( ( ! [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)],[56,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(83,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ( exists_in_world @ SX1 @ SX0 )
| ( qmltpeq @ SX1 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,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(84,plain,
! [SV1: $i] :
( ( exists_in_world @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(85,plain,
! [SV2: $i] :
( ( ! [SY421: mu] : ( exists_in_world @ ( singleton @ SY421 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(86,plain,
! [SV3: $i] :
( ( ! [SY422: mu,SY423: mu] : ( exists_in_world @ ( set_difference @ SY422 @ SY423 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(87,plain,
! [SV4: $i] :
( ( empty @ empty_set @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(88,plain,
! [SV5: $i] :
( ( ~ ! [SY424: mu] :
( ~ ( exists_in_world @ SY424 @ SV5 )
| ~ ~ ( empty @ SY424 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(89,plain,
! [SV6: $i] :
( ( ! [SY425: mu] :
( ~ ( exists_in_world @ SY425 @ SV6 )
| ! [SY426: mu] :
( ~ ( exists_in_world @ SY426 @ SV6 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY425 ) @ SY426 ) @ empty_set @ SV6 )
| ( in @ SY425 @ SY426 @ SV6 ) )
| ~ ( ~ ( in @ SY425 @ SY426 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY425 ) @ SY426 ) @ empty_set @ SV6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(90,plain,
! [SV7: $i] :
( ( ~ ! [SY427: mu] :
( ~ ( exists_in_world @ SY427 @ SV7 )
| ~ ( empty @ SY427 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(91,plain,
! [SV8: $i] :
( ( ! [SY428: mu] :
( ~ ( exists_in_world @ SY428 @ SV8 )
| ! [SY429: mu] :
( ~ ( exists_in_world @ SY429 @ SV8 )
| ~ ( qmltpeq @ SY428 @ SY429 @ SV8 )
| ( qmltpeq @ SY429 @ SY428 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(92,plain,
! [SV9: $i] :
( ( ! [SY430: mu] :
( ~ ( exists_in_world @ SY430 @ SV9 )
| ! [SY431: mu] :
( ~ ( exists_in_world @ SY431 @ SV9 )
| ~ ~ ( ~ ( qmltpeq @ SY430 @ SY431 @ SV9 )
| ~ ( empty @ SY430 @ SV9 ) )
| ( empty @ SY431 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(93,plain,
! [SV10: $i] :
( ( ! [SY432: mu] :
( ~ ( exists_in_world @ SY432 @ SV10 )
| ! [SY433: mu] :
( ~ ( exists_in_world @ SY433 @ SV10 )
| ~ ( in @ SY432 @ SY433 @ SV10 )
| ~ ( in @ SY433 @ SY432 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(94,plain,
! [SV11: $i] :
( ( ! [SY434: mu] :
( ~ ( exists_in_world @ SY434 @ SV11 )
| ! [SY435: mu] :
( ~ ( exists_in_world @ SY435 @ SV11 )
| ! [SY436: mu] :
( ~ ( exists_in_world @ SY436 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SY434 @ SY435 @ SV11 )
| ~ ( in @ SY434 @ SY436 @ SV11 ) )
| ( in @ SY435 @ SY436 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(95,plain,
! [SV12: $i] :
( ( ! [SY437: mu] :
( ~ ( exists_in_world @ SY437 @ SV12 )
| ! [SY438: mu] :
( ~ ( exists_in_world @ SY438 @ SV12 )
| ! [SY439: mu] :
( ~ ( exists_in_world @ SY439 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SY437 @ SY438 @ SV12 )
| ~ ( in @ SY439 @ SY437 @ SV12 ) )
| ( in @ SY439 @ SY438 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(96,plain,
! [SV13: $i] :
( ( ! [SY440: mu] :
( ~ ( exists_in_world @ SY440 @ SV13 )
| ! [SY441: mu] :
( ~ ( exists_in_world @ SY441 @ SV13 )
| ! [SY442: mu] :
( ~ ( exists_in_world @ SY442 @ SV13 )
| ~ ( qmltpeq @ SY440 @ SY441 @ SV13 )
| ( qmltpeq @ ( set_difference @ SY440 @ SY442 ) @ ( set_difference @ SY441 @ SY442 ) @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(97,plain,
! [SV14: $i] :
( ( ! [SY443: mu] :
( ~ ( exists_in_world @ SY443 @ SV14 )
| ! [SY444: mu] :
( ~ ( exists_in_world @ SY444 @ SV14 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SY443 ) @ SY444 ) @ ( singleton @ SY443 ) @ SV14 )
| ~ ( in @ SY443 @ SY444 @ SV14 ) )
| ~ ( ~ ~ ( in @ SY443 @ SY444 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SY443 ) @ SY444 ) @ ( singleton @ SY443 ) @ SV14 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV15: $i] :
( ( ! [SY445: mu] :
( ~ ( exists_in_world @ SY445 @ SV15 )
| ! [SY446: mu] :
( ~ ( exists_in_world @ SY446 @ SV15 )
| ~ ( qmltpeq @ SY445 @ SY446 @ SV15 )
| ( qmltpeq @ ( singleton @ SY445 ) @ ( singleton @ SY446 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(99,plain,
( ( ! [SX0: mu] :
( ~ ( exists_in_world @ SX0 @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SX0 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ SX0 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(100,plain,
! [SV16: $i] :
( ( ! [SY447: mu] :
( ~ ( exists_in_world @ SY447 @ SV16 )
| ! [SY448: mu] :
( ~ ( exists_in_world @ SY448 @ SV16 )
| ! [SY449: mu] :
( ~ ( exists_in_world @ SY449 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SY447 @ SY448 @ SV16 )
| ~ ( qmltpeq @ SY448 @ SY449 @ SV16 ) )
| ( qmltpeq @ SY447 @ SY449 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(101,plain,
! [SV17: $i] :
( ( ! [SY450: mu] :
( ~ ( exists_in_world @ SY450 @ SV17 )
| ! [SY451: mu] :
( ~ ( exists_in_world @ SY451 @ SV17 )
| ! [SY452: mu] :
( ~ ( exists_in_world @ SY452 @ SV17 )
| ~ ( qmltpeq @ SY450 @ SY451 @ SV17 )
| ( qmltpeq @ ( set_difference @ SY452 @ SY450 ) @ ( set_difference @ SY452 @ SY451 ) @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(102,plain,
! [SV18: $i] :
( ( ! [SY453: mu] :
( ~ ( exists_in_world @ SY453 @ SV18 )
| ( qmltpeq @ SY453 @ SY453 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(103,plain,
! [SV2: $i,SV19: mu] :
( ( exists_in_world @ ( singleton @ SV19 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(104,plain,
! [SV3: $i,SV20: mu] :
( ( ! [SY454: mu] : ( exists_in_world @ ( set_difference @ SV20 @ SY454 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(105,plain,
! [SV5: $i] :
( ( ! [SY424: mu] :
( ~ ( exists_in_world @ SY424 @ SV5 )
| ~ ~ ( empty @ SY424 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV6: $i,SV21: mu] :
( ( ~ ( exists_in_world @ SV21 @ SV6 )
| ! [SY455: mu] :
( ~ ( exists_in_world @ SY455 @ SV6 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SY455 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SY455 @ SV6 ) )
| ~ ( ~ ( in @ SV21 @ SY455 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SY455 ) @ empty_set @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(107,plain,
! [SV7: $i] :
( ( ! [SY427: mu] :
( ~ ( exists_in_world @ SY427 @ SV7 )
| ~ ( empty @ SY427 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(108,plain,
! [SV8: $i,SV22: mu] :
( ( ~ ( exists_in_world @ SV22 @ SV8 )
| ! [SY456: mu] :
( ~ ( exists_in_world @ SY456 @ SV8 )
| ~ ( qmltpeq @ SV22 @ SY456 @ SV8 )
| ( qmltpeq @ SY456 @ SV22 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(109,plain,
! [SV9: $i,SV23: mu] :
( ( ~ ( exists_in_world @ SV23 @ SV9 )
| ! [SY457: mu] :
( ~ ( exists_in_world @ SY457 @ SV9 )
| ~ ~ ( ~ ( qmltpeq @ SV23 @ SY457 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) )
| ( empty @ SY457 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV10: $i,SV24: mu] :
( ( ~ ( exists_in_world @ SV24 @ SV10 )
| ! [SY458: mu] :
( ~ ( exists_in_world @ SY458 @ SV10 )
| ~ ( in @ SV24 @ SY458 @ SV10 )
| ~ ( in @ SY458 @ SV24 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(111,plain,
! [SV11: $i,SV25: mu] :
( ( ~ ( exists_in_world @ SV25 @ SV11 )
| ! [SY459: mu] :
( ~ ( exists_in_world @ SY459 @ SV11 )
| ! [SY460: mu] :
( ~ ( exists_in_world @ SY460 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV25 @ SY459 @ SV11 )
| ~ ( in @ SV25 @ SY460 @ SV11 ) )
| ( in @ SY459 @ SY460 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(112,plain,
! [SV12: $i,SV26: mu] :
( ( ~ ( exists_in_world @ SV26 @ SV12 )
| ! [SY461: mu] :
( ~ ( exists_in_world @ SY461 @ SV12 )
| ! [SY462: mu] :
( ~ ( exists_in_world @ SY462 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY461 @ SV12 )
| ~ ( in @ SY462 @ SV26 @ SV12 ) )
| ( in @ SY462 @ SY461 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(113,plain,
! [SV13: $i,SV27: mu] :
( ( ~ ( exists_in_world @ SV27 @ SV13 )
| ! [SY463: mu] :
( ~ ( exists_in_world @ SY463 @ SV13 )
| ! [SY464: mu] :
( ~ ( exists_in_world @ SY464 @ SV13 )
| ~ ( qmltpeq @ SV27 @ SY463 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SY464 ) @ ( set_difference @ SY463 @ SY464 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(114,plain,
! [SV14: $i,SV28: mu] :
( ( ~ ( exists_in_world @ SV28 @ SV14 )
| ! [SY465: mu] :
( ~ ( exists_in_world @ SY465 @ SV14 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SY465 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SY465 @ SV14 ) )
| ~ ( ~ ~ ( in @ SV28 @ SY465 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SY465 ) @ ( singleton @ SV28 ) @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(115,plain,
! [SV15: $i,SV29: mu] :
( ( ~ ( exists_in_world @ SV29 @ SV15 )
| ! [SY466: mu] :
( ~ ( exists_in_world @ SY466 @ SV15 )
| ~ ( qmltpeq @ SV29 @ SY466 @ SV15 )
| ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SY466 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(116,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ sK3_SX0 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ sK3_SX0 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(117,plain,
! [SV16: $i,SV30: mu] :
( ( ~ ( exists_in_world @ SV30 @ SV16 )
| ! [SY467: mu] :
( ~ ( exists_in_world @ SY467 @ SV16 )
| ! [SY468: mu] :
( ~ ( exists_in_world @ SY468 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY467 @ SV16 )
| ~ ( qmltpeq @ SY467 @ SY468 @ SV16 ) )
| ( qmltpeq @ SV30 @ SY468 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV17: $i,SV31: mu] :
( ( ~ ( exists_in_world @ SV31 @ SV17 )
| ! [SY469: mu] :
( ~ ( exists_in_world @ SY469 @ SV17 )
| ! [SY470: mu] :
( ~ ( exists_in_world @ SY470 @ SV17 )
| ~ ( qmltpeq @ SV31 @ SY469 @ SV17 )
| ( qmltpeq @ ( set_difference @ SY470 @ SV31 ) @ ( set_difference @ SY470 @ SY469 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV18: $i,SV32: mu] :
( ( ~ ( exists_in_world @ SV32 @ SV18 )
| ( qmltpeq @ SV32 @ SV32 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV3: $i,SV33: mu,SV20: mu] :
( ( exists_in_world @ ( set_difference @ SV20 @ SV33 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV5: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY424 @ SV5 ) @ SV5 )
| ~ ~ ( empty @ ( sK4_SY424 @ SV5 ) @ SV5 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(122,plain,
! [SV6: $i,SV21: mu] :
( ( ( ~ ( exists_in_world @ SV21 @ SV6 ) )
= $true )
| ( ( ! [SY455: mu] :
( ~ ( exists_in_world @ SY455 @ SV6 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SY455 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SY455 @ SV6 ) )
| ~ ( ~ ( in @ SV21 @ SY455 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SY455 ) @ empty_set @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK5_SY427 @ SV7 ) @ SV7 )
| ~ ( empty @ ( sK5_SY427 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[107]) ).
thf(124,plain,
! [SV8: $i,SV22: mu] :
( ( ( ~ ( exists_in_world @ SV22 @ SV8 ) )
= $true )
| ( ( ! [SY456: mu] :
( ~ ( exists_in_world @ SY456 @ SV8 )
| ~ ( qmltpeq @ SV22 @ SY456 @ SV8 )
| ( qmltpeq @ SY456 @ SV22 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV9: $i,SV23: mu] :
( ( ( ~ ( exists_in_world @ SV23 @ SV9 ) )
= $true )
| ( ( ! [SY457: mu] :
( ~ ( exists_in_world @ SY457 @ SV9 )
| ~ ~ ( ~ ( qmltpeq @ SV23 @ SY457 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) )
| ( empty @ SY457 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV10: $i,SV24: mu] :
( ( ( ~ ( exists_in_world @ SV24 @ SV10 ) )
= $true )
| ( ( ! [SY458: mu] :
( ~ ( exists_in_world @ SY458 @ SV10 )
| ~ ( in @ SV24 @ SY458 @ SV10 )
| ~ ( in @ SY458 @ SV24 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV11: $i,SV25: mu] :
( ( ( ~ ( exists_in_world @ SV25 @ SV11 ) )
= $true )
| ( ( ! [SY459: mu] :
( ~ ( exists_in_world @ SY459 @ SV11 )
| ! [SY460: mu] :
( ~ ( exists_in_world @ SY460 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV25 @ SY459 @ SV11 )
| ~ ( in @ SV25 @ SY460 @ SV11 ) )
| ( in @ SY459 @ SY460 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV12: $i,SV26: mu] :
( ( ( ~ ( exists_in_world @ SV26 @ SV12 ) )
= $true )
| ( ( ! [SY461: mu] :
( ~ ( exists_in_world @ SY461 @ SV12 )
| ! [SY462: mu] :
( ~ ( exists_in_world @ SY462 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY461 @ SV12 )
| ~ ( in @ SY462 @ SV26 @ SV12 ) )
| ( in @ SY462 @ SY461 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV13: $i,SV27: mu] :
( ( ( ~ ( exists_in_world @ SV27 @ SV13 ) )
= $true )
| ( ( ! [SY463: mu] :
( ~ ( exists_in_world @ SY463 @ SV13 )
| ! [SY464: mu] :
( ~ ( exists_in_world @ SY464 @ SV13 )
| ~ ( qmltpeq @ SV27 @ SY463 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SY464 ) @ ( set_difference @ SY463 @ SY464 ) @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV14: $i,SV28: mu] :
( ( ( ~ ( exists_in_world @ SV28 @ SV14 ) )
= $true )
| ( ( ! [SY465: mu] :
( ~ ( exists_in_world @ SY465 @ SV14 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SY465 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SY465 @ SV14 ) )
| ~ ( ~ ~ ( in @ SV28 @ SY465 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SY465 ) @ ( singleton @ SV28 ) @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV15: $i,SV29: mu] :
( ( ( ~ ( exists_in_world @ SV29 @ SV15 ) )
= $true )
| ( ( ! [SY466: mu] :
( ~ ( exists_in_world @ SY466 @ SV15 )
| ~ ( qmltpeq @ SV29 @ SY466 @ SV15 )
| ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SY466 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(132,plain,
( ( ~ ( exists_in_world @ sK3_SX0 @ sK1_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(133,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ sK3_SX0 ) @ empty_set @ sK1_SY13 )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ sK3_SX0 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(134,plain,
! [SV16: $i,SV30: mu] :
( ( ( ~ ( exists_in_world @ SV30 @ SV16 ) )
= $true )
| ( ( ! [SY467: mu] :
( ~ ( exists_in_world @ SY467 @ SV16 )
| ! [SY468: mu] :
( ~ ( exists_in_world @ SY468 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY467 @ SV16 )
| ~ ( qmltpeq @ SY467 @ SY468 @ SV16 ) )
| ( qmltpeq @ SV30 @ SY468 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV17: $i,SV31: mu] :
( ( ( ~ ( exists_in_world @ SV31 @ SV17 ) )
= $true )
| ( ( ! [SY469: mu] :
( ~ ( exists_in_world @ SY469 @ SV17 )
| ! [SY470: mu] :
( ~ ( exists_in_world @ SY470 @ SV17 )
| ~ ( qmltpeq @ SV31 @ SY469 @ SV17 )
| ( qmltpeq @ ( set_difference @ SY470 @ SV31 ) @ ( set_difference @ SY470 @ SY469 ) @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(136,plain,
! [SV18: $i,SV32: mu] :
( ( ( ~ ( exists_in_world @ SV32 @ SV18 ) )
= $true )
| ( ( qmltpeq @ SV32 @ SV32 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(137,plain,
! [SV5: $i] :
( ( ~ ( exists_in_world @ ( sK4_SY424 @ SV5 ) @ SV5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(138,plain,
! [SV5: $i] :
( ( ~ ~ ( empty @ ( sK4_SY424 @ SV5 ) @ SV5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(139,plain,
! [SV6: $i,SV21: mu] :
( ( ( exists_in_world @ SV21 @ SV6 )
= $false )
| ( ( ! [SY455: mu] :
( ~ ( exists_in_world @ SY455 @ SV6 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SY455 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SY455 @ SV6 ) )
| ~ ( ~ ( in @ SV21 @ SY455 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SY455 ) @ empty_set @ SV6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV7: $i] :
( ( ~ ( exists_in_world @ ( sK5_SY427 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(141,plain,
! [SV7: $i] :
( ( ~ ( empty @ ( sK5_SY427 @ SV7 ) @ SV7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[123]) ).
thf(142,plain,
! [SV8: $i,SV22: mu] :
( ( ( exists_in_world @ SV22 @ SV8 )
= $false )
| ( ( ! [SY456: mu] :
( ~ ( exists_in_world @ SY456 @ SV8 )
| ~ ( qmltpeq @ SV22 @ SY456 @ SV8 )
| ( qmltpeq @ SY456 @ SV22 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV9: $i,SV23: mu] :
( ( ( exists_in_world @ SV23 @ SV9 )
= $false )
| ( ( ! [SY457: mu] :
( ~ ( exists_in_world @ SY457 @ SV9 )
| ~ ~ ( ~ ( qmltpeq @ SV23 @ SY457 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) )
| ( empty @ SY457 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(144,plain,
! [SV10: $i,SV24: mu] :
( ( ( exists_in_world @ SV24 @ SV10 )
= $false )
| ( ( ! [SY458: mu] :
( ~ ( exists_in_world @ SY458 @ SV10 )
| ~ ( in @ SV24 @ SY458 @ SV10 )
| ~ ( in @ SY458 @ SV24 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(145,plain,
! [SV11: $i,SV25: mu] :
( ( ( exists_in_world @ SV25 @ SV11 )
= $false )
| ( ( ! [SY459: mu] :
( ~ ( exists_in_world @ SY459 @ SV11 )
| ! [SY460: mu] :
( ~ ( exists_in_world @ SY460 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV25 @ SY459 @ SV11 )
| ~ ( in @ SV25 @ SY460 @ SV11 ) )
| ( in @ SY459 @ SY460 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(146,plain,
! [SV12: $i,SV26: mu] :
( ( ( exists_in_world @ SV26 @ SV12 )
= $false )
| ( ( ! [SY461: mu] :
( ~ ( exists_in_world @ SY461 @ SV12 )
| ! [SY462: mu] :
( ~ ( exists_in_world @ SY462 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SY461 @ SV12 )
| ~ ( in @ SY462 @ SV26 @ SV12 ) )
| ( in @ SY462 @ SY461 @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(147,plain,
! [SV13: $i,SV27: mu] :
( ( ( exists_in_world @ SV27 @ SV13 )
= $false )
| ( ( ! [SY463: mu] :
( ~ ( exists_in_world @ SY463 @ SV13 )
| ! [SY464: mu] :
( ~ ( exists_in_world @ SY464 @ SV13 )
| ~ ( qmltpeq @ SV27 @ SY463 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SY464 ) @ ( set_difference @ SY463 @ SY464 ) @ SV13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(148,plain,
! [SV14: $i,SV28: mu] :
( ( ( exists_in_world @ SV28 @ SV14 )
= $false )
| ( ( ! [SY465: mu] :
( ~ ( exists_in_world @ SY465 @ SV14 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SY465 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SY465 @ SV14 ) )
| ~ ( ~ ~ ( in @ SV28 @ SY465 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SY465 ) @ ( singleton @ SV28 ) @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(149,plain,
! [SV15: $i,SV29: mu] :
( ( ( exists_in_world @ SV29 @ SV15 )
= $false )
| ( ( ! [SY466: mu] :
( ~ ( exists_in_world @ SY466 @ SV15 )
| ~ ( qmltpeq @ SV29 @ SY466 @ SV15 )
| ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SY466 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(150,plain,
( ( exists_in_world @ sK3_SX0 @ sK1_SY13 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(151,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ sK3_SX0 ) @ empty_set @ sK1_SY13 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(152,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK2_SY418 ) @ sK3_SX0 ) @ ( singleton @ sK2_SY418 ) @ sK1_SY13 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(153,plain,
! [SV16: $i,SV30: mu] :
( ( ( exists_in_world @ SV30 @ SV16 )
= $false )
| ( ( ! [SY467: mu] :
( ~ ( exists_in_world @ SY467 @ SV16 )
| ! [SY468: mu] :
( ~ ( exists_in_world @ SY468 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SY467 @ SV16 )
| ~ ( qmltpeq @ SY467 @ SY468 @ SV16 ) )
| ( qmltpeq @ SV30 @ SY468 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV17: $i,SV31: mu] :
( ( ( exists_in_world @ SV31 @ SV17 )
= $false )
| ( ( ! [SY469: mu] :
( ~ ( exists_in_world @ SY469 @ SV17 )
| ! [SY470: mu] :
( ~ ( exists_in_world @ SY470 @ SV17 )
| ~ ( qmltpeq @ SV31 @ SY469 @ SV17 )
| ( qmltpeq @ ( set_difference @ SY470 @ SV31 ) @ ( set_difference @ SY470 @ SY469 ) @ SV17 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV18: $i,SV32: mu] :
( ( ( exists_in_world @ SV32 @ SV18 )
= $false )
| ( ( qmltpeq @ SV32 @ SV32 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV5: $i] :
( ( exists_in_world @ ( sK4_SY424 @ SV5 ) @ SV5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(157,plain,
! [SV5: $i] :
( ( ~ ( empty @ ( sK4_SY424 @ SV5 ) @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(158,plain,
! [SV21: mu,SV6: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV6 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SV34 @ SV6 ) )
| ~ ( ~ ( in @ SV21 @ SV34 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV7: $i] :
( ( exists_in_world @ ( sK5_SY427 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(160,plain,
! [SV7: $i] :
( ( empty @ ( sK5_SY427 @ SV7 ) @ SV7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(161,plain,
! [SV22: mu,SV8: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV8 )
| ~ ( qmltpeq @ SV22 @ SV35 @ SV8 )
| ( qmltpeq @ SV35 @ SV22 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(162,plain,
! [SV23: mu,SV9: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV9 )
| ~ ~ ( ~ ( qmltpeq @ SV23 @ SV36 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) )
| ( empty @ SV36 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV24: mu,SV10: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV10 )
| ~ ( in @ SV24 @ SV37 @ SV10 )
| ~ ( in @ SV37 @ SV24 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(164,plain,
! [SV25: mu,SV11: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV11 )
| ! [SY471: mu] :
( ~ ( exists_in_world @ SY471 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SY471 @ SV11 ) )
| ( in @ SV38 @ SY471 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV26: mu,SV12: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV12 )
| ! [SY472: mu] :
( ~ ( exists_in_world @ SY472 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SY472 @ SV26 @ SV12 ) )
| ( in @ SY472 @ SV39 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV27: mu,SV13: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV13 )
| ! [SY473: mu] :
( ~ ( exists_in_world @ SY473 @ SV13 )
| ~ ( qmltpeq @ SV27 @ SV40 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SY473 ) @ ( set_difference @ SV40 @ SY473 ) @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(167,plain,
! [SV28: mu,SV14: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV14 )
| ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SV41 @ SV14 ) )
| ~ ( ~ ~ ( in @ SV28 @ SV41 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 ) ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(168,plain,
! [SV29: mu,SV15: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV15 )
| ~ ( qmltpeq @ SV29 @ SV42 @ SV15 )
| ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SV42 ) @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV30: mu,SV16: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV16 )
| ! [SY474: mu] :
( ~ ( exists_in_world @ SY474 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SY474 @ SV16 ) )
| ( qmltpeq @ SV30 @ SY474 @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(170,plain,
! [SV31: mu,SV17: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV17 )
| ! [SY475: mu] :
( ~ ( exists_in_world @ SY475 @ SV17 )
| ~ ( qmltpeq @ SV31 @ SV44 @ SV17 )
| ( qmltpeq @ ( set_difference @ SY475 @ SV31 ) @ ( set_difference @ SY475 @ SV44 ) @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV5: $i] :
( ( empty @ ( sK4_SY424 @ SV5 ) @ SV5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(172,plain,
! [SV21: mu,SV6: $i,SV34: mu] :
( ( ( ~ ( exists_in_world @ SV34 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SV34 @ SV6 ) )
| ~ ( ~ ( in @ SV21 @ SV34 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV22: mu,SV8: $i,SV35: mu] :
( ( ( ~ ( exists_in_world @ SV35 @ SV8 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV22 @ SV35 @ SV8 )
| ( qmltpeq @ SV35 @ SV22 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV23: mu,SV9: $i,SV36: mu] :
( ( ( ~ ( exists_in_world @ SV36 @ SV9 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV23 @ SV36 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) )
| ( empty @ SV36 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV24: mu,SV10: $i,SV37: mu] :
( ( ( ~ ( exists_in_world @ SV37 @ SV10 ) )
= $true )
| ( ( ~ ( in @ SV24 @ SV37 @ SV10 )
| ~ ( in @ SV37 @ SV24 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV25: mu,SV11: $i,SV38: mu] :
( ( ( ~ ( exists_in_world @ SV38 @ SV11 ) )
= $true )
| ( ( ! [SY471: mu] :
( ~ ( exists_in_world @ SY471 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SY471 @ SV11 ) )
| ( in @ SV38 @ SY471 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV26: mu,SV12: $i,SV39: mu] :
( ( ( ~ ( exists_in_world @ SV39 @ SV12 ) )
= $true )
| ( ( ! [SY472: mu] :
( ~ ( exists_in_world @ SY472 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SY472 @ SV26 @ SV12 ) )
| ( in @ SY472 @ SV39 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV27: mu,SV13: $i,SV40: mu] :
( ( ( ~ ( exists_in_world @ SV40 @ SV13 ) )
= $true )
| ( ( ! [SY473: mu] :
( ~ ( exists_in_world @ SY473 @ SV13 )
| ~ ( qmltpeq @ SV27 @ SV40 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SY473 ) @ ( set_difference @ SV40 @ SY473 ) @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV28: mu,SV14: $i,SV41: mu] :
( ( ( ~ ( exists_in_world @ SV41 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SV41 @ SV14 ) )
| ~ ( ~ ~ ( in @ SV28 @ SV41 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 ) ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV29: mu,SV15: $i,SV42: mu] :
( ( ( ~ ( exists_in_world @ SV42 @ SV15 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV29 @ SV42 @ SV15 )
| ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SV42 ) @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV30: mu,SV16: $i,SV43: mu] :
( ( ( ~ ( exists_in_world @ SV43 @ SV16 ) )
= $true )
| ( ( ! [SY474: mu] :
( ~ ( exists_in_world @ SY474 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SY474 @ SV16 ) )
| ( qmltpeq @ SV30 @ SY474 @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV31: mu,SV17: $i,SV44: mu] :
( ( ( ~ ( exists_in_world @ SV44 @ SV17 ) )
= $true )
| ( ( ! [SY475: mu] :
( ~ ( exists_in_world @ SY475 @ SV17 )
| ~ ( qmltpeq @ SV31 @ SV44 @ SV17 )
| ( qmltpeq @ ( set_difference @ SY475 @ SV31 ) @ ( set_difference @ SY475 @ SV44 ) @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV21: mu,SV6: $i,SV34: mu] :
( ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SV34 @ SV6 ) )
| ~ ( ~ ( in @ SV21 @ SV34 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 ) ) ) )
= $true )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV22: mu,SV8: $i,SV35: mu] :
( ( ( exists_in_world @ SV35 @ SV8 )
= $false )
| ( ( ~ ( qmltpeq @ SV22 @ SV35 @ SV8 )
| ( qmltpeq @ SV35 @ SV22 @ SV8 ) )
= $true )
| ( ( exists_in_world @ SV22 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV23: mu,SV9: $i,SV36: mu] :
( ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV23 @ SV36 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) )
| ( empty @ SV36 @ SV9 ) )
= $true )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(186,plain,
! [SV24: mu,SV10: $i,SV37: mu] :
( ( ( exists_in_world @ SV37 @ SV10 )
= $false )
| ( ( ~ ( in @ SV24 @ SV37 @ SV10 )
| ~ ( in @ SV37 @ SV24 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV24 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV25: mu,SV11: $i,SV38: mu] :
( ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( ! [SY471: mu] :
( ~ ( exists_in_world @ SY471 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SY471 @ SV11 ) )
| ( in @ SV38 @ SY471 @ SV11 ) ) )
= $true )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(188,plain,
! [SV26: mu,SV12: $i,SV39: mu] :
( ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( ! [SY472: mu] :
( ~ ( exists_in_world @ SY472 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SY472 @ SV26 @ SV12 ) )
| ( in @ SY472 @ SV39 @ SV12 ) ) )
= $true )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV27: mu,SV13: $i,SV40: mu] :
( ( ( exists_in_world @ SV40 @ SV13 )
= $false )
| ( ( ! [SY473: mu] :
( ~ ( exists_in_world @ SY473 @ SV13 )
| ~ ( qmltpeq @ SV27 @ SV40 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SY473 ) @ ( set_difference @ SV40 @ SY473 ) @ SV13 ) ) )
= $true )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(190,plain,
! [SV28: mu,SV14: $i,SV41: mu] :
( ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( ~ ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SV41 @ SV14 ) )
| ~ ( ~ ~ ( in @ SV28 @ SV41 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 ) ) ) )
= $true )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(191,plain,
! [SV29: mu,SV15: $i,SV42: mu] :
( ( ( exists_in_world @ SV42 @ SV15 )
= $false )
| ( ( ~ ( qmltpeq @ SV29 @ SV42 @ SV15 )
| ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SV42 ) @ SV15 ) )
= $true )
| ( ( exists_in_world @ SV29 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV30: mu,SV16: $i,SV43: mu] :
( ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( ! [SY474: mu] :
( ~ ( exists_in_world @ SY474 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SY474 @ SV16 ) )
| ( qmltpeq @ SV30 @ SY474 @ SV16 ) ) )
= $true )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV31: mu,SV17: $i,SV44: mu] :
( ( ( exists_in_world @ SV44 @ SV17 )
= $false )
| ( ( ! [SY475: mu] :
( ~ ( exists_in_world @ SY475 @ SV17 )
| ~ ( qmltpeq @ SV31 @ SV44 @ SV17 )
| ( qmltpeq @ ( set_difference @ SY475 @ SV31 ) @ ( set_difference @ SY475 @ SV44 ) @ SV17 ) ) )
= $true )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SV34 @ SV6 ) )
| ~ ( ~ ( in @ SV21 @ SV34 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 ) ) )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV8: $i,SV35: mu,SV22: mu] :
( ( ( ~ ( qmltpeq @ SV22 @ SV35 @ SV8 ) )
= $true )
| ( ( qmltpeq @ SV35 @ SV22 @ SV8 )
= $true )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false )
| ( ( exists_in_world @ SV22 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV9: $i,SV36: mu,SV23: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV23 @ SV36 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) ) )
= $true )
| ( ( empty @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV10: $i,SV37: mu,SV24: mu] :
( ( ( ~ ( in @ SV24 @ SV37 @ SV10 ) )
= $true )
| ( ( ~ ( in @ SV37 @ SV24 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV10 )
= $false )
| ( ( exists_in_world @ SV24 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV38: mu,SV25: mu,SV11: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV11 )
| ~ ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SV45 @ SV11 ) )
| ( in @ SV38 @ SV45 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV39: mu,SV26: mu,SV12: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV12 )
| ~ ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SV46 @ SV26 @ SV12 ) )
| ( in @ SV46 @ SV39 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV40: mu,SV27: mu,SV13: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV13 )
| ~ ( qmltpeq @ SV27 @ SV40 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SV47 ) @ ( set_difference @ SV40 @ SV47 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SV41 @ SV14 ) )
| ~ ( ~ ~ ( in @ SV28 @ SV41 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 ) ) )
= $false )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV15: $i,SV42: mu,SV29: mu] :
( ( ( ~ ( qmltpeq @ SV29 @ SV42 @ SV15 ) )
= $true )
| ( ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SV42 ) @ SV15 )
= $true )
| ( ( exists_in_world @ SV42 @ SV15 )
= $false )
| ( ( exists_in_world @ SV29 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(203,plain,
! [SV43: mu,SV30: mu,SV16: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV16 )
| ~ ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) )
| ( qmltpeq @ SV30 @ SV48 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(204,plain,
! [SV44: mu,SV31: mu,SV17: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV17 )
| ~ ( qmltpeq @ SV31 @ SV44 @ SV17 )
| ( qmltpeq @ ( set_difference @ SV49 @ SV31 ) @ ( set_difference @ SV49 @ SV44 ) @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV17 )
= $false )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(205,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SV34 @ SV6 ) ) )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(206,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( ~ ( ~ ( in @ SV21 @ SV34 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 ) ) )
= $false )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(207,plain,
! [SV8: $i,SV35: mu,SV22: mu] :
( ( ( qmltpeq @ SV22 @ SV35 @ SV8 )
= $false )
| ( ( qmltpeq @ SV35 @ SV22 @ SV8 )
= $true )
| ( ( exists_in_world @ SV35 @ SV8 )
= $false )
| ( ( exists_in_world @ SV22 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(208,plain,
! [SV9: $i,SV36: mu,SV23: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV23 @ SV36 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) ) )
= $false )
| ( ( empty @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV10: $i,SV37: mu,SV24: mu] :
( ( ( in @ SV24 @ SV37 @ SV10 )
= $false )
| ( ( ~ ( in @ SV37 @ SV24 @ SV10 ) )
= $true )
| ( ( exists_in_world @ SV37 @ SV10 )
= $false )
| ( ( exists_in_world @ SV24 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV38: mu,SV25: mu,SV11: $i,SV45: mu] :
( ( ( ~ ( exists_in_world @ SV45 @ SV11 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SV45 @ SV11 ) )
| ( in @ SV38 @ SV45 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(211,plain,
! [SV39: mu,SV26: mu,SV12: $i,SV46: mu] :
( ( ( ~ ( exists_in_world @ SV46 @ SV12 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SV46 @ SV26 @ SV12 ) )
| ( in @ SV46 @ SV39 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(212,plain,
! [SV40: mu,SV27: mu,SV13: $i,SV47: mu] :
( ( ( ~ ( exists_in_world @ SV47 @ SV13 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV27 @ SV40 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SV47 ) @ ( set_difference @ SV40 @ SV47 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(213,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SV41 @ SV14 ) ) )
= $false )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(214,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ( ~ ~ ( in @ SV28 @ SV41 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 ) ) )
= $false )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(215,plain,
! [SV15: $i,SV42: mu,SV29: mu] :
( ( ( qmltpeq @ SV29 @ SV42 @ SV15 )
= $false )
| ( ( qmltpeq @ ( singleton @ SV29 ) @ ( singleton @ SV42 ) @ SV15 )
= $true )
| ( ( exists_in_world @ SV42 @ SV15 )
= $false )
| ( ( exists_in_world @ SV29 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(216,plain,
! [SV43: mu,SV30: mu,SV16: $i,SV48: mu] :
( ( ( ~ ( exists_in_world @ SV48 @ SV16 ) )
= $true )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) )
| ( qmltpeq @ SV30 @ SV48 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(217,plain,
! [SV44: mu,SV31: mu,SV17: $i,SV49: mu] :
( ( ( ~ ( exists_in_world @ SV49 @ SV17 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV31 @ SV44 @ SV17 )
| ( qmltpeq @ ( set_difference @ SV49 @ SV31 ) @ ( set_difference @ SV49 @ SV44 ) @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV17 )
= $false )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(218,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
| ( in @ SV21 @ SV34 @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(219,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( ~ ( in @ SV21 @ SV34 @ SV6 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 ) )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(220,plain,
! [SV9: $i,SV36: mu,SV23: mu] :
( ( ( ~ ( qmltpeq @ SV23 @ SV36 @ SV9 )
| ~ ( empty @ SV23 @ SV9 ) )
= $true )
| ( ( empty @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(221,plain,
! [SV10: $i,SV24: mu,SV37: mu] :
( ( ( in @ SV37 @ SV24 @ SV10 )
= $false )
| ( ( in @ SV24 @ SV37 @ SV10 )
= $false )
| ( ( exists_in_world @ SV37 @ SV10 )
= $false )
| ( ( exists_in_world @ SV24 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(222,plain,
! [SV38: mu,SV25: mu,SV11: $i,SV45: mu] :
( ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SV45 @ SV11 ) )
| ( in @ SV38 @ SV45 @ SV11 ) )
= $true )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(223,plain,
! [SV39: mu,SV26: mu,SV12: $i,SV46: mu] :
( ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SV46 @ SV26 @ SV12 ) )
| ( in @ SV46 @ SV39 @ SV12 ) )
= $true )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(224,plain,
! [SV40: mu,SV27: mu,SV13: $i,SV47: mu] :
( ( ( exists_in_world @ SV47 @ SV13 )
= $false )
| ( ( ~ ( qmltpeq @ SV27 @ SV40 @ SV13 )
| ( qmltpeq @ ( set_difference @ SV27 @ SV47 ) @ ( set_difference @ SV40 @ SV47 ) @ SV13 ) )
= $true )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(225,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
| ~ ( in @ SV28 @ SV41 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(226,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ~ ( in @ SV28 @ SV41 @ SV14 )
| ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(227,plain,
! [SV43: mu,SV30: mu,SV16: $i,SV48: mu] :
( ( ( exists_in_world @ SV48 @ SV16 )
= $false )
| ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) )
| ( qmltpeq @ SV30 @ SV48 @ SV16 ) )
= $true )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(228,plain,
! [SV44: mu,SV31: mu,SV17: $i,SV49: mu] :
( ( ( exists_in_world @ SV49 @ SV17 )
= $false )
| ( ( ~ ( qmltpeq @ SV31 @ SV44 @ SV17 )
| ( qmltpeq @ ( set_difference @ SV49 @ SV31 ) @ ( set_difference @ SV49 @ SV44 ) @ SV17 ) )
= $true )
| ( ( exists_in_world @ SV44 @ SV17 )
= $false )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(229,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 ) )
= $true )
| ( ( in @ SV21 @ SV34 @ SV6 )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(230,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( ~ ( in @ SV21 @ SV34 @ SV6 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(231,plain,
! [SV9: $i,SV36: mu,SV23: mu] :
( ( ( ~ ( qmltpeq @ SV23 @ SV36 @ SV9 ) )
= $true )
| ( ( ~ ( empty @ SV23 @ SV9 ) )
= $true )
| ( ( empty @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(232,plain,
! [SV45: mu,SV11: $i,SV38: mu,SV25: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SV45 @ SV11 ) ) )
= $true )
| ( ( in @ SV38 @ SV45 @ SV11 )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(233,plain,
! [SV46: mu,SV12: $i,SV39: mu,SV26: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SV46 @ SV26 @ SV12 ) ) )
= $true )
| ( ( in @ SV46 @ SV39 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(234,plain,
! [SV47: mu,SV13: $i,SV40: mu,SV27: mu] :
( ( ( ~ ( qmltpeq @ SV27 @ SV40 @ SV13 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV27 @ SV47 ) @ ( set_difference @ SV40 @ SV47 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV47 @ SV13 )
= $false )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(235,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV28 @ SV41 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(236,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ~ ( in @ SV28 @ SV41 @ SV14 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
= $true )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(237,plain,
! [SV48: mu,SV16: $i,SV43: mu,SV30: mu] :
( ( ( ~ ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) ) )
= $true )
| ( ( qmltpeq @ SV30 @ SV48 @ SV16 )
= $true )
| ( ( exists_in_world @ SV48 @ SV16 )
= $false )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(238,plain,
! [SV49: mu,SV17: $i,SV44: mu,SV31: mu] :
( ( ( ~ ( qmltpeq @ SV31 @ SV44 @ SV17 ) )
= $true )
| ( ( qmltpeq @ ( set_difference @ SV49 @ SV31 ) @ ( set_difference @ SV49 @ SV44 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV49 @ SV17 )
= $false )
| ( ( exists_in_world @ SV44 @ SV17 )
= $false )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(239,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
= $false )
| ( ( in @ SV21 @ SV34 @ SV6 )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(240,plain,
! [SV6: $i,SV34: mu,SV21: mu] :
( ( ( in @ SV21 @ SV34 @ SV6 )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV21 ) @ SV34 ) @ empty_set @ SV6 )
= $true )
| ( ( exists_in_world @ SV34 @ SV6 )
= $false )
| ( ( exists_in_world @ SV21 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV9: $i,SV36: mu,SV23: mu] :
( ( ( qmltpeq @ SV23 @ SV36 @ SV9 )
= $false )
| ( ( ~ ( empty @ SV23 @ SV9 ) )
= $true )
| ( ( empty @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV45: mu,SV11: $i,SV38: mu,SV25: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SV45 @ SV11 ) ) )
= $false )
| ( ( in @ SV38 @ SV45 @ SV11 )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV46: mu,SV12: $i,SV39: mu,SV26: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SV46 @ SV26 @ SV12 ) ) )
= $false )
| ( ( in @ SV46 @ SV39 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV47: mu,SV13: $i,SV40: mu,SV27: mu] :
( ( ( qmltpeq @ SV27 @ SV40 @ SV13 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV27 @ SV47 ) @ ( set_difference @ SV40 @ SV47 ) @ SV13 )
= $true )
| ( ( exists_in_world @ SV47 @ SV13 )
= $false )
| ( ( exists_in_world @ SV40 @ SV13 )
= $false )
| ( ( exists_in_world @ SV27 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
= $false )
| ( ( ~ ( in @ SV28 @ SV41 @ SV14 ) )
= $true )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(246,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( ~ ( in @ SV28 @ SV41 @ SV14 ) )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
= $true )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV48: mu,SV16: $i,SV43: mu,SV30: mu] :
( ( ( ~ ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) ) )
= $false )
| ( ( qmltpeq @ SV30 @ SV48 @ SV16 )
= $true )
| ( ( exists_in_world @ SV48 @ SV16 )
= $false )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV49: mu,SV17: $i,SV44: mu,SV31: mu] :
( ( ( qmltpeq @ SV31 @ SV44 @ SV17 )
= $false )
| ( ( qmltpeq @ ( set_difference @ SV49 @ SV31 ) @ ( set_difference @ SV49 @ SV44 ) @ SV17 )
= $true )
| ( ( exists_in_world @ SV49 @ SV17 )
= $false )
| ( ( exists_in_world @ SV44 @ SV17 )
= $false )
| ( ( exists_in_world @ SV31 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV36: mu,SV9: $i,SV23: mu] :
( ( ( empty @ SV23 @ SV9 )
= $false )
| ( ( qmltpeq @ SV23 @ SV36 @ SV9 )
= $false )
| ( ( empty @ SV36 @ SV9 )
= $true )
| ( ( exists_in_world @ SV36 @ SV9 )
= $false )
| ( ( exists_in_world @ SV23 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(250,plain,
! [SV45: mu,SV11: $i,SV38: mu,SV25: mu] :
( ( ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 )
| ~ ( in @ SV25 @ SV45 @ SV11 ) )
= $true )
| ( ( in @ SV38 @ SV45 @ SV11 )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(251,plain,
! [SV46: mu,SV12: $i,SV39: mu,SV26: mu] :
( ( ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 )
| ~ ( in @ SV46 @ SV26 @ SV12 ) )
= $true )
| ( ( in @ SV46 @ SV39 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(252,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( in @ SV28 @ SV41 @ SV14 )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
= $false )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(253,plain,
! [SV14: $i,SV41: mu,SV28: mu] :
( ( ( in @ SV28 @ SV41 @ SV14 )
= $true )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ SV28 ) @ SV41 ) @ ( singleton @ SV28 ) @ SV14 )
= $true )
| ( ( exists_in_world @ SV41 @ SV14 )
= $false )
| ( ( exists_in_world @ SV28 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(254,plain,
! [SV48: mu,SV16: $i,SV43: mu,SV30: mu] :
( ( ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 )
| ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) )
= $true )
| ( ( qmltpeq @ SV30 @ SV48 @ SV16 )
= $true )
| ( ( exists_in_world @ SV48 @ SV16 )
= $false )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(255,plain,
! [SV45: mu,SV11: $i,SV38: mu,SV25: mu] :
( ( ( ~ ( qmltpeq @ SV25 @ SV38 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV45 @ SV11 ) )
= $true )
| ( ( in @ SV38 @ SV45 @ SV11 )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(256,plain,
! [SV46: mu,SV12: $i,SV39: mu,SV26: mu] :
( ( ( ~ ( qmltpeq @ SV26 @ SV39 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV46 @ SV26 @ SV12 ) )
= $true )
| ( ( in @ SV46 @ SV39 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(257,plain,
! [SV48: mu,SV16: $i,SV43: mu,SV30: mu] :
( ( ( ~ ( qmltpeq @ SV30 @ SV43 @ SV16 ) )
= $true )
| ( ( ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) )
= $true )
| ( ( qmltpeq @ SV30 @ SV48 @ SV16 )
= $true )
| ( ( exists_in_world @ SV48 @ SV16 )
= $false )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(258,plain,
! [SV45: mu,SV11: $i,SV38: mu,SV25: mu] :
( ( ( qmltpeq @ SV25 @ SV38 @ SV11 )
= $false )
| ( ( ~ ( in @ SV25 @ SV45 @ SV11 ) )
= $true )
| ( ( in @ SV38 @ SV45 @ SV11 )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(259,plain,
! [SV46: mu,SV12: $i,SV39: mu,SV26: mu] :
( ( ( qmltpeq @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( ~ ( in @ SV46 @ SV26 @ SV12 ) )
= $true )
| ( ( in @ SV46 @ SV39 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(260,plain,
! [SV48: mu,SV16: $i,SV43: mu,SV30: mu] :
( ( ( qmltpeq @ SV30 @ SV43 @ SV16 )
= $false )
| ( ( ~ ( qmltpeq @ SV43 @ SV48 @ SV16 ) )
= $true )
| ( ( qmltpeq @ SV30 @ SV48 @ SV16 )
= $true )
| ( ( exists_in_world @ SV48 @ SV16 )
= $false )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(261,plain,
! [SV38: mu,SV11: $i,SV45: mu,SV25: mu] :
( ( ( in @ SV25 @ SV45 @ SV11 )
= $false )
| ( ( qmltpeq @ SV25 @ SV38 @ SV11 )
= $false )
| ( ( in @ SV38 @ SV45 @ SV11 )
= $true )
| ( ( exists_in_world @ SV45 @ SV11 )
= $false )
| ( ( exists_in_world @ SV38 @ SV11 )
= $false )
| ( ( exists_in_world @ SV25 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(262,plain,
! [SV39: mu,SV12: $i,SV26: mu,SV46: mu] :
( ( ( in @ SV46 @ SV26 @ SV12 )
= $false )
| ( ( qmltpeq @ SV26 @ SV39 @ SV12 )
= $false )
| ( ( in @ SV46 @ SV39 @ SV12 )
= $true )
| ( ( exists_in_world @ SV46 @ SV12 )
= $false )
| ( ( exists_in_world @ SV39 @ SV12 )
= $false )
| ( ( exists_in_world @ SV26 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(263,plain,
! [SV30: mu,SV16: $i,SV48: mu,SV43: mu] :
( ( ( qmltpeq @ SV43 @ SV48 @ SV16 )
= $false )
| ( ( qmltpeq @ SV30 @ SV43 @ SV16 )
= $false )
| ( ( qmltpeq @ SV30 @ SV48 @ SV16 )
= $true )
| ( ( exists_in_world @ SV48 @ SV16 )
= $false )
| ( ( exists_in_world @ SV43 @ SV16 )
= $false )
| ( ( exists_in_world @ SV30 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(264,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,263,262,261,253,252,249,248,244,240,239,221,215,207,171,160,159,156,155,152,151,150,120,103,87,84]) ).
thf(265,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET926^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 14:51:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/0.36
% 0.62/0.36 No.of.Axioms: 18
% 0.62/0.36
% 0.62/0.36 Length.of.Defs: 5540
% 0.62/0.36
% 0.62/0.36 Contains.Choice.Funs: false
% 0.62/0.36 .................
% 0.62/0.36
% 0.62/0.36 ********************************
% 0.62/0.36 * All subproblems solved! *
% 0.62/0.36 ********************************
% 0.62/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:264,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.62/0.36
% 0.62/0.36 %**** Beginning of derivation protocol ****
% 0.62/0.36 % SZS output start CNFRefutation
% See solution above
% 0.62/0.37
% 0.62/0.37 %**** End of derivation protocol ****
% 0.62/0.37 %**** no. of clauses in derivation: 261 ****
% 0.62/0.37 %**** clause counter: 264 ****
% 0.62/0.37
% 0.62/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:19,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:264,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------